diff --git "a/data_all_eng_slimpj/shuffled/split2/finalzzrtfu" "b/data_all_eng_slimpj/shuffled/split2/finalzzrtfu" new file mode 100644--- /dev/null +++ "b/data_all_eng_slimpj/shuffled/split2/finalzzrtfu" @@ -0,0 +1,5 @@ +{"text":" \nVolume 10227\n\nLecture Notes in Computer ScienceProgramming and Software Engineering\n\nSeries Editors\n\nDavid Hutchison\n\nLancaster University, Lancaster, United Kingdom\n\nTakeo Kanade\n\nCarnegie Mellon University, Pittsburgh, Pennsylvania, USA\n\nJosef Kittler\n\nUniversity of Surrey, Guildford, United Kingdom\n\nJon M. Kleinberg\n\nCornell University, Ithaca, New York, USA\n\nFriedemann Mattern\n\nInst. Pervasive Computing, ETH Zurich, Z\u00fcrich, Switzerland\n\nJohn C. Mitchell\n\nStanford, California, USA\n\nMoni Naor\n\nWeizmann Institute of Science, Rehovot, Israel\n\nC. Pandu Rangan\n\nMadras, Indian Institute of Technology, Chennai, India\n\nBernhard Steffen\n\nFakult\u00e4t Informatik, TU Dortmund, Dortmund, Germany\n\nDemetri Terzopoulos\n\nUniversity of California, Los Angeles, California, USA\n\nDoug Tygar\n\nUniversity of California, Berkeley, California, USA\n\nGerhard Weikum\n\nMax Planck Institute for Informatics, Saarbr\u00fccken, Saarland, Germany\n\nCommenced Publication in 1973\n\nFounding and Former Series Editors:\n\nGerhard Goos, Juris Hartmanis, and Jan van Leeuwen\n\nMore information about this series at http:\/\/\u200bwww.\u200bspringer.\u200bcom\/\u200bseries\/\u200b7408\n\nEditors\n\nClark Barrett, Misty Davies and Temesghen Kahsai\n\nNASA Formal Methods9th International Symposium, NFM 2017, Moffett Field, CA, USA, May 16\u201318, 2017, Proceedings\n\nEditors\n\nClark Barrett\n\nStanford University, Palo Alto, California, USA\n\nMisty Davies\n\nNASA Ames Research Center, Moffett Field, California, USA\n\nTemesghen Kahsai\n\nNASA Ames Research Center, Moffett Field, California, USA\n\nISSN 0302-9743e-ISSN 1611-3349\n\nLecture Notes in Computer Science\n\nISBN 978-3-319-57287-1e-ISBN 978-3-319-57288-8\n\nDOI 10.1007\/978-3-319-57288-8\n\nLibrary of Congress Control Number: 2017937299\n\n\u00a9 Springer International Publishing AG 2017\n\nThis work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed.\n\nThe use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.\n\nThe publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.\n\nPrinted on acid-free paper\n\nThis Springer imprint is published by Springer Nature\n\nThe registered company is Springer International Publishing AG\n\nThe registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland\n\nPreface\n\nThe NASA Formal Methods (NFM) Symposium is a forum to foster collaboration between theoreticians and practitioners from NASA, academia, and industry, with the goal of identifying challenges and providing solutions to achieving assurance in mission- and safety-critical systems. Examples of such systems include advanced separation assurance algorithms for aircraft, next-generation air transportation, autonomous rendezvous and docking for spacecraft, autonomous on-board software for unmanned aerial systems (UAS), UAS traffic management, autonomous robots, and systems for fault detection, diagnosis, and prognostics. The topics covered by the NASA Formal Methods Symposia include: model checking, theorem proving, SAT and SMT solving, symbolic execution, automated testing and verification, static and dynamic analysis, model-based development, runtime verification, software and system testing, safety assurance, fault tolerance, compositional verification, security and intrusion detection, design for verification and correct-by-design techniques, techniques for scaling formal methods, formal methods for multi-core GPU-based implementations, generation, specification, and validation of requirements, human\u2013machine interaction analysis, certification, and applications of formal methods in systems development.\n\nThis volume contains the papers presented at NFM 2017, the 9th NASA Formal Methods Symposium, held at the NASA Ames Research Center, Moffett Field, CA, during May 16\u201318, 2017. Previous symposia were held in Minneapolis, MN (2016), Pasadena, CA (2015), Houston, TX (2014), Moffett Field, CA (2013), Norfolk, VA (2012), Pasadena, CA (2011), Washington, DC (2010), and Moffett Field, CA (2009). The series started as the Langley Formal Methods Workshop, and was held under that name in 1990, 1992, 1995, 1997, 2000, and 2008. Papers were solicited for NFM 2017 under two categories: regular papers describing fully developed work and complete results, and short papers describing tools, experience reports, or work in progress with preliminary results. The symposium received 77 submissions for review (60 regular papers and 17 short papers) out of which 31 were accepted for publication (23 regular papers and eight short papers). These submissions went through a rigorous reviewing process, where each paper was first independently reviewed by at least three reviewers and then subsequently discussed by the Program Committee.\n\nIn addition to the refereed papers, the symposium featured five invited presentations: \"Formal Methods for the Informal World,\" by Michael Wagner, Senior Commercialization Specialist at the Robotics Institute at Carnegie Mellon University, Pittsburgh, PA; \"Agile Aerospace at Planet,\" by Ben Haldeman, Technologist and Program Manager at Planet, San Francisco, CA; \"Moving Fast with High Reliability: Static Analysis at Uber,\" by Manu Sridharan, Senior Software Engineer at Uber, Palo Alto, CA; \"Challenges in Designing for the Next Era of Human Space Exploration,\" by Jason Crusan, Director of the Advanced Exploration Systems Division within the Human Exploration and Operations Mission Directorate at NASA, Washington, DC; and \"A Tour of Formal Methods in Support of Aerospace Products Development,\" by Alexandre Arnold, Research Engineer at Airbus. The symposium also featured a panel that discussed how to make more real problems and case studies from NASA and the aerospace industry available to researchers.\n\nThe organizers are grateful to the authors for submitting their work to NFM 2017 and to the invited speakers for sharing their insights. NFM 2017 would not have been possible without the collaboration of the outstanding Program Committee and additional reviewers, the support of the Steering Committee, the efforts of the staff at the NASA Ames Research Center, and the general support of the NASA Formal Methods community. The NFM 2017 website can be found at: https:\/\/\u200bti.\u200barc.\u200bnasa.\u200bgov\/\u200bevents\/\u200bnfm-2017 .\n\nClark Barrett\n\nMisty Davies\n\nTemesghen Kahsai\n\nMay 2017\n\nOrganization\n\n## Program Committee\n\nElla Atkins\n\nUniversity of Michigan, USA\n\nDomagoj Babic\n\nGoogle, USA\n\nJulia Badger\n\nNASA Johnson Space Center, USA\n\nClark Barrett\n\nStanford University, USA\n\nKirstie Bellman\n\nThe Aerospace Corporation, USA\n\nDirk Beyer\n\nLMU Munich, Germany\n\nNikolaj Bjorner\n\nMicrosoft Research, USA\n\nKalou Cabrera Castillos\n\nLAAS-CNRS, France\n\nAlessandro Cimatti\n\nFBK-IRST, Italy\n\nMisty Davies\n\nNASA Ames Research Center, USA\n\nEwen Denney\n\nStinger Ghaffarian Technologies and NASA Ames Research Center, USA\n\nDino Distefano\n\nFacebook, UK\n\nEric Feron\n\nGeorgia Institute of Technology, USA\n\nPierre-Loic Garoche\n\nONERA, France\n\nPatrice Godefroid\n\nMicrosoft Research, USA\n\nAlwyn Goodloe\n\nNASA Langley Research Center, USA\n\nAlberto Griggio\n\nFBK-IRST, Italy\n\nAarti Gupta\n\nPrinceton University, USA\n\nArie Gurfinkel\n\nUniversity of Waterloo, Canada\n\nJohn Harrison\n\nIntel Corporation, USA\n\nKlaus Havelund\n\nJet Propulsion Laboratory, California Institute of Technology, USA\n\nKelly Hayhurst\n\nNASA Langley Research Center, USA\n\nMats Heimdahl\n\nUniversity of Minnesota, USA\n\nMike Hinchey\n\nLero-the Irish Software Engineering Research Centre, Ireland\n\nSusmit Jha\n\nSRI International, USA\n\nRajeev Joshi\n\nLaboratory for Reliable Software, Jet Propulsion Laboratory, USA\n\nDejan Jovanovi\u0107\n\nSRI International, USA\n\nTemesghen Kahsai\n\nNASA Ames Research Center\/CMU, USA\n\nGerwin Klein\n\nData61, CSIRO, Australia\n\nDaniel Kroening\n\nUniversity of Oxford, UK\n\nWenchao Li\n\nBoston University, USA\n\nLowry Michael\n\nNASA Ames Research Center, USA\n\nJorge A Navas\n\nSRI International, USA\n\nNatasha Neogi\n\nNASA Langley Research Center, USA\n\nMeeko Oishi\n\nUniversity of New Mexico, USA\n\nLee Pike\n\nGalois, Inc., USA\n\nZvonimir Rakamaric\n\nUniversity of Utah, USA\n\nMurali Rangarajan\n\nThe Boeing Company, USA\n\nKristin Yvonne Rozier\n\nIowa State University, USA\n\nLael Rudd\n\nDraper, USA\n\nPhilipp Ruemmer\n\nUppsala University, Sweden\n\nNeha Rungta\n\nAmazon Web Services, USA\n\nJohn Rushby\n\nSRI International, USA\n\nSriram Sankaranarayanan\n\nUniversity of Colorado, Boulder, USA\n\nMartin Sch\u00e4f\n\nSRI International, USA\n\nCesare Tinelli\n\nThe University of Iowa, USA\n\nChristoph Torens\n\nGerman Aerospace Center, Institute of Flight Systems, Germany\n\nVirginie Wiels\n\nONERA\/DTIM, France\n\n## Additional Reviewers\n\nBackeman, Peter\n\nBackes, John\n\nBittner, Benjamin\n\nBlackshear, Sam\n\nCalder\u00f3n Trilla, Jos\u00e9 Manuel\n\nCattaruzza, Dario\n\nChowdhury, Omar\n\nCohen, Raphael\n\nDangl, Matthias\n\nDimjasevic, Marko\n\nElliott, Trevor\n\nErkok, Levent\n\nGalea, John\n\nGay, David\n\nGross, Kerianne\n\nHamon, Arnaud\n\nHe, Shaobo\n\nHendrix, Joe\n\nHowar, Falk\n\nLuckow, Kasper\n\nMattarei, Cristian\n\nMercer, Eric\n\nMote, Mark\n\nMukherjee, Rajdeep\n\nPoetzl, Daniel\n\nReynolds, Andrew\n\nSanchez, Huascar\n\nSun, Youcheng\n\nTkachuk, Oksana\n\nZelji\u0107, Aleksandar\n\nContents\n\nAn Automata-Theoretic Approach to Modeling Systems and Specifications over Infinite Data 1\n\nHadar Frenkel, Orna Grumberg and Sarai Sheinvald\n\nLearning from Faults:\u200b Mutation Testing in Active Automata Learning 19\n\nBernhard K. Aichernig and Martin Tappler\n\nParametric Model Checking Timed Automata Under Non-Zenoness Assumption 35\n\n\u00c9tienne Andr\u00e9, Hoang Gia Nguyen, Laure Petrucci and Jun Sun\n\nMulti-timed Bisimulation for Distributed Timed Automata 52\n\nJames Ortiz, Moussa Amrani and Pierre-Yves Schobbens\n\nAuto-Active Proof of Red-Black Trees in SPARK 68\n\nClaire Dross and Yannick Moy\n\nAnalysing Security Protocols Using Refinement in iUML-B 84\n\nColin Snook, Thai Son Hoang and Michael Butler\n\nOn Learning Sparse Boolean Formulae for Explaining AI Decisions 99\n\nSusmit Jha, Vasumathi Raman, Alessandro Pinto, Tuhin Sahai and Michael Francis\n\nEvent-Based Runtime Verification of Temporal Properties Using Time Basic Petri Nets 115\n\nMatteo Camilli, Angelo Gargantini, Patrizia Scandurra and Carlo Bellettini\n\nModel-Counting Approaches for Nonlinear Numerical Constraints 131\n\nMateus Borges, Quoc-Sang Phan, Antonio Filieri and Corina S. P\u0103s\u0103reanu\n\nInput Space Partitioning to Enable Massively Parallel Proof 139\n\nAshlie B. Hocking, M. Anthony Aiello, John C. Knight and Nikos Ar\u00e9chiga\n\nCompositional Model Checking of Interlocking Systems for Lines with Multiple Stations 146\n\nHugo Daniel Macedo, Alessandro Fantechi and Anne E. Haxthausen\n\nModular Model-Checking of a Byzantine Fault-Tolerant Protocol 163\n\nBenjamin F. Jones and Lee Pike\n\nImproved Learning for Stochastic Timed Models by State-Merging Algorithms 178\n\nBraham Lotfi Mediouni, Ayoub Nouri, Marius Bozga and Saddek Bensalem\n\nVerifying Safety and Persistence Properties of Hybrid Systems Using Flowpipes and Continuous Invariants 194\n\nAndrew Sogokon, Paul B. Jackson and Taylor T. Johnson\n\nA Relational Shape Abstract Domain 212\n\nHugo Illous, Matthieu Lemerre and Xavier Rival\n\nFloating-Point Format Inference in Mixed-Precision 230\n\nMatthieu Martel\n\nA Verification Technique for Deterministic Parallel Programs 247\n\nSaeed Darabi, Stefan C. C. Blom and Marieke Huisman\n\nSystematic Predicate Abstraction Using Variable Roles 265\n\nYulia Demyanova, Philipp R\u00fcmmer and Florian Zuleger\n\n specgen : A Tool for Modeling Statecharts in CSP 282\n\nBrandon Shapiro and Chris Casinghino\n\n H y P ro : A C++ Library of State Set Representations for Hybrid Systems Reachability Analysis 288\n\nStefan Schupp, Erika \u00c1brah\u00e1m, Ibtissem Ben Makhlouf and Stefan Kowalewski\n\n Asm2C++ : A Tool for Code Generation from Abstract State Machines to Arduino 295\n\nSilvia Bonfanti, Marco Carissoni, Angelo Gargantini and Atif Mashkoor\n\nSPEN:\u200b A Solver for Separation Logic 302\n\nConstantin Enea, Ond\u0159ej Leng\u00e1l, Mihaela Sighireanu and Tom\u00e1\u0161 Vojnar\n\nFrom Hazard Analysis to Hazard Mitigation Planning:\u200b The Automated Driving Case 310\n\nMario Gleirscher and Stefan Kugele\n\nEvent-B at Work:\u200b Some Lessons Learnt from an Application to a Robot Anti-collision Function 327\n\nArnaud Dieumegard, Ning Ge and Eric Jenn\n\nReasoning About Safety-Critical Information Flow Between Pilot and Computer 342\n\nSeth Ahrenbach\n\nCompositional Falsification of Cyber-Physical Systems with Machine Learning Components 357\n\nTommaso Dreossi, Alexandre Donz\u00e9 and Sanjit A. Seshia\n\nVerifying a Class of Certifying Distributed Programs 373\n\nKim V\u00f6llinger and Samira Akili\n\nCompact Proof Witnesses 389\n\nMarie-Christine Jakobs and Heike Wehrheim\n\nQualification of a Model Checker for Avionics Software Verification 404\n\nLucas Wagner, Alain Mebsout, Cesare Tinelli, Darren Cofer and Konrad Slind\n\nSpeAR v2.\u200b0:\u200b Formalized Past LTL Specification and Analysis of Requirements 420\n\nAaron W. Fifarek, Lucas G. Wagner, Jonathan A. Hoffman, Benjamin D. Rodes, M. Anthony Aiello and Jennifer A. Davis\n\nJust Formal Enough?\u200b Automated Analysis of EARS Requirements 427\n\nLevi L\u00facio, Salman Rahman, Chih-Hong Cheng and Alistair Mavin\n\nAuthor Index435\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_1\n\n# An Automata-Theoretic Approach to Modeling Systems and Specifications over Infinite Data\n\nHadar Frenkel1 , Orna Grumberg1 and Sarai Sheinvald2\n\n(1)\n\nDepartment of Computer Science, The Technion, Haifa, Israel\n\n(2)\n\nDepartment of Software Engineering, ORT Braude Academic College, Karmiel, Israel\n\nHadar Frenkel\n\nEmail: hfrenkel@cs.technion.ac.il\n\nAbstract\n\nData-parameterized systems model finite state systems over an infinite data domain. VLTL is an extension of LTL that uses variables in order to specify properties of computations over infinite data, and as such VLTL is suitable for specifying properties of data-parameterized systems. We present Alternating Variable B\u00fcchi Word Automata (AVBWs), a new model of automata over infinite alphabets, capable of modeling a significant fragment of VLTL. While alternating and non-deterministic B\u00fcchi automata over finite alphabets have the same expressive power, we show that this is not the case for infinite data domains, as we prove that AVBWs are strictly stronger than the previously defined Non-deterministic Variable B\u00fcchi Word Automata (NVBWs). However, while the emptiness problem is easy for NVBWs, it is undecidable for AVBWs. We present an algorithm for translating AVBWs to NVBWs in cases where such a translation is possible. Additionally, we characterize the structure of AVBWs that can be translated to NVBWs with our algorithm, and identify fragments of VLTL for which a direct NVBW construction exists. Since the emptiness problem is crucial in the automata-theoretic approach to model checking, our results give rise to a model-checking algorithm for a rich fragment of VLTL and systems over infinite data domains.\n\n## 1 Introduction\n\nInfinite data domains become increasingly relevant and wide-spread in real-life systems, and are integral in communication systems, e-commerce systems, large databases and more. Systems over infinite data domains were studied in several contexts and especially in the context of datalog systems [4] and XML documents [5, 7], that are the standard of web documents.\n\nTemporal logic, particularly LTL, is widely used for specifying properties of ongoing systems. However, LTL is unable to specify computations that handle infinite data. Consider, for example, a system of processes and a scheduler. If the set of processes is finite and known in advance, we can express and verify properties such as \"every process is eventually active\". However, if the system is dynamic, in which new processes can log in and out, and the total number of processes is unbounded, LTL is unable to express such a property.\n\nVLTL (LTL with variables) [11] extends LTL with variables that range over an infinite domain, making it a natural logic for specifying ongoing systems over infinite data domains. For the example above, a VLTL formula can be , where x ranges over the process IDs. Thus, the formula specifies that for every process ID, once it is logged in, it will eventually be active. Notice that this formula now specifies this property for an unbounded number of processes. As another example, the formula , where x ranges over the message contents (or message IDs), specifies that in every step of the computation, some message is sent, and this particular message is eventually received. Using variables enables handling infinitely many messages along a single computation.\n\nIn the automata-theoretic approach to model checking [18, 19], both the system and the specification are modeled by automata whose languages match the set of computations of the system and the set of satisfying computations of the formula. Model-checking is then reduced to reasoning about these automata. For ongoing systems, automata over infinite words, particularly nondeterministic and alternating B\u00fcchi automata (NBWs and ABWs, respectively) are used [18]. Thus, for ongoing systems with infinite data and VLTL, a similar model is needed, capable of handling infinite alphabets. In [10, 11], the authors suggested non-deterministic variable B\u00fcchi word automata (NVBWs), a model that augments NBWs with variables, and used it to construct a model-checking algorithm for a fragment of VLTL that is limited to -quantifiers that appear only at the head of the formula.\n\nThe emptiness problem for NVBWs is NLOGSPACE-complete. Since the emptiness problem is crucial for model checking, NVBWs are an attractive model. However, they are quite weak. For example, NVBWs are unable to model the formula above.\n\nIn this work, we present a new model for VLTL specifications, namely alternating variable B\u00fcchi word automata (AVBWs). These are an extension of NVBWs, which we prove to be stronger and able to express a much richer fragment of VLTL. Specifically, we show that AVBWs are able to express the entire fragment of -VLTL, which is a fragment of VLTL with only -quantifiers, whose position in the formula is unrestricted.\n\nWe now elaborate more on NVBWs and AVBWs. As mentioned, an NVBW uses variables that range over an infinite alphabet . A run of on a word w assigns values to the variables in a way that matches the letters in w. For example, if a letter a.8 occurs in w, then a run of may read a.x, where x is assigned 8. In addition, the variables may be reset at designated states along the run, and so a.x can be later used for reading another letter a.5, provided that x has been reset. Resetting then allows reading an unbounded number of letters using a fixed set of variables. Another component of NVBWs is an inequality set , that allows restricting variables from being assigned with the same value. Our new model of AVBWs extends NVBWs by adding alternation. An alternating automaton may split its run and continue reading the input along several different paths simultaneously, all of which must accept.\n\nThere is a well-known translation from LTL to ABW [18]. Thus, AVBWs are a natural candidate for modeling VLTL. Indeed, as we show, AVBWs are able to express all -VLTL, following a translation that is just as natural as the LTL to ABW translation. Existential quantifiers (anywhere) in the formula are translated to corresponding resets in the automaton. Moreover, unlike the finite alphabet case, in which NBWs and ABWs are equally expressive, in the infinite alphabet case alternation proves to be not only syntactically stronger but also semantically stronger, as we show that AVBWs are more expressive than NVBWs.\n\nAs we have noted, our goal is to provide a model which is suitable for a model-checking algorithm for VLTL, and that such a model should be easily tested for emptiness. However, we show that the strength of AVBWs comes with a price, and their emptiness problem is unfortunately undecidable. To keep the advantage of ease of translation of VLTL to AVBWs, as well as the ease of using NVBWs for model-checking purposes, we would then like to translate AVBWs to NVBWs, in cases where such a translation is possible. This allows us to enjoy the benefit of both models, and gives rise to a model-checking algorithm that is able to handle a richer fragment of VLTL than the one previously studied.\n\nWe present such a translation algorithm, inspired by the construction of [14]. As noted, such a translation is not always possible. Moreover, we show that there is no algorithm that is both sound and complete, even if we restrict completeness to require returning \"no translation possible\". Our algorithm is then sound but incomplete, and we present an example for which it will not halt. However, we give a characterization for AVBWs for which our algorithm does halt, relying on the graphical structure of the underlying automaton. The essence of the characterization is that translatable AVBWs do not have a cycle that contains a reset action which leads to an accepting state. Consider once again . Here, we keep sending messages that must arrive eventually. However, there is no bound on when they will arrive. Since this is a global requirement, there must be some cycle that verifies it, and such cycles are exactly the ones that prevent the run of the translation algorithm from halting.\n\nThe importance of our algorithm and structural characterization is a twofold: (1) given an AVBW , one does not need to know the semantics of in order to know if it is translatable, and to automatically translate to an equivalent NVBW; and (2) Given a general -VLTL formula, one can easily construct an equivalent AVBW , use our characterization to check whether it is translatable, and continue with the NVBW that our translation outputs.\n\nIn addition to the results above, we also study fragments of -VLTL that have a direct construction to NVBWs, making them an \"easy\" case for modeling and model checking.\n\nRelated Work. Other models of automata over infinite alphabets have been defined and studied. In [13] the authors define register automata over infinite alphabets, and study their decidability properties. [16] use register automata as well as pebble automata to reason about first order logic and monadic second order logic, and to describe XML documents. [3] limit the number of variables and use extended first order logic to reason about both XML and some verification properties. In [4] the authors model infinite state systems as well as infinite data domains, in order to express some extension of monadic first order logic. Our model is closer to finite automata over infinite words than the models above, making it easier to understand. Moreover, due to their similarity to ABWs, we were able to construct a natural translation of -VLTL to AVBWs, inspired by [18]. We then translate AVBWs to NVBWs. Our construction is consistent with [14] which provides an algorithm for translating ABWs to NBWs. However, in our case additional manipulations are needed in order to handle the variables and track their possible assignments.\n\nThe notion of LTL over infinite data domains was studied also in the field of runtime verification (RV) [1, 2, 8]. Specifically, in [1], the authors suggest a model of quantified automata with variables, in order to capture traces of computations with different data values. The purpose in RV is to check whether a single given trace satisfies the specification. Moreover, the traces under inspection are finite traces. This comes into play in [1] where the authors use the specific data values that appear on such a trace in order to evaluate satisfiability. In [2] the authors suggest a 3-valued semantics in order to capture the uncertainty derived from the fact that traces are finite. Our work approaches infinite data domains in a different manner. Since we want to capture both infinite data domains and infinite traces, we need a much more expressive model, and this is where AVBWs come into play.\n\n## 2 Preliminaries\n\nGiven a finite set of directions D, a D-tree T is a set . The root of T is the empty word . A node x of T is a word over D that describes the path from the root of T to x. That is, for a word there is a path in the tree such that every word is a successor of the previous word . For a word where and , if then , i.e. the tree is prefix closed. A successor of a node is of the form for .\n\nGiven a set L, an L-labeled D-tree is a pair where T is a D-tree, and is a labeling function that labels each node in T by an element of L.\n\nA non-deterministic B\u00fcchi automaton over infinite words (NBW) [6] is a tuple where is a finite alphabet; Q is a finite set of states; is the initial state; is a set of accepting states; and is the transition function. For a word , we denote by the letter of in position i.\n\nA run of on a word is an infinite sequence of states , that is consistent with , i.e., is the initial state and . A run of is accepting if it visits some state of infinitely often. We say that accepts a word if there exists an accepting run of on . The language of , denoted , is the set of words accepted by .\n\nAn alternating B\u00fcchi automaton over infinite words (ABW) [15] is a tuple where and are as in NBW. The transition relation is , where is the set of positive boolean formulas over the set of states, i.e. formulas that include only the boolean operators and 1. For example, if , then, by reading a from q, the ABW moves to either both and , or to . We assume that is given in a disjunctive normal form (DNF).\n\nA run of an ABW is a Q-labeled Q-tree. Disjunctions are equivalent to non- deterministic choices, and so every disjunct induces a tree. A conjunction induces a split to two or more successors. For example, induces two trees. In the first, q has two successors, and . In the second tree the only successor of q is . A run is accepting if every infinite path in the corresponding tree visits a state from infinitely often, and every finite path ends with . The notions of acceptance and language are as in NBWs.\n\nWe say that an automaton (either NBW or ABW) is a labeled automaton if its definition also includes a labeling function for its states, where L is a set of labels. We use this notion to conveniently define variable automata later on.\n\nWe assume that the reader is familiar with the syntax and semantics of LTL.\n\nVariable LTL, or VLTL, as defined in [11], extends LTL by augmenting atomic propositions with variables. Let AP be a set of parameterized atomic propositions, let X be a finite set of variables, and let be a vector of variables. Then, the formulas in VLTL are over , thus allowing the propositions to carry data from an infinite data domain. We inductively define the syntax of VLTL.\n\n * For every and the formulas a.x and are VLTL formulas2.\n\n * For a VLTL formula and , the formulas and are in VLTL.\n\n * If and are VLTL formulas, then so are ; ; ; ; ; ; and , where is the release operator, which is the dual operator of .\n\nGiven an alphabet , an assignment , and a word , we denote if under the standard semantics of LTL. For example, for it holds that for .\n\nWe denote if there exists an assignment to the variable x such that , where is as defined before. We denote if for every assignment to the variable x, it holds that .\n\nWe say that a formula is closed if every occurrence of a variable in is under the scope of a quantifier. Notice that the satisfaction of closed formulas is independent of specific assignments. For a closed formula over , we then write .\n\nThe logic -VLTL is the set of all closed VLTL formulas in negation normal form (NNF) that only use the -quantifier. Note that the -quantifier may appear anywhere in the formula. The logic -VLTL is the set of all -VLTL formulas in prenex normal form, i.e., -quantifiers appear only at the beginning of the formula.\n\nThe language of a formula , denoted , is the set of computations that satisfy .\n\nWe now define non-deterministic variable B\u00fcchi automata over infinite words (NVBWs). Our definition is tailored to model VLTL formulas, and thus is slightly different from the definition in [10]. Specifically, the alphabet consists of subsets of , where AP is a finite set of parameterized atomic propositions.\n\nAn NVBW is a tuple , where is a labeled NBW, X is a finite set of variables, is a labeling function that labels each state q with the set of variables that are reset at q, the set is an inequality set over X, and is an infinite alphabet.\n\nA run of an NVBW on a word , where is a pair where , is an infinite sequence of states, and is a sequence of mappings such that:\n\n 1. 1.\n\nThere exists a word such that and is a run of on z. We say that z is a symbolic word that is consistent on with the concrete word .\n\n 2. 2.\n\nThe run respects the reset actions: for every , if then .\n\n 3. 3.\n\nThe run respects : for every and for every inequality it holds that .\n\nA run on is accepting if is an accepting run of on a symbolic word z that corresponds to on , i.e. visits infinitely often. The notion of acceptance and language are as in NBWs.\n\nIntuitively, a run of an NVBW on a word assigns each occurrence of a variable a letter from . A variable can \"forget\" its value only if a reset action occurred. The inequality set prevents from certain variables to be assigned with the same value.\n\nWe say that an NVBW expresses a formula if .\n\nExample 1\n\nConsider the concrete word . In an NVBW , a corresponding symbolic word can be . If includes reset actions for and in every even state in some path of , then another concrete word consistent with z can be , since the values of and can change at every even state.\n\n## 3 Variable Automata: Non-determinism Vs. Alternation\n\nIn Sect. 5 we show that NVBWs are useful for model checking in our setting, since they have good decidability properties. In particular, there is a polynomial construction for intersection of NVBWs, and their emptiness problem is NLOGSPACE-complete [10]. In Sect. 4 we describe a translation of -VLTL formulas to NVBWs. We now show that NVBWs are too weak to express all VLTL formulas, or even all -VLTL formulas. It follows that -VLTL is strictly more expressive than -VLTL. Nevertheless, we use NVBWs for model checking at least for some fragments of -VLTL.\n\nBefore discussing the properties of variable automata, we first give some motivation for their definition, as given in Sect. 2. In particular, we give motivation for the reset labeling function and for , the inequity set.\n\nExample 2\n\nWe begin with resets. Consider the -VLTL formula . One possible computation satisfying is . No NVBW with a finite number of variables can read , unless some variable is reassigned. The reset action allows these reassignments.\n\nExample 3\n\nTo see the necessity of the inequality set , consider the -VLTL formula . We can use a variable x to store a value that never appears along the computation with a. Imposing inequality restrictions on x with all other variables makes sure that the value assigned to x does not appear along the computation via assignments to other variables. Note that if the logic does not allow negations at all, the inequality set is not needed.\n\n### 3.1 NVBWs Are Not Expressive Enough for -VLTL\n\nWe first show that NVBWs cannot express every -VLTL formula.\n\nLemma 1\n\nThe formula cannot be expressed by an NVBW.\n\nProof\n\nConsider the following word over and .\n\ni.e., b.(i) occurs in , and occurs for the first time in and continues until .\n\nIt is easy to see that satisfies since at step t for we have that b.t holds, and at some point in the future, specifically at step , the proposition a.t will hold.\n\nAssume, by way of contradiction, that is an NVBW with m variables that expresses . Then over a sub-word with more than m values for b, one variable must be reset and used for two different values. We can then create a different computation in which the value that was \"forgotten\" never appears with a, thus not satisfying , but accepted by , a contradiction.\n\nNot only -quantifiers are problematic for NVBWs. NVBWs cannot handle -quantifiers, even in PNF. The proof of the following Lemma is almost identical to the proof of Lemma 1.\n\nLemma 2\n\nThe formula cannot be expressed by an NVBW.\n\n### 3.2 Alternating Variable B\u00fcchi Automata\n\nIn Sect. 3.1 we have shown that NVBWs are not expressive enough, even when considering only the fragment of -VLTL. We now introduce alternating variable B\u00fcchi automata over infinite words (AVBW), and show that they can express all of -VLTL. We study their expressibility and decidability properties.\n\nDefinition 1\n\nAn AVBW is a tuple where is a labeled ABW, X is a finite set of variables, is a labeling function that labels every state q with the set of variables that are reset at q, the set is an inequality set, and is an infinite alphabet. We only allow words in which a proposition for appears at most once in every computation step, i.e., no word can contain both and for at the same position.\n\nA run of an AVBW on a word is a pair where T is a Q-labeled Q-tree and r labels each node t of T by a function such that:\n\n 1. 1.\n\nThe root of T is labeled with .\n\n 2. 2.\n\nFor each path on T there exists a symbolic word such that .\n\n 3. 3.\n\nThe run respects : for each node labeled by q of depth i on path , the successors of t are labeled by iff one of the conjuncts in is exactly .\n\n 4. 4.\n\nThe run respects the reset actions: if is a child node of t labeled by q and , then .\n\n 5. 5.\n\nThe run respects : for every and for every node it holds that .\n\nIntuitively, much like in NVBWs, the variables in every node in the run tree are assigned values in a way that respects the resets and the inequality set.\n\nA run on is accepting if every infinite path is labeled infinitely often with states in . The notion of acceptance and language are as usual. Note that the same variable can be assigned different values on different paths.\n\nJust like ABWs, AVBWs are naturally closed under union and intersection. However, unlike ABWs, they are not closed under complementation. We prove this in Sect. 3.4.\n\n### 3.3 AVBWs Can Express All of -VLTL\n\nWe now show that AVBWs can express -VLTL. Together with Lemma 1, we reach the following surprising theorem.\n\nTheorem 1\n\nAVBWs are strictly more expressive than NVBWs.\n\nThis is in contrast to the finite alphabet case, where there are known algorithms for translating ABWs to NBWs [14].\n\nTheorem 2\n\nEvery -VLTL formula can be expressed by an AVBW .\n\nWe start with an example AVBW for from Lemma 1.\n\nExample 4\n\nLet where .\n\n * ,\n\n *\n\nIntuitively, makes sure that at each step there is some value with which b holds. The run then splits to both and . The state waits for a with the same value as was seen in (since is not reset along this path, it must be the same value), and uses to ignore other values that are attached to a, b. The state continues to read values of b (which again splits the run), while using to ignore values assigned to a. See Fig. 1 for a graphic representation of .\n\nFig. 1.\n\nThe AVBW described in Example 4 and an example of a run. The double arch between transitions represents an \"and\" in .\n\nWe now proceed to the proof of Theorem 2.\n\nProof\n\nLet be an -VLTL formula. We present an explicit construction of , based on the construction of [18] and by using resets to handle the -quantifiers, and inequalities to handle negations. First, we rename the variables in and get an equivalent formula , where each existential quantifier bounds a variable with a different name. For example, if then . Let denote all sub-formulas of and let denote the set of variables that appear in .\n\nLet where and where\n\n *\n\n *\n\n * and, for , we have .\n\n * .\n\n * consists of all states of the form .\n\nThe set of states Q consists of all sub-formulas of . Intuitively, at every given point there is an assignment to the variables, that may change via resets. If an accepting run of on visits a state , then the suffix of that is read from satisfies under the current assignment to the variables. The set of variables X consists of all variables in , as well as a variable for every atomic proposition . The additional variables enable the run to read and ignore currently irrelevant inputs. For example, for , we want to read (and ignore) values of a and b until occurs with some .\n\nLet A be a subset of (recall that is defined over the alphabet ). We define as follows.\n\n * if and if\n\n * if and if\n\n * .\n\n *\n\n *\n\n *\n\n *\n\n *\n\nNote that since we only use formulas in NNF, we define for both \"and\" and \"or\", as well as for (until) and (release) operators.\n\nCorrectness. It can be shown that a word is accepted from a state with a variable assignment r iff . We elaborate on how the construction handles the -quantifier and negations.\n\nThe -quantifier is handled by resetting the variables under its scope. Indeed, according to the semantics of , for of the form , the suffix of holds if holds for some assignment to x. Resetting x allows the run to correctly assign x in a way that satisfies . Notice also that from this point on, due to the quantifier, the previous value assigned to x may be forgotten.\n\nRecall that we only allow negations on atomic propositions. We handle these negations with inequalities. If is a sub-formula of , then we do not want the value assigned to x to appear with a when reading a from state . Thus, all variables that a can occur with from state must be assigned different values from the value currently assigned to x. We express this restriction with the inequality set .\n\n### 3.4 AVBWs Are Not Complementable\n\nAs mentioned before, unlike ABWs, AVBWs are not complementable. To prove this, we show that -VLTL cannot generally be expressed by AVBWs. Since negating an -VLTL formula produces a -VLTL formula, the result follows.\n\nTheorem 3\n\nThere is no AVBW that expresses .\n\nProof\n\nObviously, if the alphabet is not countable, then it cannot be enumerated by a computation. However, the claim holds also for countable alphabets. Assume by way of contradiction that there exists an AVBW that expresses for . Then accepts . Since the variables are not sensitive to their precise contents but only to inequalities among the values, it is easy to see that the accepting run of on w can also be used to read , in which the value 0 never occurs.\n\nThe negation of the above is in -VLTL, thus there is an AVBW that expresses it.\n\nCorollary 1\n\nAVBWs are not complementable.\n\nCorollary 2\n\n -VLTL is not expressible by AVBWs.\n\n### 3.5 Variable Automata: From AVBW to NVBW\n\nThe emptiness problem for NVBWs is NLOGSPACE-complete [10]. In the context of model checking, this is an important property. We now show that for AVBWs, the emptiness problem is undecidable.\n\nLemma 3\n\nThe emptiness problem for AVBWs is undecidable.\n\nProof\n\nAccording to [17], the satisfiability problem for -VLTL is undecidable. The satisfiability of a formula is equivalent to the nonemptiness of an automaton that expresses . Since we have showed that every -VLTL formula can be expressed by an AVBW, the proof follows.\n\nSince the emptiness problem for NVBWs is easy, we are motivated to translate AVBWs to NVBWs in order to model check properties that are expressed by AVBWs. In particular, it will enable us to model check -VLTL properties. This, however, is not possible in general since AVBWs are strictly more expressive than NVBWs (Theorem 1).\n\nIn this section we present an incomplete algorithm, which translates an interesting subset of AVBWs to equivalent NVBWs. We later give a structural characterization for AVBWs that can be translated by our algorithm to NVBWs.\n\n#### 3.5.1 From AVBW to NVBW\n\nOur algorithm is inspired by the construction of [14] for translating ABW to NBW. In [14] the states of the NBW are of the form where S is the set of the states the ABW is currently at, and O is the set of states from paths that \"owe\" a visit to an accepting state. While running the NBW on a word , accepting states are removed from O, until . Thus, when , all paths have visited an accepting state at least once. Now, O is again set to be S, and a new round begins. The accepting states of the NBW are states of the form .\n\nHere, we wish to translate an AVBW to an NVBW . For simplicity, we assume that . The changes for the case where are described later.\n\nIn our case, the variables make the translation harder, and as shown before, even impossible in some cases. In addition to S, O we must also remember which variables are currently in use, and might hold values from previous states. In our translation, the states of the NVBW are tuples containing S, O and the sets of variables in use. Since AVBWs allow different paths to assign different values to the same variable, the translation to an NVBW must allocate a new variable for each such assignment. We also need to release variables that were reset in the AVBW, in order to reuse them in the NVBW to avoid defining infinitely many variables. Since we need to know which variables are in use at each step of a run of , we dynamically allocate both the states and the transitions of .\n\nThus, , the transition function of , is defined dynamically during the run of our algorithm, as do the states of . Moreover, since each path may allocate different values to the same variable, it might be the case that the same variable holds infinitely many values (from different paths). Such a variable induces an unbounded number of variables in . Our algorithm halts when no new states are created, and since the fresh variables are part of the created states, creating infinitely many such variables causes our algorithm not to halt. Therefore, the algorithm is incomplete.\n\nAlgorithm Let be an AVBW, where . For simplicity we assume that is defined over the alphabet instead of . Recall that we assume that is in DNF for all . Let be an NVBW where , and3:\n\nTo handle cases where , instead of mapping x to any unmapped variable , each variable x may be mapped only to a unique set . Then, we define . Notice that this does not change the cardinality of Z.\n\n#### 3.5.2 A Structural Characterization of Translatable AVBWs\n\nIn order to define a structural characterization, we wish to refer to an AVBW as a directed graph whose nodes are the states of . There is an edge from q to iff is in for some . For example, if then there are edges from q to and .\n\nDefinition 2\n\nAn x-cycle in an AVBW A is a cycle where , of states in such that:\n\n 1. 1.\n\nFor all it holds that is in for some .\n\n 2. 2.\n\nThere exists such that is in for and . i.e. there is an edge from one state to another on the cycle, labeled x.\n\nTheorem 4\n\nAssume the preprocessing of stage 1 in the algorithm has been applied, resulting in an AVBW . Algorithm AVBWtoNVBW halts on and returns an equivalent NVBW iff for every x-cycle in one of the following holds:\n\n 1. 1.\n\nFor every q on it holds that .\n\n 2. 2.\n\nFor every state q on a path from the initial state to with for , such that is on the cycle and leads to an accepting state, it holds that every x-cycle on a path from to an accepting state contains a state with .\n\nProof\n\nFirst, notice that Algorithm AVBWtoNVBW halts iff Z is of a finite size, i.e., the number of variables it produces is finite.\n\nFor the first direction we show that running AVBWtoNVBW on an AVBW with the above properties results in an NVBW with Z of a finite size. In each of the two cases, we can bound the distance between two reset actions for the same variable, or between a reset action and an accepting state, along every possible run. This, since we can bound the length of the longest path from a state on an x-cycle to an accepting state. Thus all variables in X induce a finite number of variables in Z.\n\nFor the other direction, since 1\u20132 do not hold, there exists a state q that leads both to an x-cycle on which x is reset, and to an x-cycle with no , on a way to an accepting state. While running our algorithm, a new mapping is introduced at every visit to on . At the same time, cannot be removed from , because of the visits to , which does not reset x, and thus its value must be kept. Therefore, the algorithm continuously creates new assignments for . Thus contains an unbounded set of variables. The fact that there is a path to an accepting state is needed in order for this cycle to \"survive\" the preprocessing.\n\n#### 3.5.3 Completeness and Soundness\n\nAs we mentioned before, no translation algorithm from AVBWs to NVBWs can be both sound and complete, and have a full characterization of inputs for which the algorithm halts. We now prove this claim.\n\nTheorem 5\n\nThere is no algorithm that translates AVBWs into NVBWs such that all the following hold.\n\n 1. 1.\n\nCompleteness - for every that has an equivalent NVBW, halts and returns such an equivalent NVBW.\n\n 2. 2.\n\nSoundness - If halts and returns an NVBW , then is equivalent to A.\n\n 3. 3.\n\nThere is a full characterization of AVBWs for which halts.\n\nProof\n\nAs we have shown in Lemma 3, the emptiness problem of AVBWs is undecidable. Assume there is a translation algorithm as described in Theorem 5. Then consider the following procedure. Given an AVBW , if halts, check if is empty. If does not halt on input , we know it in advance due to the full characterization. Moreover, we know that is not empty (otherwise, since is complete, would halt on , since there is an NVBW for the empty language). Hence, a translation algorithm as described in Theorem 5 gives us a procedure to decide the emptiness problem for AVBWs, a contradiction.\n\nFor our algorithm, we have shown a full characterization for halting. Now we prove that our algorithm is sound, and demonstrate its incompleteness by an example of an AVBW for the empty language, for which our algorithm does not halt.\n\nTheorem 6\n\nAlgorithm AVBWtoNVBW is sound.\n\nProof\n\nFirst we show that the definition of is correct. Indeed, every is derived from , and each is induced from only one variable, . Therefore, preserves exactly the inequalities of . Now, is defined according to such that if is induced from x, and x is reset in a state q then is reset in states that include q. Therefore allows fresh values only when does. The correctness of the rest of the construction follows from the correctness of [14] and from the explanations in the body of the algorithm.\n\nExample 5\n\nIncompleteness of the algorithm Let where and . The definition of is: . The language of is empty, since in order to reach an accepting state on the path from , the input must be exactly for some , but the cycle of only allows to read , without any b.i. Although there is an NVBW for the empty language, our algorithm does not halt on : it keeps allocating new variables to x, thus new states are created and the algorithm does not reach a fixed point.\n\n## 4 Fragments of -VLTL Expressible by NVBWs\n\nWe now present several sub-fragments of -VLTL with a direct NVBW construction.\n\nWe can construct an NVBW for -VLTL formula in prenex normal form, denoted -VLTL. The construction relies on the fact that variables cannot change values throughout the run. Since every -VLTL formula is expressible with an NVBW, together with Lemma 1, we have the following corollary.\n\nCorollary 3\n\n -VLTL is stronger than -VLTL.4.\n\nAnother easy fragment is - -VLTL, which is -VLTL with only the temporal operators, similar to the definitions of [9]. and are interchangeable. Thus, every - -VLTL formula is equivalent to an -VLTL, which has a direct construction to an NVBW.\n\nA direct construction from VLTL to NVBWs exists also for -VLTL formulas in which all quantifiers are either at the beginning of the formula, or adjacent to a parameterized atomic proposition. This extends the construction for -VLTL by adding resets to some of the states.\n\n## 5 Model Checking in Practice\n\nThe model-checking problem over infinite data domains asks whether an NVBW accepts a computation that satisfies an -VLTL formula , which specifies \"bad\" behaviors. If is one of the types mentioned in Sect. 4, we can build an equivalent NVBW for . For a general , we build an equivalent AVBW according to Sect. 3.3 and if the structure of agrees with the structural conditions of Theorem 4, we translate to an equivalent NVBW according to Sect. 3.5.1. Now, if exists, the intersection includes all computations of that are also computations of . Checking the emptiness of the intersection decides whether has a \"bad\" behavior that satisfies .\n\n## 6 Conclusions and Future Work\n\nWe defined AVBWs, a new model of automata over infinite alphabets that describes all -VLTL formulas. We showed that AVBWs, unlike ABWs, are not complementable and are stronger than NVBWs. Nevertheless, we presented an algorithm for translating AVBWs to NVBWs when possible, in order to preform model checking. Moreover, we defined a structural characterization of translatable AVBWs. Finally, we presented the full process of model checking a model M given as an NVBW against an -VLTL formula. A natural extension of our work is to use the techniques presented in this paper in order to preform model checking for VCTL [12] formulas as well.\n\nReferences\n\n1.\n\nBarringer, H., Falcone, Y., Havelund, K., Reger, G., Rydeheard, D.: Quantified event automata: towards expressive and efficient runtime monitors. In: Giannakopoulou, D., M\u00e9ry, D. (eds.) FM 2012. LNCS, vol. 7436, pp. 68\u201384. Springer, Heidelberg (2012). doi:10.\u200b1007\/\u200b978-3-642-32759-9_\u200b9 CrossRef\n\n2.\n\nBauer, A., Leucker, M., Schallhart, C.: Runtime verification for LTL and TLTL. ACM Trans. Softw. Eng. Methodol. 20(4), 14:1\u201314:64 (2011)CrossRef\n\n3.\n\nBoja\u0144czyk, M., Muscholl, A., Schwentick, T., Segoufin, L., David, C.: Two-variable logic on words with data. In: 21st IEEE Symposium on Logic in Computer Science (LICS 2006), 12\u201315, Seattle, WA, USA, Proceedings, pp. 7\u201316. IEEE Computer Society, 2006, August 2006\n\n4.\n\nBouajjani, A., Habermehl, P., Jurski, Y., Sighireanu, M.: Rewriting systems with data. In: Csuhaj-Varj\u00fa, E., \u00c9sik, Z. (eds.) FCT 2007. LNCS, vol. 4639, pp. 1\u201322. Springer, Heidelberg (2007). doi:10.\u200b1007\/\u200b978-3-540-74240-1_\u200b1 CrossRef\n\n5.\n\nBrambilla, M., Ceri, S., Comai, S., Fraternali, P., Manolescu, I.: Specification and design of workflow-driven hypertexts. J. Web Eng. 1(2), 163\u2013182 (2003)\n\n6.\n\nJ. R. Buechi. On a decision method in restricted second-order arithmetic. In International Congress on Logic, Methodology, and Philosophy of Science, pp. 1\u201311. Stanford University Press, (1962)\n\n7.\n\nCeri, S., Matera, M., Rizzo, F., Demald\u00e9, V.: Designing data-intensive web applications for content accessibility using web marts. Commun. ACM 50(4), 55\u201361 (2007)CrossRef\n\n8.\n\nColin, S., Mariani, L.: Run-time verification. In: Broy, M., Jonsson, B., Katoen, J.-P., Leucker, M., Pretschner, A. (eds.) Model-Based Testing of Reactive Systems. LNCS, vol. 3472, pp. 525\u2013555. Springer, Heidelberg (2005). doi:10.\u200b1007\/\u200b11498490_\u200b24 CrossRef\n\n9.\n\nEmerson, E.A., Halpern, J.Y.: \"sometimes\" and \"not never\" revisited: on branching versus linear time temporal logic. J. ACM 33(1), 151\u2013178 (1986)MathSciNetCrossRefMATH\n\n10.\n\nGrumberg, O., Kupferman, O., Sheinvald, S.: Variable Automata over Infinite Alphabets. In: Dediu, A.-H., Fernau, H., Mart\u00edn-Vide, C. (eds.) LATA 2010. LNCS, vol. 6031, pp. 561\u2013572. Springer, Heidelberg (2010). doi:10.\u200b1007\/\u200b978-3-642-13089-2_\u200b47 CrossRef\n\n11.\n\nGrumberg, O., Kupferman, O., Sheinvald, S.: Model checking systems and specifications with parameterized atomic propositions. In: Chakraborty, S., Mukund, M. (eds.) ATVA 2012. LNCS, pp. 122\u2013136. Springer, Heidelberg (2012). doi:10.\u200b1007\/\u200b978-3-642-33386-6_\u200b11 CrossRef\n\n12.\n\nGrumberg, O., Kupferman, O., Sheinvald, S.: A game-theoretic approach to simulation of data-parameterized systems. In: Cassez, F., Raskin, J.-F. (eds.) ATVA 2014. LNCS, vol. 8837, pp. 348\u2013363. Springer, Cham (2014). doi:10.\u200b1007\/\u200b978-3-319-11936-6_\u200b25\n\n13.\n\nKaminski, M., Francez, N.: Finite-memory automata. Theor. Comput. Sci. 134(2), 329\u2013363 (1994)MathSciNetCrossRef90242-9)MATH\n\n14.\n\nMiyano, S., Hayashi, T.: Alternating finite automata on omega-words. Theor. Comput. Sci. 32, 321\u2013330 (1984)MathSciNetCrossRef90049-5)MATH\n\n15.\n\nMuller, D., Schupp, P.E.: Alternating automata on infinite objects, determinacy and Rabin's theorem. In: Nivat, M., Perrin, D. (eds.) LITP 1984. LNCS, vol. 192, pp. 99\u2013107. Springer, Heidelberg (1985). doi:10.\u200b1007\/\u200b3-540-15641-0_\u200b27 CrossRef\n\n16.\n\nNeven, F., Schwentick, T., Vianu, V.: Towards regular languages over infinite alphabets. In: Sgall, J., Pultr, A., Kolman, P. (eds.) MFCS 2001. LNCS, vol. 2136, pp. 560\u2013572. Springer, Heidelberg (2001). doi:10.\u200b1007\/\u200b3-540-44683-4_\u200b49 CrossRef\n\n17.\n\nSong, F., Wu, Z.: Extending temporal logics with data variable quantifications. In: Raman, V., Suresh, S.P. (eds.) 34th International Conference on Foundation of Software Technology and Theoretical Computer Science, FSTTCS 15\u201317, 2014, New Delhi, India, vol. 29 of LIPIcs, pp. 253\u2013265. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2014, December 2014\n\n18.\n\nVardi, M.Y.: An automata-theoretic approach to linear temporal logic. In: Moller, F., Birtwistle, G. (eds.) Logics for Concurrency. LNCS, vol. 1043, pp. 238\u2013266. Springer, Heidelberg (1996). doi:10.\u200b1007\/\u200b3-540-60915-6_\u200b6 CrossRef\n\n19.\n\nVardi, M.Y., Wolper, P.: An automata-theoretic approach to automatic program verification (preliminary report). In: Proceedings of the Symposium on Logic in Computer Science (LICS 1986), Cambridge, Massachusetts, USA, June 16\u201318, pp. 332\u2013344. IEEE Computer Society (1986)\n\nFootnotes\n\n1\n\nIn particular, the negation operator is not included.\n\n2\n\nThe semantics of is regarding a specific value. I.e., if then a.d does not hold, but for may hold.\n\n3\n\nComments to the algorithm are given in gray.\n\n4\n\nIn [17] the authors conjecture without proof that the formula does not have an equivalent in PNF. In Lemma 1 we showed does not have an equivalent NVBW, thus it does not have an equivalent -VLTL formula. This is a different formula from , but the conclusion remains the same.\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_2\n\n# Learning from Faults: Mutation Testing in Active Automata Learning\n\nMutation Testing in Active Automata Learning\n\nBernhard K. Aichernig1 and Martin Tappler1\n\n(1)\n\nInstitute of Software Technology, Graz University of Technology, Graz, Austria\n\nBernhard K. Aichernig\n\nEmail: aichernig@ist.tugraz.at\n\nMartin Tappler (Corresponding author)\n\nEmail: martin.tappler@ist.tugraz.at\n\nAbstract\n\nSystem verification is often hindered by the absence of formal models. Peled et al. proposed black-box checking as a solution to this problem. This technique applies active automata learning to infer models of systems with unknown internal structure.\n\nThis kind of learning relies on conformance testing to determine whether a learned model actually represents the considered system. Since conformance testing may require the execution of a large number of tests, it is considered the main bottleneck in automata learning.\n\nIn this paper, we describe a randomised conformance testing approach which we extend with fault-based test selection. To show its effectiveness we apply the approach in learning experiments and compare its performance to a well-established testing technique, the partial W-method. This evaluation demonstrates that our approach significantly reduces the cost of learning \u2013 in one experiment by a factor of more than twenty.\n\nKeywords\n\nConformance testingMutation testingFSM-based testingActive automata learningMinimally adequate teacher framework\n\n## 1 Introduction\n\nSince Peled et al. [21] have shown that active automata learning can provide models of black-box systems to enable formal verification, this kind of learning has turned into an active area of research in formal methods. Active learning of automata in the minimally adequate teacher (MAT) framework, as introduced by Angluin [2], assumes the existence of a teacher. In the non-stochastic setting, this teacher must be able to answer two types of queries, membership and equivalence queries. The former corresponds to a single test of the system under learning (SUL) to check whether a sequence of actions can be executed or to determine the outputs produced in response to a sequence of inputs. Equivalence queries on the other hand correspond to the question whether a hypothesis model produced by the learner represents the SUL. The teacher either answers affirmatively or with a counterexample showing non-equivalence between the SUL and the hypothesis.\n\nThe first type of query is simple to implement for learning black-box systems. It generally suffices to reset the system, execute a single test and record observations. Equivalence queries however, are more difficult to implement. Peled et al. [21], as one of the first to combine learning and formal verification, proposed to implement these queries via conformance testing. In particular, they suggested to use the conformance testing algorithm by Vasilevskii [30] and Chow [6].\n\nThis method is also referred to as W-method and there exist optimisations of it, like the partial W-method [11] or an approach by Lee and Yannankakis [16], but all have the same worst-case complexity [4]. All three methods share two issues. They require a fixed upper bound on the number of states of the black-box system which is generally unknown. Additionally, the size of the constructed test suite is exponential in this bound. Therefore, implementing the equivalence oracle can be considered \"the true bottleneck of automata learning\" [4].\n\nIn practice, there is limited time for testing and thereby also for learning. The ZULU challenge [7] addressed this issue by limiting the number of tests to be executed [12]. More concretely, competitors learned finite automata from a limited number of membership queries without explicit equivalence queries. Equivalence queries thus had to be approximated through clever selection of membership queries. This led to a different view of the problem: rather than \"trying to prove equivalence\", the new target was \"finding counterexamples fast\" [12].\n\nIn this paper we propose an implementation of equivalence queries based on mutation testing [15], more specifically on model-based mutation testing [1]. This approach follows the spirit of the ZULU challenge by trying to minimise the number of tests for executing equivalence queries. We use a combination of random testing, to achieve high variability of tests, and mutation analysis, to address coverage appropriately. To illustrate the effectiveness of our approach, which has been implemented based on the LearnLib library [14], we will mainly compare it to the partial W-method [11] and show that the cost of testing can be significantly reduced while still learning correctly. In other words, our method reliably finds counterexamples with less testing. In addition to that, we also compare it to purely random testing and to an effective implementation of a randomised conformance testing method described by Smeenk et al. [26].\n\nWe target systems which can be modelled with a moderately large number of states, i.e. with up to fifty states. This restriction is necessary, because mutation analysis is generally a computationally intensive task for large systems. Nevertheless, there exists a wealth of non-trivial systems, such as implementations of communication protocols, which can be learned nonetheless. The rest of this paper is structured as follows. Section 2 discusses related work and Sect. 3 introduces preliminaries. The main parts, the test-suite generation approach and its evaluation, are presented in Sects. 4 and 5. We conclude the paper in Sect. 6. The implementation used in our evaluation is available at [27].\n\n## 2 Related Work\n\nWe address conformance testing in active automata learning. Hence, there is a relationship to the W-method [6, 30] and the partial W-method [11], two conformance testing methods implemented in LearnLib [14]. However, we handle fault coverage differently. By generating tests to achieve transition coverage, we also test for \"output\" faults, but do not check for \"transfer\" faults. Instead we present a fault model directly related to the specifics of learning in Sect. 4.3.\n\nWe combine model-based mutation testing and random testing, which we discussed in previous work [1]. Generally, random testing is able to detect a large number of mutants fast, such that only a few subtle mutants need to be checked with directed search techniques. While we do not aim at detecting all mutants, i.e. we do not apply directed search, this property provides a certain level of confidence. By analysing mutation coverage of random tests, we can guarantee that detected mutations do not affect the learned model.\n\nHowar et al. noted that it is necessary to find counterexamples with few tests for automata learning to be practically applicable [12]. We generally follow this approach. Furthermore, one of the heuristics described in [12] is based on Rivest and Schapire's counterexample processing [23], similar to the fault model discussed in Sect. 4.3. More recent work in this area has been performed by Smeenk et al. [26], who implemented a partly randomised conformance testing technique. In order to keep the number of tests small, they applied a technique to determine an adaptive distinguishing sequence described by Lee and Yannakakis [17]. With this technique and domain-specific knowledge, they succeeded in learning a large model of industrial control software. The same technique has also been used to learn models of Transmission Control Protocol (TCP) implementations [10].\n\n## 3 Preliminaries\n\n### 3.1 Mealy Machines\n\nWe use Mealy machines because they are well-suited to model reactive systems and they have successfully been used in contexts combining learning and some form of verification [10, 18, 24, 28]. In addition to that, the Java-library LearnLib [14] provides efficient algorithms for learning Mealy machines.\n\nBasically, Mealy machines are finite state automata with inputs and outputs. The execution of such a Mealy machine starts in an initial state and by executing inputs it changes its state. Additionally, exactly one output is produced in response to each input. Formally, Mealy machines can be defined as follows.\n\nDefinition 1\n\nA Mealy machine is a 6-tuple where\n\n * Q is a finite set of states\n\n * is the initial state,\n\n * I\/O is a finite set of input\/output symbols,\n\n * is the state transition function, and\n\n * is the output function.\n\nWe require Mealy machines to be input-enabled and deterministic. The former demands that outputs and successor states must be defined for all inputs and all states, i.e. and must be surjective. A Mealy machine is deterministic if it defines at most one output and successor state for every pair of input and state, i.e. and must be functions in the mathematical sense.\n\nNotational Conventions. Let be two sequences of input\/output symbols, i.e. or , then denotes the concatenation of these sequences. The empty sequence is represented by . The length of a sequence is given by |s|. We implicitly lift single elements to sequences, thus for we have with . As a result, the concatenation is also defined.\n\nWe extend and to sequences of inputs in the standard way. Let be an input sequence and be a state, then is the state reached by executing s starting in state q. For and , the output function returns the outputs produced in response to s executed in state q. Furthermore, let . For state q the set contains the access sequences of q, i.e. the sequences leading to q. Note that other authors define a unique access sequence for each q [13].\n\nFinally we need a basis for determining whether two Mealy machines are equivalent. Equivalence is usually defined with respect to outputs [10], i.e. two deterministic Mealy machines are equivalent if they produce the same outputs for all input sequences. A Mealy machine is equivalent to another Mealy machine iff . A counterexample to equivalence is thus an such that .\n\n### 3.2 Active Automata Learning\n\nWe consider learning in the minimally adequate teacher (MAT) framework [2]. Algorithms in this framework infer models of black-box systems, also referred to as SULs, through interaction with a so-called teacher.\n\nMinimally Adequate Teacher Framework. The interaction is carried out via two types of queries posed by the learning algorithm and answered by a MAT. These two types of queries are usually called membership queries and equivalence queries. In order to understand these basic notions of queries consider that Angluin's original algorithm is used to learn a deterministic finite automaton (DFA) representing a regular language known to the teacher [2]. Given some alphabet, the algorithm repeatedly selects strings and asks membership queries to check whether these strings are in the language to be learned. The teacher may answer either yes or no.\n\nAfter some queries the learning algorithm uses the knowledge gained so far and forms a hypothesis, i.e. a DFA consistent with the obtained information which should represent the regular language under consideration. The algorithm presents the hypothesis to the teacher and issues an equivalence query in order to check whether the language to be learned is equivalent to the language represented by the hypothesis automaton. The response to this kind of query is either yes signalling that the correct DFA has been learned or a counterexample to equivalence. Such a counterexample is a witness showing that the learned model is not yet correct, i.e. it is a word from the symmetric difference of the language under learning and the language accepted by the hypothesis.\n\nAfter processing a counterexample, learning algorithms start a new round of learning. The new round again involves membership queries and a concluding equivalence query. This general mode of operation is used by basically all algorithms in the MAT framework with some adaptations. These adaptations may for instance enable the learning of Mealy machines as described in the following.\n\nLearning Mealy Machines. Margaria et al. [18] and Niese [20] were one of the first to infer Mealy-machine models of reactive systems using an -based algorithm. Another -based learning algorithm for Mealy machines has been presented by Shahbaz and Groz [25]. They reuse the structure of , but substitute membership queries for output queries. Instead of checking whether a string is accepted, they provide inputs and the teacher responds with the corresponding outputs. For a more practical discussion, consider the instantiation of a teacher. Usually we want to learn the behaviour of a black-box SUL of which we only know the interface. Hence, output queries are conceptually simple: provide inputs to the SUL and observe produced outputs. However, there is a slight difficulty hidden. Shahbaz and Groz [25] assume that outputs are produced in response to inputs executed from the initial state. Consequently, we need to have some means to reset a system. As discussed in the introduction, we generally cannot check for equivalence. It is thus necessary to approximate equivalence queries, e.g., via conformance testing as implemented in LearnLib [14]. To summarise, a learning algorithm for Mealy machines relies on three operations:\n\nreset:\n\nresets the SUL\n\noutput query:\n\nperforms a single test executing inputs and recording outputs\n\nequivalence query:\n\nconformance testing between SUL and hypothesis.\n\nAs shown in Fig. 1, the teacher is usually a component communicating with the SUL. An equivalence query results in a positive answer if all conformance tests pass, i.e. the SUL produces the same outputs as the hypothesis. If there is a failing test, the corresponding input sequence is returned as counterexample.\n\nFig. 1.\n\nThe interaction between SUL, teacher and learning algorithm (based on [26]).\n\nDue to the incompleteness of testing, learned models may be incorrect. If, e.g., the W-method [6, 30] is used for testing, the learned model may be incorrect if assumptions placed on the maximum number of states of the SUL do not hold.\n\n## 4 Test-Suite Generation\n\nWe had shown previously \"that by adding mutation testing to a random testing strategy approximately the same number of bugs were found with fewer test cases\" [1]. Motivated by this, we developed a simple and yet effective test-suite generation technique. The test-suite generation has two parts, (1) generating a large set of tests T and (2) selecting a subset to be run on the SUL.\n\n### 4.1 Test-Case Generation\n\nThe goal of the test-case generation is to achieve high coverage of the model under consideration combined with variability through random testing. The test-case generation may start with a random walk through the model and then iterates two operations. First, a transition of the model is chosen randomly and a path leading to it is executed. If the transition is not reachable, another target transition is chosen. Second, another short random walk is executed. These two operations are repeated until a stopping criterion is reached.\n\nStopping. Test-case generation stops as soon as the test has a length greater than a maximum number of steps . Alternatively, it may also stop dependent on probabilities and . The first one controls the probability of continuing in case a selected transition is not reachable while the second one controls the probability of stopping prematurely.\n\nRandom Functions. The generation procedure uses three random functions. A function defined for by and . The function selects a single sample from a set according to a uniform distribution, i.e. . The function takes a set S and a bound and creates a sequence of length consisting of elements from S chosen via , whereby l is chosen uniformly from [0..b].\n\nWe assume a given Mealy machine in the following. Algorithm 1 realises the test-case generation based on . As additional inputs, it takes stopping parameters and , an upper bound on the number of steps executed between visiting two transitions. The function returns a path leading from the current state to another state. Currently, this is implemented via breadth-first exploration but other approaches are possible as long as they satisfy iff and such that , where denotes that no such path exists.\n\n### 4.2 Test-Case Selection\n\nTo account for variations in the quality of randomly generated tests, not all generated tests are executed on the SUL, but rather a selected subset. This selection is based on coverage, e.g. transition coverage.\n\nFor the following discussion, assume that a set of tests of fixed size should be selected from a previously generated set T to cover elements from a set C. In a simple case, C can be instantiated to the set of all transitions, i.e. as uniquely identifies a transition because of determinism. The selection comprises the following three steps:\n\n 1. 1.\n\nThe coverage of single test cases is analysed, i.e. each test case is associated with a set covered by t.\n\n 2. 2.\n\nThe actual selection has the objective of optimising the overall coverage of C. We greedily select test cases until either the upper bound is reached, all elements in C are covered, or we do not improve coverage. More formally:\n\n 3. 3.\n\nIf tests have not yet been selected, then further tests are selected which individually achieve high coverage. For that are sorted in descending size of and the first tests are selected.1\n\n### 4.3 Mutation-Based Selection\n\nA particularly interesting selection criterion is mutation-based selection. The choice of this criterion is motivated by the fact that model-based mutation testing can effectively be combined with random testing [1]. Generally, in this fault-based test-case generation technique, known faults are injected into a model creating so-called mutants. Test cases are then generated which distinguish these mutants from the original model and thereby test for the corresponding faults.\n\nThus, in our case we alter the hypothesis , creating a set of mutants . The objective is now to distinguish mutants from the hypothesis, i.e. we want tests that show that mutants are observably different from the hypothesis. Hence, we can set and .\n\nType of Mutation. The type of faults injected into a model is governed by mutation operators, which basically map a model to a set of mutated models (mutants). There is a variety of operators for programs [15] and also finite-state machines [9]. As an example, consider a mutation operator change output which changes the output of each transition and thereby creates one mutant per transition. Since there is exactly one mutant that can be detected by executing each transition, selection based on such mutants is equivalent to selection with respect to transition coverage. Hence, mutation can simulate other coverage criteria. In fact, for our evaluation we implemented transition coverage via mutation.\n\nBlindly using all available mutation operators may not be effective. Fault-based testing should rather target faults likely to occur in the considered application domain [22]. Thus, we developed a family of mutation operators, called split-state operators, directly addressing active automata learning.\n\nSplit-State Operator Family. There are different ways to process counterexamples in the MAT framework, such as by adding all prefixes to the used data structures [2]. An alternative technique due to Rivest and Schapire [23] takes the \"distinguishing power\" of a counterexample into account. The basic idea is to decompose a counterexample into a prefix u, a single action a and a suffix v such that v is able to distinguish access sequences in the current hypothesis. In other words, the distinguishing sequence v shows that two access sequences, which were hypothesised to lead to the same state, actually lead to observably nonequivalent states. This knowledge is then integrated into the data structures.\n\nSince it is an efficient form of processing counterexamples, adaptations of it have been used in other learning algorithms such as the TTT algorithm [13]. This algorithm makes the effect of this decomposition explicit. It splits a state q reached by an access sequence derived from u and a. The splitting further involves (1) adding a new state reached by another access sequence derived from u and a (which originally led to q) and (2) adding sequences to the internal data structures which can distinguish q and .\n\nThe development of the split-state family of mutation operators is motivated by the principle underlying the TTT and related algorithms. Basically, we collect pairs of access sequences of a state q, add a new state and redirect to . Furthermore, we add transitions such that behaves the same as q except for a distinguishing sequence v. Example 1 illustrates this mutation operator.\n\nExample 1\n\n(Split State Mutation). A hypothesis produced by a learning algorithm may be of the form shown in Fig. 2a. Note that not all edges are shown in the figure and dashed edges represent sequences of transitions. The access sequences of thus include and . A possible corresponding black-box SUL is shown in Fig. 2b. In this case, the hypothesis incorrectly assumes that and lead to the same state. We can model a transformation from the hypothesis to the SUL by splitting and and changing the output produced in the new state as indicated in Fig. 2b. State has to be split as well to introduce a distinguishing sequence of length 2 while still maintaining determinism. A test case covering the mutation is .\n\nFig. 2.\n\nDemonstration of split state.\n\nA mutant models a SUL containing two different states q and which are assumed to be equivalent by the hypothesis. By executing a test covering a mutant , we either find an actual counterexample to equivalence between SUL and hypothesis or prove that the SUL does not implement . Hence, it is possible to guarantee that the SUL possesses certain properties. This is similar to model-based mutation testing in general, where the absence of certain faults, those modelled by mutation operators, can be guaranteed [1].\n\nSplit state is a family of mutation operators as the effectiveness of the approach is influenced by several parameters, such that the instantiation of parameters can be considered a unique operator. The parameters are:\n\nMax. number of sequences :\n\nan upper bound on the number of mutated access sequences leading to a single state.\n\nLength of distinguishing sequences k :\n\nfor each splitting operation we create mutants, one for each sequence of length k. Note that this requires the creation of k new states. Coverage of all mutants generated with length k implies coverage of all mutants with length .\n\nSplit at prefix flag:\n\nredirecting a sequence from q to usually amounts to changing to . However, if the other access sequence in the pair is with , this is not possible because it would introduce non-determinism. This flag specifies whether the access sequence pair is ignored or whether further states are added to enable redirecting . We generally set it to .\n\nEfficiency Considerations. While test-case generation can efficiently be implemented, mutation-based selection is computationally intensive. It is necessary to check which of the mutants is covered by each test case. Since the number of mutants may be as large as , this may become a bottleneck.\n\nConsequently, cost reduction techniques for mutation [15] need to be considered. We reduce execution cost by avoiding the explicit creation of mutants. Essentially only the difference to the hypothesis is stored and executed. Since this does not solve the problem completely, mutant reduction techniques need to be considered as well. Jia and Harman identify four techniques to reduce the number of mutants [15]. We use two of them: Selective Mutation applies only a subset of effective mutation operators. In our case, we apply only one mutation operator. With Mutant Sampling only a subset of mutants is randomly selected and analysed while the rest is discarded.\n\nIn essence, the choice of the bound on the number of access sequences, the number of selected tests, the sample size, etc. needs to take the cost of executing tests on the SUL into account. Thus, it is tradeoff between the cost of mutation analysis and testing, as a more extensive analysis can be assumed to produce better tests and thereby require fewer test executions. Additionally, the number of mutants may be reduced as follows.\n\nMutation analysis of executed tests:\n\nwe keep track of all tests executed on the SUL. Prior to test-case selection, these test cases are examined to determine which mutants are covered by the tests. These mutants can be discarded because we know for all executed tests t and covered mutants that and which implies , i.e. the mutants are not implemented by the SUL. This extension prevents unnecessary coverage of already covered mutants and reduces the number of mutants to be analysed. This takes the iterative nature of learning into account as suggested in [12] in the context of equivalence testing.\n\nAdapting to learning algorithm:\n\nby considering the specifics of a learning algorithm, the number of access sequences could be reduced. For instance in discrimination-tree-based approaches [13], it would be possible to create mutants only for access sequences S stored in the discrimination tree and for their extensions . However, this has not been implemented yet.\n\n## 5 Evaluation\n\nIn the following, we evaluate two variations of our new test-suite generation approach. We will refer to test-case generation with transition-coverage-based selection as transition coverage. The combination with mutation-based selection will be referred to as split state. We compare these two techniques to alternatives in the literature: the partial W-method [11] and the random version of the approach discussed in [26] available at [19]. We refer to the latter as random L & Y. Note that this differs slightly from [10, 26] in which also non-randomised test, i.e. complete up to some bound, were generated.\n\nWe evaluate the different conformance testing methods based on two case studies from the domain of communication protocols. The examined systems are given in Table 1. This table includes the number of states and inputs of the true Mealy machine model and a short description of each system. Due to space limitations, we refer to other publications for in-depth descriptions.\n\nTable 1.\n\nA short description of examined systems.\n\nSystem | # States | # Inputs | Short description\n\n---|---|---|---\n\nTCP server (Ubuntu) | 57 | 12 | Models of TCP server\/client implementations from three different vendors have been learned and analysed by Fiter\u0103u-Bro\u015ftean et al. [10]. We simulated the server model of Ubuntu available at [29].\n\nMQTT broker (emqtt [8]) | 18 | 9 | Model of an MQTT [3] broker interacting with two clients. We discussed the learning setup in [28].\n\n### 5.1 Measurement Setup\n\nTo objectively evaluate randomised conformance testing, we investigate the probability of learning the correct model with a limited number of interactions with the SUL, i.e. only a limited number of tests may be executed. We generally base the cost of learning on the number of executed inputs rather than on the number of tests\/resets. This decision follows from the observation that resets in the target application area, protocols, can be done fast (simply start a new session), whereas timeouts and quiescent behaviour cause long test durations [24, 28]. Note that we take previously learned models as SULs. Their simulation ensures fast test execution which enables a thorough evaluation.\n\nTo estimate the probability of learning the correct models, we performed each learning run 50 times and calculated the relative frequency of learning the correct model. In the following, we refer to such a repetition as a single experiment. Note that given the expected number of states of each system, we can efficiently determine whether the correct model has been learned, since learned models are minimal with respect to the number of states [2].\n\nIn order to find a lower limit on the number of tests required by each method to work reliably, we bounded the number of tests executed for each equivalence query and gradually increased this bound. Once all learning runs of an experiment succeeded we stopped this procedure. For learning with the partial W-method [11] we gradually increased the depth parameter implemented in LearnLib [14] until we learned the correct model. Since this method does not use randomisation, we did not run repeated experiments and report the measurement results for the lowest possible depth-parameter value.\n\nAs all algorithms can be run on standard notebooks, we will only exemplarily comment on runtime. For a fair comparison, we evaluated all equivalence-testing approaches in combination with the same learning algorithm, i.e. with Rivest and Schapire's counterexample-handling implemented by LearnLib 0.12 [14].\n\nTCP \u2013 Ubuntu. The number of tests and steps required to reliably learn the Ubuntu TCP-server are given in Table 2. In order to perform these experiments, we generated 100,000 tests and selected the number of tests given in the first line of Table 2 to perform each equivalence query. For the partial W-method this line includes the depth-parameter value. Note that the mean values of tests\/steps represent the numbers summed over all rounds of learning (but averaged over 50 runs), while the bound on the number of tests applies to only a single round. The test-case generation with Algorithm 1 has been performed with parameters , , , and . The chosen parameters for split state selection are (max. access sequences per state) and (length of distinguishing sequence). Additionally, we performed mutant sampling by first reducing the number of mutants to one quarter of the original mutants and then to 10,000 if necessary.\n\nTable 2.\n\nPerformance measurements for learning an Ubuntu TCP-server-model. | Transition coverage | Split state | Partial W-method | Random L & Y\n\n---|---|---|---|---\n\nBound on # equivalence tests\/depth parameter | 10,000 | 4,000 | 2 | 46,000\n\nMean # tests [equivalence] | 12,498 | 4,786 | 793,939 | 71,454\n\nMean # steps [equivalence] | 239,059 | 138,840 | 7,958,026 | 823,623\n\nMean # tests [membership] | 9,633 | 10,017 | 13,962 | 11,445\n\nMean # steps [membership] | 127,684 | 129,214 | 147,166 | 136,827\n\nWe see in the table that the average number of tests and steps required for membership queries is roughly the same for all techniques. This is what we expected as the same learning algorithm is used in all cases, but the numbers shall demonstrate that techniques requiring less tests do not trade membership for equivalence tests. With this out of the way, we can concentrate on equivalence testing. We see that split state pays off in this experiment with transition coverage requiring 1.7 times as many steps. The average cost of test selection is 104 seconds for split state and 4 seconds for transition coverage. However, considering the large savings in actual test execution, split state performs better.\n\nWe also evaluated random L & Y with a middle sequence of expected length 4 (similar to [10]). For this setup, random L & Y requires significantly more steps and tests than both alternatives. There may be more suitable parameters, however, which would improve the performance of random L & Y. Nevertheless, the model structure of Ubuntu's TCP-server seems to be beneficial for our approach.\n\nAll randomised approaches outperformed the partial W-method. In particular split state is able to reduce the number of test steps by a factor of 57. Taking the membership queries into account, the overall cost of learning is reduced by a factor of about 22. The relative gap between tests, a reduction by a factor of 166, is even larger. This is an advantage of our approach as we can flexibly control test length and thereby account for systems with expensive resets. Purely random testing is not a viable choice in this case. An experiment with 1,000,000 tests per equivalence query succeeded in learning correctly in only 4 of 50 runs.\n\nMQTT \u2013 emqtt. The number of tests and steps required to reliably learn models of the emqtt broker are given in Table 3. In order to perform these experiments, we used largely the same setup and the same sampling strategy as for the TCP experiments, but generated only 10,000 tests as a basis for selection. Furthermore, we set , , , , and .\n\nIn Table 3, we see a similarly large improvement with respect to the partial W-method. The partial W-method requires about 52 times as many test steps as split state. Other than that, we see that the improvement of split state over transition coverage is not as drastic as for the Ubuntu TCP-server and testing with random L & Y also performs well. Figure 3 depicts the learning performance of the three different approaches and undirected random testing. It shows the dependency between the average number of equivalence-test steps and the estimated probability of learning the correct model. The graph shows that significantly more testing is required by random testing.\n\nTable 3.\n\nPerformance measurements for learning an emqtt-broker model. | Transition coverage | Split state | Partial W-method | Random L & Y\n\n---|---|---|---|---\n\nBound on # equivalence tests\/depth parameter | 275 | 125 | 2 | 1100\n\nMean # tests [equivalence] | 345 | 182 | 72,308 | 1,679\n\nMean # steps [equivalence] | 13,044 | 7,755 | 487,013 | 11,966\n\nMean # tests [membership] | 1,592 | 1,623 | 1,808 | 1,683\n\nMean # steps [membership] | 12,776 | 13,160 | 11,981 | 12,005\n\nFig. 3.\n\nAverage number of equivalence-test steps required to reliably learn the correct emqtt-broker model.\n\nDiscussion and Threats to Validity. The results shown above suggest that transition coverage and especially split state perform well. However, the performance depends on the system structure. There are systems for which transition coverage performs slightly better with regard to the required number of steps than split state, as the latter favours longer tests. In these cases, split state may simply add no value because transition coverage already performs well.\n\nFor the TCP-server case study, we report effectiveness superior to that of random L & Y. The performance of our technique depends on the concrete instantiation of more parameters than the performance of random L & Y. Finding suitable parameters is thus more difficult for our approach and relative performance gains may decrease for unsuitable choices. Additionally, random L & Y generates tests much more efficiently than split state. Split-state mutation analysis is only feasible for moderate-sized models, whereas random L & Y has successfully been applied for learning of a system with more than 3,000 states [26]. Mutation-based test-case selection would be hindered by the large number of mutants and tests forming the basis for selection \u2013 to our experience the number of tests should be increased with model size. More concretely, applying the technique to systems with significantly more than 100 states would likely not pay off. Aggressive mutant sampling would be necessary, rendering the mutation-based selection less effective. Without sampling, the decreased testing duration would not compensate for the cost of mutation analysis.\n\n## 6 Conclusion\n\nWe presented a simple test-case generation technique which accompanied with appropriate test-case selection yields effective test suites. In particular, we further motivated and described a fault-based test selection approach with a fault model tailored towards learning. First experiments showed it is possible to reliably learn system models with a significantly lower number of test cases as compared to complete conformance testing with, e.g., the partial W-method [11].\n\nA potential drawback of our approach, especially of split-state-based test selection, is the large number of parameters, which according to our experience heavily influence learning performance. Additionally, mutation-based selection applies mutant sampling, thus it is of interest to determine the influence of sampling and whether corresponding observations made for program mutation [15] also hold for FSM mutation. Nevertheless, alternative mutant reduction techniques are not entirely exhausted. As indicated in Sect. 4.3, information stored by learning algorithms could help to reduce the number of mutants.\n\nWe conclude that mutation-based test-suite generation is a promising technique for conformance testing in active automata learning. Despite initial success, we believe that it could show its full potential for testing more expressive types of models like extended finite state machines [5]. This would enable the application of more comprehensive fault models. Finally, alternatives to the simple greedy test-selection may also provide benefits.\n\nAcknowledgment\n\nThis work was supported by the TU Graz LEAD project \"Dependable Internet of Things in Adverse Environments\". We would also like to thank the developers of LearnLib and of the test-case generator available at [19].\n\nReferences\n\n1.\n\nAichernig, B.K., Brandl, H., J\u00f6bstl, E., Krenn, W., Schlick, R., Tiran, S.: Killing strategies for model-based mutation testing. Softw. Test. Verif. Reliab. 25(8), 716\u2013748 (2015)CrossRef\n\n2.\n\nAngluin, D.: Learning regular sets from queries and counterexamples. Inf. Comput. 75(2), 87\u2013106 (1987)MathSciNetCrossRef90052-6)MATH\n\n3.\n\nBanks, A., Gupta, R. (eds.): MQTT Version 3.1.1. OASIS Standard, October 2014. Latest version: http:\/\/\u200bdocs.\u200boasis-open.\u200borg\/\u200bmqtt\/\u200bmqtt\/\u200bv3.\u200b1.\u200b1\/\u200bos\/\u200bmqtt-v3.\u200b1.\u200b1-os.\u200bhtml\n\n4.\n\nBerg, T., Grinchtein, O., Jonsson, B., Leucker, M., Raffelt, H., Steffen, B.: On the correspondence between conformance testing and regular inference. In: Cerioli, M. (ed.) FASE 2005. LNCS, vol. 3442, pp. 175\u2013189. Springer, Heidelberg (2005). doi:10.\u200b1007\/\u200b978-3-540-31984-9_\u200b14 CrossRef\n\n5.\n\nCassel, S., Howar, F., Jonsson, B., Steffen, B.: Active learning for extended finite state machines. Formal Asp. Comput. 28(2), 233\u2013263 (2016)MathSciNetCrossRefMATH\n\n6.\n\nChow, T.S.: Testing software design modeled by finite-state machines. IEEE Trans. Softw. Eng. 4(3), 178\u2013187 (1978)CrossRefMATH\n\n7.\n\nCombe, D., de la Higuera, C., Janodet, J.-C.: Zulu: an interactive learning competition. In: Yli-Jyr\u00e4, A., Kornai, A., Sakarovitch, J., Watson, B. (eds.) FSMNLP 2009. LNCS (LNAI), vol. 6062, pp. 139\u2013146. Springer, Heidelberg (2010). doi:10.\u200b1007\/\u200b978-3-642-14684-8_\u200b15 CrossRef\n\n8.\n\nemqtt. http:\/\/\u200bemqtt.\u200bio\/\u200b. Accessed 29 Nov 2016\n\n9.\n\nFabbri, S., Delamaro, M.E., Maldonado, J.C., Masiero, P.C.: Mutation analysis testing for finite state machines. In: ISSRE 1994, pp. 220\u2013229. IEEE (1994)\n\n10.\n\nFiter\u0103u-Bro\u015ftean, P., Janssen, R., Vaandrager, F.: Combining model learning and model checking to analyze TCP implementations. In: Chaudhuri, S., Farzan, A. (eds.) CAV 2016. LNCS, vol. 9780, pp. 454\u2013471. Springer, Cham (2016). doi:10.\u200b1007\/\u200b978-3-319-41540-6_\u200b25\n\n11.\n\nFujiwara, S., von Bochmann, G., Khendek, F., Amalou, M., Ghedamsi, A.: Test selection based on finite state models. IEEE Trans. Softw. Eng. 17(6), 591\u2013603 (1991)CrossRef\n\n12.\n\nHowar, F., Steffen, B., Merten, M.: From ZULU to RERS - lessons learned in the ZULU challenge. In: Margaria, T., Steffen, B. (eds.) ISoLA 2010. LNCS, vol. 6415, pp. 687\u2013704. Springer, Heidelberg (2010). doi:10.\u200b1007\/\u200b978-3-642-16558-0_\u200b55 CrossRef\n\n13.\n\nIsberner, M., Howar, F., Steffen, B.: The TTT algorithm: a redundancy-free approach to active automata learning. In: Bonakdarpour, B., Smolka, S.A. (eds.) RV 2014. LNCS, vol. 8734, pp. 307\u2013322. Springer, Cham (2014). doi:10.\u200b1007\/\u200b978-3-319-11164-3_\u200b26\n\n14.\n\nIsberner, M., Howar, F., Steffen, B.: The open-source LearnLib. In: Kroening, D., P\u0103s\u0103reanu, C.S. (eds.) CAV 2015. LNCS, vol. 9206, pp. 487\u2013495. Springer, Cham (2015). doi:10.\u200b1007\/\u200b978-3-319-21690-4_\u200b32 CrossRef\n\n15.\n\nJia, Y., Harman, M.: An analysis and survey of the development of mutation testing. IEEE Trans. Softw. Eng. 37(5), 649\u2013678 (2011)CrossRef\n\n16.\n\nLee, D., Yannakakis, M.: Principles and methods of testing finite state machines - a survey. Proc. IEEE 84(8), 1090\u20131123 (1996)CrossRef\n\n17.\n\nLee, D., Yannakakis, M.: Testing finite-state machines: state identification and verification. IEEE Trans. Comput. 43(3), 306\u2013320 (1994)MathSciNetCrossRef\n\n18.\n\nMargaria, T., Niese, O., Raffelt, H., Steffen, B.: Efficient test-based model generation for legacy reactive systems. In: Ninth IEEE International High-Level Design Validation and Test Workshop 2004, pp. 95\u2013100. IEEE Computer Society (2004)\n\n19.\n\nMoerman, J.: Yannakakis - test-case generator. https:\/\/\u200bgitlab.\u200bscience.\u200bru.\u200bnl\/\u200bmoerman\/\u200bYannakakis. Accessed 30 Nov 2016\n\n20.\n\nNiese, O.: An integrated approach to testing complex systems. Ph.D. thesis, Dortmund University of Technology (2003)\n\n21.\n\nPeled, D., Vardi, M.Y., Yannakakis, M.: Black box checking. In: Wu, J., Chanson, S.T., Gao, Q. (eds.) FORTE XII\/PSTV XIX 1999. IFIP AICT, vol. 28, pp. 225\u2013240. Springer, Boston (1999). doi:10.\u200b1007\/\u200b978-0-387-35578-8_\u200b13 CrossRef\n\n22.\n\nPretschner, A.: Defect-based testing. In: Dependable Software Systems Engineering, NATO Science for Peace and Security Series, D: Information and Communication Security, vol. 40, pp. 224\u2013245. IOS Press (2015)\n\n23.\n\nRivest, R.L., Schapire, R.E.: Inference of finite automata using homing sequences. Inf. Comput. 103(2), 299\u2013347 (1993)MathSciNetCrossRefMATH\n\n24.\n\nde Ruiter, J., Poll, E.: Protocol state fuzzing of TLS implementations. In: USENIX Security 15, pp. 193\u2013206. USENIX Association (2015)\n\n25.\n\nShahbaz, M., Groz, R.: Inferring Mealy machines. In: Cavalcanti, A., Dams, D.R. (eds.) FM 2009. LNCS, vol. 5850, pp. 207\u2013222. Springer, Heidelberg (2009). doi:10.\u200b1007\/\u200b978-3-642-05089-3_\u200b14 CrossRef\n\n26.\n\nSmeenk, W., Moerman, J., Vaandrager, F., Jansen, D.N.: Applying automata learning to embedded control software. In: Butler, M., Conchon, S., Za\u00efdi, F. (eds.) ICFEM 2015. LNCS, vol. 9407, pp. 67\u201383. Springer, Cham (2015). doi:10.\u200b1007\/\u200b978-3-319-25423-4_\u200b5 CrossRef\n\n27.\n\nTappler, M.: mut-learn - randomised mutation-based equivalence testing. https:\/\/\u200bgithub.\u200bcom\/\u200bmtappler\/\u200bmut-learn. Accessed 07 Dec 2016\n\n28.\n\nTappler, M., Aichernig, B.K., Bloem, R.: Model-based testing IoT communication via active automata learning. In: ICST 2017. IEEE Computer Society (2017)\n\n29.\n\nTCP models. https:\/\/\u200bgitlab.\u200bscience.\u200bru.\u200bnl\/\u200bpfiteraubrostean\u200b\/\u200btcp-learner\/\u200btree\/\u200bcav-aec\/\u200bmodels. Accessed 14 Nov 2016\n\n30.\n\nVasilevskii, M.P.: Failure diagnosis of automata. Cybernetics 9(4), 653\u2013665 (1973)MathSciNetCrossRef\n\nFootnotes\n\n1\n\nNote that more sophisticated test suite reduction\/prioritisation strategies could be used. However, this is beyond the scope of this paper.\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_3\n\n# Parametric Model Checking Timed Automata Under Non-Zenoness Assumption\n\n\u00c9tienne Andr\u00e91, Hoang Gia Nguyen1 , Laure Petrucci1 and Jun Sun2\n\n(1)\n\nLIPN, CNRS UMR 7030, Universit\u00e9 Paris 13, Sorbonne Paris Cit\u00e9, Villetaneuse, France\n\n(2)\n\nISTD, Singapore University of Technology and Design, Singapore, Singapore\n\nHoang Gia Nguyen\n\nEmail: hoanggia.nguyen@lipn.univ-paris13.fr\n\nAbstract\n\nReal-time systems often involve hard timing constraints and concurrency, and are notoriously hard to design or verify. Given a model of a real-time system and a property, parametric model-checking aims at synthesizing timing valuations such that the model satisfies the property. However, the counter-example returned by such a procedure may be Zeno (an infinite number of discrete actions occurring in a finite time), which is unrealistic. We show here that synthesizing parameter valuations such that at least one counterexample run is non-Zeno is undecidable for parametric timed automata (PTAs). Still, we propose a semi-algorithm based on a transformation of PTAs into Clock Upper Bound PTAs to derive all valuations whenever it terminates, and some of them otherwise.\n\nThis work is partially supported by the ANR national research program PACS (ANR-14-CE28-0002).\n\n## 1 Introduction\n\nTimed automata (TAs) [1] are a popular formalism for real-time systems modeling and verification, providing explicit manipulation of clock variables. Real-time behavior is captured by clock constraints on system transitions, setting or resetting clocks, etc. TAs have been studied in various settings (such as planning [19]) and benefit from powerful tools such as Uppaal [21] or PAT [24].\n\nModel checking TAs consists of checking whether there exists an accepting cycle (i. e. a cycle that visits infinitely often a given set of locations) in the automaton made of the product of the TA modeling the system with the TA representing a violation of the desired property (often the negation of a property expressed, e. g. in CTL). However, such an accepting cycle does not necessarily mean that the property is violated: indeed, a known problem of TAs is that they allow Zeno behaviors. An infinite run is non-Zeno if it takes an unbounded amount of time; otherwise it is Zeno. Zeno runs are infeasible in reality and thus must be pruned during system verification. That is, it is necessary to check whether a run is Zeno or not so as to avoid presenting Zeno runs as counterexamples. The problem of checking whether a timed automaton accepts at least one non-Zeno run, i. e. the emptiness checking problem, has been tackled previously (e. g. [11, 15, 16, 25\u201327]).\n\nIt is often desirable not to fix a priori all timing constants in a TA: either for tuning purposes, or to evaluate robustness when clock values are imprecise. For that purpose, parametric timed automata (PTAs) extend TAs with parameters [2]. Although most problems of interest are undecidable for PTAs [3], some (semi-)algorithms were proposed to tackle practical parameter synthesis (e. g. [4, 9, 18, 20]). We address here the synthesis of parameter valuations for which there exists a non-Zeno cycle in a PTA; this is highly desirable when performing parametric model-checking for which the parameter valuations violating the property should not allow only Zeno-runs. As far as the authors know, this is the first work on parametric model checking of timed automata with the non-Zenoness assumption. Just as for TAs, the parametric zone graph of PTAs (used in e. g. [4, 17, 18]) cannot be used to check whether a cycle is non-Zeno. Therefore, we propose here a technique based on clock upper bound PTAs (CUB-PTAs), a subclass of PTAs satisfying some syntactic restriction, and originating in CUB-TAs for which the non-Zeno checking problem is most efficient [27]. In contrast to regular PTAs, we show that synthesizing valuations for CUB-PTAs such that there exists an infinite non-Zeno cycle can be done based on (a light extension of) the parametric zone graph. We make the following technical contributions:\n\n 1. 1.\n\nWe show that the parameter synthesis problem for PTAs with non-Zenoness assumption is undecidable.\n\n 2. 2.\n\nWe show that any PTA can be transformed into a finite list of CUB-PTAs;\n\n 3. 3.\n\nWe develop a semi-algorithm to solve the non-Zeno synthesis problem using CUB-PTAs, implemented in IMITATOR and validated using benchmarks.\n\nOutline. Section 2 recalls the necessary preliminaries. Section 3 shows the undecidability of non-Zeno-B\u00fcchi emptiness. We then present the concept of CUB-PTAs (Sect. 4), and show how to transform a PTA into a list of CUB-PTAs. Zeno-free parametric model-checking of CUB-PTA is addressed in Sect. 5, and experiments reported in Sect. 6. Finally, Sect. 7 concludes and gives perspectives for future work.\n\n## 2 Preliminaries\n\nThroughout this paper, we assume a set of clocks, i. e. real-valued variables that evolve at the same rate. A clock valuation is a function . We write for . Given , denotes the valuation such that , for all .\n\nWe assume a set of parameters, i. e. unknown constants. A parameter valuation is a function . A strictly positive parameter valuation is a valuation .\n\nIn the following, we assume and . Throughout this paper, denotes a linear term over of the form , with . Similarly, denotes a parametric linear term over , that is a linear term without clocks ( for all i). A constraint (i. e. a convex polyhedron) over is a set of inequalities of the form , with two linear terms. We denote by (resp. ) the constraint that corresponds to the set of all possible (resp. the empty set of) valuations. Given a parameter valuation , denotes the constraint over obtained by replacing each parameter in with . Likewise, given a clock valuation , denotes the expression obtained by replacing each clock in with . We say that satisfies , denoted by , if the set of clock valuations satisfying is non-empty. We say that is satisfiable if s.t. evaluates to true. We define the time elapsing of , denoted by , as the constraint over and obtained from by delaying all clocks by an arbitrary amount of time. Given , we define the reset of , denoted by , as the constraint obtained from by resetting the clocks in , and keeping the other clocks unchanged. We denote by the projection of onto , i. e. obtained by eliminating the clock variables using existential quantification.\n\nA guard is a constraint over defined by inequalities of the form . We assume w.l.o.g. that, in each guard, given a clock , at most one inequality is in the form , that is a clock has a single upper bound (or none). A non-parametric guard is a guard over , i. e. with inequalities , with . A parametric zone is a constraint over defined by inequalities of the form . A parametric constraint is a constraint over defined by inequalities of the form , with two parametric linear terms. We use the notation to indicate that valuating parameters with in evaluates to true. We denote by (resp. ) the parametric constraint that corresponds to the set of all possible (resp. the empty set of) parameter valuations. Given two parametric constraints and , we write whenever for all , .\n\nDefinition 1\n\nA PTA is a tuple , where: (i) is a finite set of actions, (ii) is a finite set of locations, (iii) is the initial location, (iv) is a set of clocks, (v) is a set of parameters, (vi) is the initial parameter constraint, (vii) is the invariant, assigning to every a guard , (viii) is a set of edges where are the source and target locations, , is a set of clocks to be reset, and is a guard.\n\nThe initial constraint is used to constrain some parameters (as in, e. g. [4, 17]); in other words, it defines a domain of valuation for the parameters. For example, given two parameters and , we may want to ensure that . Given , we write as a shortcut for the initial constraint of . In addition, given , we denote by the PTA where is replaced with .\n\nObserve that, as in [27], we do not define accepting locations. In our work, we are simply interested in computing valuations for which there is a non-Zeno cycle. A more realistic parametric model checking approach would require additionally that the cycle is accepting, i. e. it contains at least one accepting location. However, this has no specific theoretical interest, and would impact the readability of our expos\u00e9.\n\nGiven a parameter valuation , we denote by the non-parametric TA where all occurrences of a parameter have been replaced by .\n\nDefinition 2\n\n(Concrete semantics of a TA). Given a PTA , and a parameter valuation , the concrete semantics of is given by the timed transition system , with , , and consists of the discrete and (continuous) delay transition relations:\n\n * discrete transitions: , if , there exists , , and is true.\n\n * delay trans.: , with , if .\n\nA (concrete) run is a sequence s.t. . We consider as usual that concrete runs strictly alternate delays and discrete transitions and we thus write concrete runs in the form . We refer to a state of a run starting from the initial state of a TA as a concrete state of . Note that when a run is finite, it must end with a concrete state. Given a concrete state , we say that is reachable (or that reaches ) if belongs to a run of . By extension, we say that is reachable in , if there exists a concrete state that is reachable.\n\nAn infinite run is said to be Zeno if it contains an infinite number of discrete transitions within a finite delay, i. e. if the sum of all delays is bounded.\n\nSymbolic Semantics. Let us recall the symbolic semantics of PTAs (as in e. g. [4, 18]). A symbolic state is a pair where is a location, and its associated parametric zone. The initial symbolic state of is . That is, the initial state corresponds to all clocks equal to 0 followed by time-elapsing, intersected with the initial invariant and the initial parameter constraint. The symbolic semantics relies on the operation. Given a symbolic state and an edge , , with . The operation is effectively computable, using polyhedra operations: note that the successor of a parametric zone is a parametric zone. A symbolic run of a PTA is an alternating sequence of symbolic states and edges starting from the initial symbolic state, of the form , such that for all , we have , and . The symbolic semantics is often given in the form of a parametric zone graph, i. e. symbolic states of and transitions whenever . Given a symbolic run , its untimed support is the sequence . Two runs (symbolic or concrete) are equivalent if they have the same untimed support.\n\nLet us recall a lemma relating concrete and symbolic runs.\n\nLemma 1\n\nLet be a PTA, and let be a symbolic run of reaching . Let . There exists an equivalent concrete run in iff .\n\nProof\n\nFrom [17, Propositions 3.17 and 3.18].\n\nGiven a symbolic run reaching , we call the concrete runs associated with the concrete runs equivalent to in , for all .\n\nProblems. In this paper, we aim at addressing the following two problems.\n\n## 3 Undecidability of the Non-Zeno Emptiness Problem\n\nAs reachability is undecidable for PTAs [2], it is unsurprising that the existence of a valuation for which there exists a non-Zeno infinite run is undecidable too.\n\nTheorem 1\n\nThe non-Zeno emptiness problem is undecidable for PTAs.\n\nProof\n\nBy reduction from the halting problem of a deterministic 2-counter-machine, which is undecidable [22]. We encode a 2-counter machine (2CM) using PTAs, following an encoding in [8]. This encoding is such that the location encoding the halting state of the 2CM is reachable iff the 2CM halts, and for valuations of the (unique) parameter such that is larger than or equal to the maximum value of the counters along the (unique) run of the machine. Then, since this encoding is such that for any parameter valuation, the encoding stops after discrete steps, the encoding has no infinite run for any valuation.\n\nThen, from the location encoding the halting location (i. e. ), we add a transition resetting to a new location . This location has a self-loop guarded with and resetting (where is any of the four clocks used in the encoding in [8]). Hence whenever is reachable, there is an infinite non-Zeno run looping on . That is, there is an infinite non-Zeno run iff the 2CM halts.\n\nSince the emptiness problem is undecidable, the synthesis problem becomes intractable. In the remainder of this paper, we will devise a semi-algorithm to address non-Zeno synthesis, i. e. an algorithm that computes the exact solution if it terminates. Otherwise, we compute an under-approximation of the result.\n\n## 4 CUB-Parametric Timed Automata\n\nIt has been shown (e.g. [11, 25]) that checking whether a run of TA is infeasible based on the symbolic semantics alone. In [27], the authors identified a subclass of TAs called CUB-TAs for which non-Zenoness checking based on the symbolic semantics is feasible. Furthermore, they show that an arbitrary TA can be transformed into a CUB-TA. Based on their work, we first show that arbitrary PTAs can be transformed into a parametric version of CUB-TAs, and then solve the non-Zeno synthesis problem based on parametric CUB-TAs.\n\nAs defined in [27], a clock upper bound is either or a pair where (recall that is either < or ). We write to denote and ; to denote , or if , then either is or both and are <. Further, we write where d is a constant to denote . We define to be if , and otherwise. Given a clock and a non-parametric guard , we write to denote the upper bound of given . Formally,\n\nDefinition 3\n\nA TA is a CUB-TA if for each edge , for all clocks , we have (i) , and (ii) if , then .\n\nIntuitively, every clock in a CUB-TA has a non-decreasing upper bound along any path until it is reset.\n\n### 4.1 Parametric Clock Upper Bounds\n\nLet us define clock upper bounds in a parametric setting. A parametric clock upper bound is either or a pair .\n\nGiven a clock and a guard , we denote by the parametric upper bound of given . This upper bound is a parametric linear term. Formally,\n\nRecall that, in each guard, given a clock , at most one inequality is in the form . In that case, at most one of the two terms is not and therefore the minimum is well-defined (with the usual definition that .1\n\nWe write to denote the constraint\n\nThat is, we constrain the first parametric clock upper bound to be smaller than or equal to the second one, depending on the comparison operator.\n\nGiven two parametric clock upper bounds and , we write to denote the constraint\n\nThis yields an inequality constraining the first parametric clock upper bound to be smaller than or equal to the second one.\n\n### 4.2 CUB Parametric Timed Automata\n\nWe extend the definition of CUB-TAs to parameters as follows:\n\nDefinition 4\n\nA PTA is a CUB-PTA if for each edge , for all clocks , the following conditions hold: (i) , and (ii) if , then .\n\nHence, a PTA is a CUB-PTA iff every clock has a non-decreasing upper bound along any path before it is reset, for all parameter valuations satisfying the initial constraint .\n\nNote that, interestingly enough, the class of hardware circuits modeled using a bi-bounded inertial delay2 fits into CUB-PTAs (for all parameter valuations).\n\nExample 1\n\nConsider the PTA in Fig. 1a s.t. . Then is not CUB: for x, the upper bound in is whereas that of the guard on the transition outgoing is . yields . Then, ; for example, does not satisfy .\n\nConsider again the PTA in Fig. 1a, this time assuming that . This PTA is a CUB-PTA. (The largest constraint making this PTA a CUB will be computed in Example 2.)\n\nLemma 2\n\nLet be a CUB-PTA. Let . Then is a CUB-TA.\n\nProof\n\nLet . Let be an edge. Given a clock , from Definition 4, we have that , and therefore . This matches the first case of Definition 3. The second case ( ) is similar.\n\nFig. 1.\n\nExamples of PTAs to illustrate the CUB concept\n\n### 4.3 CUB PTA Detection\n\nGiven an arbitrary PTA, our approach works as follows. Firstly, we check whether it is a CUB-PTA for some valuations. If it is, we proceed to the synthesis problem, using the cycle detection synthesis algorithm (Sect. 5); however, the result may be partial, as it will only be valid for the valuations for which the PTA is CUB. This incompleteness may come at the benefit of a more efficient synthesis. If it is CUB for no valuation, it has to be transformed into an equivalent CUB-PTA (which will be considered in Sect. 4.4).\n\nOur procedure to detect whether a PTA is CUB for some valuations is given in Algorithm 1. For each edge in the PTA, we enforce the CUB condition on each clock by constraining the upper bound in the invariant of the source location to be smaller than or equal to the upper bound of the edge guard (line 4). Additionally, if the clock is not reset along this edge, then the upper bound of the source location invariant should be smaller than or equal to that of the target location (line 5). If the resulting set of constraints accepts parameter valuations (i. e. is not empty), then the PTA is a CUB-PTA for these valuations.\n\nExample 2\n\nConsider again the PTA in Fig. 1a, assuming that . This PTA is CUB for .\n\nConsider the PTA in Fig. 1b, with . When handling location and clock x, line 4 yields and then, from line 5, . Hence, there is no valuation for which this PTA is CUB.\n\nProposition 1\n\nLet . Then is a CUB-PTA.\n\nProof\n\nFrom the fact that Algorithm 1 gathers constraints to match Definition 4.\n\n### 4.4 Transforming a PTA into a Disjunctive CUB-PTA\n\nIn this section, we show that an arbitrary PTA can be transformed into an extension of CUB-PTAs (namely disjunctive CUB-PTA), while preserving the symbolic runs.\n\nFor non-parametric TAs, it is shown in [27] that any TA can be transformed into an equivalent CUB-TA. This does not lift to CUB-PTAs.\n\nExample 3\n\nNo equivalent CUB-PTA exists for the PTA in Fig. 2b where . Indeed, the edge from to (resp. ) requires (resp. ). It is impossible to transform this PTA into a PTA where (which is ) is included in both and .\n\nTherefore, in order to overcome this limitation, we propose an alternative definition of disjunctive CUB-PTAs. They can be seen as a union (as defined in the timed automata patterns of, e. g. [13]) of CUB-PTAs.\n\nDefinition 5\n\nA disjunctive CUB-PTA is a list of CUB-PTAs.\n\nGiven a disjunctive CUB-PTA , with , the PTA associated with this disjunctive PTA is , where with .\n\nBasically, the PTA associated with a disjunctive CUB-PTA is just an additional initial location that connects to each of the CUB-PTAs initial locations, with its initial constraint on the guard.3\n\nExample 4\n\nIn Fig. 2d (without the dotted, blue elements), two CUB-PTAs are depicted, one (say ) on the left with locations superscripted by 1, and one (say ) on the right superscripted with 2. Assume is and is . Then the full Fig. 2d (including dotted elements) is the PTA associated with the disjunctive CUB-PTA made of and .\n\nThe key idea behind the transformation from a TA into a CUB-TA in [27] is as follows: whenever a location is followed by an edge and a location for which or for some if , otherwise , location is split into two locations: one (say ) with a \"decreased upper bound\", i. e. , that is then connected to ; and one (say ) with the same invariant as in , and with no transition to . Therefore, the original behavior is maintained. Note that this transformation induces some non-determinism (one must non-deterministically choose whether one enters or , which will impact the future ability to enter ) but this has no impact on the existence of a non-Zeno cycle.\n\nHere, we extend this principle to CUB-PTAs. A major difference is that, in the parametric setting, comparing two clock upper bounds does not give a Boolean answer but a parametric answer. For example, in a TA, holds (this is true), whereas in a PTA denotes the constraint . Therefore, the principle of our transformation is that, whenever we have to compare two parametric clock upper bounds, we consider both cases: here either (in which case the first location does not need to be split) or (in which case the first location shall be split). This yields a finite list of CUB-PTAs: each of these CUB-PTAs consists in one particular ordering of all parametric linear terms used as upper bounds in guards and invariants. (In practice, in order to reduce the complexity, we only define an order on the parametric linear terms the comparison of which is needed during the transformation.)\n\nFig. 2.\n\nExamples: detection of and transformation into CUB-PTAs\n\nExample 5\n\nLet us transform the PTA in Fig. 2a: if then the PTA is already CUB, and does not need to be split. This yields a first CUB-PTA, depicted on the left-hand side of Fig. 2d. However, if , then needs to be split into (where time cannot go beyond ) and into (where time can go beyond , until ), but the self-loop cannot be taken anymore (otherwise the associated guard makes the PTA not CUB). This yields a second CUB-PTA, depicted on the right-hand side of Fig. 2d. Both make a disjunctive CUB-PTA equivalent to Fig. 2a.\n\nSimilarly, we give the transformation of Fig. 2b in Fig. 2e.\n\n## 5 Zeno-Free Cycle Synthesis in CUB-PTAs\n\nTaking a disjunctive CUB-PTA as input, we show in this section that synthesizing the parameter valuations for which there exists at least one non-Zeno cycle (and therefore an infinite non-Zeno run) reduces to an SCC (strongly connected component) synthesis problem.\n\nFirst, we define a light extension of the parametric zone graph as follows. The extended parametric zone graph of a PTA is identical to its parametric zone graph, except that any transition is replaced with , where is a Boolean flag which is true if time can potentially elapse between and . In practice, can be computed as follows, given and edge :\n\n 1. 1.\n\nadd a fresh extra clock to the constraint , i. e. compute\n\n 2. 2.\n\ncompute the successor of via edge\n\n 3. 3.\n\ncheck whether : if so, then ; otherwise .\n\nIntroducing such a clock is cheap: the check is not expensive, and the extra clock does not impact the size of the parametric zone graph: is 0 in all nodes of the zone graph and can be eliminated from the memory, therefore not requiring more space nor extra states.\n\nIn contrast to non-parametric TAs, the flag does not necessarily mean that time can necessarily elapse for all parameter valuations. Consider the example in Fig. 2c. After taking one loop, we have that : therefore, is not necessarily 0, and is . But consider such that : then in time can never elapse. However, we show in the following lemma that the flag does denote time elapsing for strictly positive parameters.\n\nLemma 3\n\nLet be a transition of the extended parametric zone graph of a PTA . Then, for any strictly positive parameter valuation in , there exists an equivalent transition in in which time can elapse.\n\nProof\n\nFirst note that, for any , an equivalent concrete transition exists in , from Lemma 1. Now, since is true, the extra clock in the state of the extended parametric zone graph corresponding to is either unbounded, or bounded by some parametric linear term . If it is unbounded, then time can elapse for any valuation, and the lemma holds trivially. Assume for some . As our parameters are strictly positive, then for any valuation , evaluates to a strictly positive rational, and therefore time can elapse along this transition in .\n\nDefinition 6\n\nAn infinite symbolic run is non-Zeno if all its associated concrete runs are non-Zeno.\n\nIn the remainder of this section, given an edge , denotes that the clocks in reset along .\n\nThe following theorem states that an infinite symbolic run is non-Zeno iff the time can (potentially) elapse along infinitely many edges and, whenever a clock is bounded from above, then eventually either this clock is reset or it becomes unbounded.\n\nTheorem 2\n\nLet be an infinite symbolic run of the extended parametric zone graph of a CUB-PTA . is non-Zeno if and only if\n\n * there exist infinitely many k such that ; and\n\n * for all , for all , given , if , there exists j such that and or .\n\nWe now show that synthesizing parameter valuations for which there exists a non-Zeno infinite run reduces to an SCC searching problem.\n\nFirst, given an SCC , we denote by the parameter constraint associated with , i. e. , where is any state of the SCC.4\n\nTheorem 3\n\nLet be a CUB-PTA of finite extended parametric zone graph . Let be a strictly positive parameter valuation. contains a non-Zeno infinite run if and only if contains a reachable SCC such that and\n\n * contains a transition such that ; and\n\n * for every clock in , given , if for some state in , there exists a transition in with label such that .\n\nTherefore, from Theorem 3, synthesizing valuations yielding an infinite symbolic run reduces to an SCC searching problem in the extended parametric zone graph. Then, we need to test each SCC against two conditions: whether it contains a transition which can be locally delayed (i. e. whether it contains a transition where ); and whether every clock having an upper bound other than at some state is reset along some transition in the SCC. Then, for all SCCs matching these two conditions, we return the associated parameter constraint.\n\nWe give in Algorithm 2 an algorithm to solve the non-Zeno synthesis problem for CUB-PTAs. simply iterates on the SCCs, and gathers their associated parameter constraints whenever they satisfy the conditions in Theorem 3.\n\nIf is finite, then the correctness and completeness of immediately follow from Theorem 3. If only an incomplete part of is computed (e. g. by bounding the exploration depth, or the number of explored states, or the execution time) then only the direction of Theorem 3 holds: in that case, the result of is correct but non-complete, i. e. it is a valid under-approximation. In the context of parametric model checking, knowing which parameter valuations violate the property is already very helpful to the designer, as it helps to discard unsafe valuations, and to refine the model.\n\n## 6 Experiments\n\nWe implemented our algorithms in IMITATOR [5].5 The Parma Polyhedra Library (PPL) [10] is integrated inside the core of IMITATOR in order to solve mainly linear inequality system problems. Experiments were run on an Intel Core 2 Duo P8600 at 2.4 GHz and 4 GiB of memory.\n\nWe compare three approaches: (1) A cycle detection synthesis without the non-Zenoness assumption (called ). The result may be an over-approximation of the actual result, as some of the parameters synthesized may yield only Zeno cycles. If does not terminate, its result is an under-approximation of an over-approximation, therefore considered as potentially invalid; that is, there is no guarantee of correctness for the synthesized constraint. (2) Our CUB-detection (Algorithm 1) followed by synthesis (Algorithm 2): the result may be under-approximated, as only the valuations for which the PTA is CUB are considered. (3) Our CUB-transformation ( ) followed by synthesis (Algorithm 2) on the resulting disjunctive CUB-PTA. If the algorithm terminates, then the result is exact, otherwise it may be under-approximated.\n\nWe consider various benchmarks: protocols (CSMA\/CD, Fischer [2], RCP, WFAS), hardware circuits (And-Or, flip-flop), scheduling problems (Sched5), a networked automation system (simop) and various academic benchmarks.\n\nWe give from left to right in Table 1 the case study name and its number of clocks, parameters and locations. For , we give the computation time (TO denotes a time-out at 3600 s), the constraint type ( , or another constraint) and the validity of the result: if terminates, the result is an over-approximation, otherwise it is potentially invalid. For (resp. ) we give the detection (resp. transformation) time, the total time (including ), the result, and whether it is an under-approximation or an exact result. We also mention whether outputs that all, none or some valuations make the PTA CUB; and we give the number of locations in the transformed disjunctive CUB-PTA output by . The percentage is used to compare the number of valuations (comparison obtained by discretization) output by the algorithms, with as the basis (as the result is exact).\n\nThe toy benchmark CUBPTA1 is a good illustration: terminates after 0.073 s (and therefore its result is exact) with some constraint. is faster (0.015 s) but infers that only some valuations are CUB and analyzes only these valuations; the synthesized result is only 69% of the expected result. In contrast, is much faster (0.006 s) but obtains too many valuations (208% of the expected result) as it infers many Zeno valuations.\n\nTable 1.\n\nExperimental comparison of the three algorithms\n\nLet us discuss the results. First, almost always outputs a possibly invalid result (neither an under- nor an over-approximation), which justifies the need for techniques handling non-Zeno assumptions. In only one case (CUBPTA1), it outputs a non-trivial over-approximation. In two cases, it happens to give an exact answer, as the over-approximation of necessarily means that is the exact result. In contrast, gives an exact result in five cases, a non-trivial under-approximation in two cases; the five remaining cases are a disappointing result in which is output as an under-approximation. By studying the model manually, we realized that some non-Zeno cycles actually exist for some valuations, but our synthesis algorithm was not able to derive them. Only in one of these cases (Sched5), outputs a more interesting result than .\n\nThe transformation is relatively reasonable both in terms of added locations (in the worst case, there are 40 instead of 10 locations, hence four times more, for WFAS) and in terms of transformation time (the worst case is 1.2 s for Sched5). Our experiments do not allow us to fairly compare the time of (without non-Zenoness) and (with non-Zenoness assumption) as, without surprise due to the undecidability, most analyses do not terminate. Only two benchmarks terminate for both algorithms, but are not significant (<1 s).\n\nNote that flip-flop is a hardware circuit modeled using a bi-bounded inertial delay, and is therefore CUB for all valuations.\n\nAn interesting benchmark is WFAS, for which our transformation procedure terminates whereas does not. Therefore, we get an exact result while the traditional procedure cannot produce any valuable output.\n\nAs a conclusion, seems to be faster but less complete than . As for , its result is almost always more valuable than , and therefore is the most interesting algorithm.\n\n## 7 Conclusion\n\nWe proposed a technique to synthesize valuations for which there exists a non-Zeno infinite run in a PTA. By adding accepting states, this allows for parametric model checking with non-Zenoness assumption. Our techniques rely on a transformation to a disjunctive CUB-PTA (or in some cases on a simple detection of the valuation for which the PTA is already CUB), and then on a dedicated cycle synthesis algorithm. We implemented our techniques in IMITATOR and compared our algorithms on a set of benchmarks.\n\nFuture Works. Our technique relying on CUB-PTAs extends the technique of CUB-TAs: this technique is shown in [27] to be the most efficient for performing non-Zeno model checking for TAs. However, for PTAs, other techniques (such as yet to be defined parametric extensions of strongly non-Zeno TAs [26] or guessing zone graph [16]) could turn more efficient and should be investigated.\n\nIn addition, parametric stateful timed CSP (PSTCSP) [7] is a formalism for which the CUB assumption seems to be natively verified. Therefore, studying non-Zeno parametric model checking for PSTCSP, as well as transforming PTAs into PSTCSP models, would be an interesting direction of research.\n\nStudying the decidability of the underlying decision problem should be done for famous subclasses of PTAs constraining the use of parameters (namely L\/U-PTAs, L-PTAs and U-PTAs [17]) as well as for new semantic subclasses that we recently proposed and that benefit from decidability results (namely integer-point PTAs and reset-PTAs [6]).\n\nAn interesting future will be to design a multi-core extension of our non-Zeno synthesis algorithm; this could be done by reusing parallel depth first search algorithms for finding cycles [14].\n\nFinally, combining our synthesis algorithms with IC3 [12], as well as extending them to hybrid systems [23] is also of high practical interest.\n\nReferences\n\n1.\n\nAlur, R., Dill, D.L.: A theory of timed automata. Theoret. Comput. Sci. 126(2), 183\u2013235 (1994)MathSciNetCrossRef90010-8)MATH\n\n2.\n\nAlur, R., Henzinger, T.A., Vardi, M.Y.: Parametric real-time reasoning. In: STOC, pp. 592\u2013601. ACM (1993)\n\n3.\n\nAndr\u00e9, \u00c9.: What's decidable about parametric timed automata? In: Artho, C., \u00d6lveczky, P.C. (eds.) FTSCS 2015. CCIS, vol. 596, pp. 52\u201368. Springer, Cham (2016). doi:10.\u200b1007\/\u200b978-3-319-29510-7_\u200b3 CrossRef\n\n4.\n\nAndr\u00e9, \u00c9., Chatain, T., Encrenaz, E., Fribourg, L.: An inverse method for parametric timed automata. IJFCS 20(5), 819\u2013836 (2009)MathSciNetMATH\n\n5.\n\nAndr\u00e9, \u00c9., Fribourg, L., K\u00fchne, U., Soulat, R.: IMITATOR 2.5: a tool for analyzing robustness in scheduling problems. In: Giannakopoulou, D., M\u00e9ry, D. (eds.) FM 2012. LNCS, vol. 7436, pp. 33\u201336. Springer, Heidelberg (2012). doi:10.\u200b1007\/\u200b978-3-642-32759-9_\u200b6 CrossRef\n\n6.\n\nAndr\u00e9, \u00c9., Lime, D., Roux, O.H.: Decision problems for parametric timed automata. In: Ogata, K., Lawford, M., Liu, S. (eds.) ICFEM 2016. LNCS, vol. 10009, pp. 400\u2013416. Springer, Cham (2016). doi:10.\u200b1007\/\u200b978-3-319-47846-3_\u200b25 CrossRef\n\n7.\n\nAndr\u00e9, \u00c9., Liu, Y., Sun, J., Dong, J.S.: Parameter synthesis for hierarchical concurrent real-time systems. Real-Time Syst. 50(5\u20136), 620\u2013679 (2014)CrossRefMATH\n\n8.\n\nAndr\u00e9, \u00c9., Markey, N.: Language preservation problems in parametric timed automata. In: Sankaranarayanan, S., Vicario, E. (eds.) FORMATS 2015. LNCS, vol. 9268, pp. 27\u201343. Springer, Cham (2015). doi:10.\u200b1007\/\u200b978-3-319-22975-1_\u200b3 CrossRef\n\n9.\n\nA\u015ftef\u0103noaei, L., Bensalem, S., Bozga, M., Cheng, C.-H., Ruess, H.: Compositional parameter synthesis. In: Fitzgerald, J., Heitmeyer, C., Gnesi, S., Philippou, A. (eds.) FM 2016. LNCS, vol. 9995, pp. 60\u201368. Springer, Cham (2016). doi:10.\u200b1007\/\u200b978-3-319-48989-6_\u200b4\n\n10.\n\nBagnara, R., Hill, P.M., Zaffanella, E.: The Parma Polyhedra Library: toward a complete set of numerical abstractions for the analysis and verification of hardware and software systems. Sci. Comput. Program. 72(1\u20132), 3\u201321 (2008)MathSciNetCrossRef\n\n11.\n\nBowman, H., G\u00f3mez, R.: How to stop time stopping. Formal Aspects Comput. 18(4), 459\u2013493 (2006)CrossRefMATH\n\n12.\n\nCimatti, A., Griggio, A., Mover, S., Tonetta, S.: Parameter synthesis with IC3. In: FMCAD, pp. 165\u2013168. IEEE (2013)\n\n13.\n\nDong, J.S., Hao, P., Qin, S., Sun, J., Yi, W.: Timed automata patterns. IEEE Trans. Softw. Eng. 34(6), 844\u2013859 (2008)CrossRef\n\n14.\n\nEvangelista, S., Laarman, A., Petrucci, L., van de Pol, J.: Improved multi-core nested depth-first search. In: Chakraborty, S., Mukund, M. (eds.) ATVA 2012. LNCS, vol. 7561, pp. 269\u2013283. Springer, Heidelberg (2012). doi:10.\u200b1007\/\u200b978-3-642-33386-6_\u200b22 CrossRef\n\n15.\n\nG\u00f3mez, R., Bowman, H.: Efficient detection of Zeno runs in timed automata. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 195\u2013210. Springer, Heidelberg (2007). doi:10.\u200b1007\/\u200b978-3-540-75454-1_\u200b15 CrossRef\n\n16.\n\nHerbreteau, F., Srivathsan, B., Walukiewicz, I.: Efficient emptiness check for timed B\u00fcchi automata. Formal Methods Syst. Des. 40(2), 122\u2013146 (2012)CrossRefMATH\n\n17.\n\nHune, T., Romijn, J., Stoelinga, M., Vaandrager, F.W.: Linear parametric model checking of timed automata. JLAP 52\u201353, 183\u2013220 (2002)MathSciNetMATH\n\n18.\n\nJovanovi\u0107, A., Lime, D., Roux, O.H.: Integer parameter synthesis for timed automata. Trans. Softw. Eng. 41(5), 445\u2013461 (2015)CrossRefMATH\n\n19.\n\nKhatib, L., Muscettola, N., Havelund, K.: Mapping temporal planning constraints into timed automata. In: TIME, pp. 21\u201327. IEEE Computer Society (2001)\n\n20.\n\nKnapik, M., Penczek, W.: Bounded model checking for parametric timed automata. Trans. Petri Nets Models Concurr. 5, 141\u2013159 (2012)CrossRefMATH\n\n21.\n\nLarsen, K.G., Pettersson, P., Yi, W.: UPPAAL in a nutshell. Int. J. STTT 1(1\u20132), 134\u2013152 (1997)CrossRefMATH\n\n22.\n\nMinsky, M.L.: Computation: Finite and Infinite Machines. Prentice-Hall, Inc., Upper Saddle River (1967)MATH\n\n23.\n\nSchupp, S., \u00c1brah\u00e1m, E., Chen, X., Makhlouf, I.B., Frehse, G., Sankaranarayanan, S., Kowalewski, S.: Current challenges in the verification of hybrid systems. In: Berger, C., Mousavi, M.R. (eds.) CyPhy 2015. LNCS, vol. 9361, pp. 8\u201324. Springer, Cham (2015). doi:10.\u200b1007\/\u200b978-3-319-25141-7_\u200b2 CrossRef\n\n24.\n\nSun, J., Liu, Y., Dong, J.S., Pang, J.: PAT: towards flexible verification under fairness. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 709\u2013714. Springer, Heidelberg (2009). doi:10.\u200b1007\/\u200b978-3-642-02658-4_\u200b59 CrossRef\n\n25.\n\nTripakis, S.: Verifying progress in timed systems. In: Katoen, J.-P. (ed.) ARTS 1999. LNCS, vol. 1601, pp. 299\u2013314. Springer, Heidelberg (1999). doi:10.\u200b1007\/\u200b3-540-48778-6_\u200b18 CrossRef\n\n26.\n\nTripakis, S., Yovine, S., Bouajjani, A.: Checking timed B\u00fcchi automata emptiness efficiently. Formal Methods Syst. Des. 26(3), 267\u2013292 (2005)CrossRefMATH\n\n27.\n\nWang, T., Sun, J., Wang, X., Liu, Y., Si, Y., Dong, J.S., Yang, X., Li, X.: A systematic study on explicit-state non-Zenoness checking for timed automata. IEEE Trans. Softw. Eng. 41(1), 3\u201318 (2015)CrossRef\n\nFootnotes\n\n1\n\nNote that if a clock has more than a single upper bound in a guard, then the minimum can be encoded as a disjunction of constraints, and our results would still apply with non-convex constraints (that can be implemented using a finite list of convex constraints).\n\n2\n\nThis model assumes that, after the change of a signal in the input of a gate, the output changes after a delay which is modeled using a parametric closed interval.\n\n3\n\nA purely parametric constraint (e. g. ) is generally not allowed by the PTA syntax, but can be simulated using appropriate clocks (e. g. ). Such parametric constraints are allowed in the input syntax of IMITATOR.\n\n4\n\nFollowing a well-known result for PTAs, all symbolic states belonging to a same cycle in a parametric zone graph have the same parameter constraint.\n\n5\n\nFor experimental data including source and binary, see http:\/\/\u200bimitator.\u200bfr\/\u200bstatic\/\u200bNFM17.\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_4\n\n# Multi-timed Bisimulation for Distributed Timed Automata\n\nJames Ortiz1 , Moussa Amrani1 and Pierre-Yves Schobbens1\n\n(1)\n\nComputer Science Faculty, University of Namur, Namur, Belgium\n\nJames Ortiz\n\nEmail: james.ortizvega@unamur.be\n\nMoussa Amrani (Corresponding author)\n\nEmail: moussa.amrani@unamur.be\n\nPierre-Yves Schobbens\n\nEmail: pierre-yves.schobbens@unamur.be\n\nAbstract\n\nTimed bisimulation is an important technique which can be used for reasoning about behavioral equivalence between different components of a complex real-time system. The verification of timed bisimulation is a difficult and challenging problem because the state explosion caused by both functional and timing constraints must be taken into account. Timed bisimulation was shown decidable for Timed Automata (TA). Distributed TA and TA with Independent Clocks (icTA) were introduced to model Distributed Real-time Systems. They are a variant of TA with local clocks that may not run at the same rate. In this paper, we first propose to extend the theory of Timed Labeled Transition Systems to Multi-Timed Labeled Transition Systems, and relate them by an extension of timed bisimulation to multi-timed bisimulation. We prove the decidability of multi-timed bisimulation and present an EXPTIME algorithm for deciding whether two icTA are multi-timed bisimilar. For multi-timed bisimilarity, an extension of the standard refinement algorithm is described.\n\n## 1 Introduction\n\nDistributed Real-Time Systems (DTS) are increasing with the scientific and technological advances of computer networks. The high demand for computer networks has caused the development of new complex applications which benefit from the high performance and resources offered by modern telecommunications networks. Current researches in the area of DTS have emerged from the need to specify and analyze the behavior of these systems, where both distributed behavior and timing constraints are present. Formal verification methods, such as model checking, have been used to verify the correctness of complex DTS. Model checking over DTS becomes rapidly intractable because the state space often grows exponentially with the number of components considered. A technique to reduce the state space is to merge states with the same behaviour. For untimed systems, the notion of bisimulation [13] is classically used to this end, and its natural extension for real-time systems, timed bisimulation, was already shown decidable for Timed Automata (TA) [2, 12]. A timed automaton is a finite automaton augmented with real-valued clocks, represented as variables that increase at the same rate as time progresses. TA assume perfect clocks: all clocks have infinite precision and are perfectly synchronized. In this paper, we study two variants of TA called Distributed Timed Automata (DTA) and Timed Automata with Independent Clocks (icTA) proposed by [1, 11, 16] to model DTS, where the clocks are not necessarily synchronized. TA have been used to model DTS such as Controller Area Network [14] and WirelessHART Networks [10]. But, TA, icTA and timed bisimulation are based on a sequential semantics of a Timed Labelled Transition Systems (TLTS), i.e., a run of a TLTS is given by a sequence of actions and timestamps.\n\nUnfortunately, a sequential semantics does not describe completely the behavior of the DTS, because interactions between processes with their associated local clocks that are running at the same rate and distribution of the actions over the components are not considered. Also, model-checking and bisimulation equivalence algorithms have been implemented in tools [19, 20] for the sequential semantics used by the model (e.g., TA, TLTS, etc.). In contrast, behavioral equivalences for DTS have only been introduced in [3]. It is, however, not clear whether such equivalences agree with the distributed timed properties in DTS. Therefore, we propose an alternative semantics to the classical sequential semantics for TLTS and icTA: specifically, a run of a system in our alternative semantics is given by the sequences of pairs (action, tuples of timestamps). We propose an alternative semantics in order to be able to consider a semantics which expresses the distribution of the actions and timestamps over the components. With this alternative, it becomes possible to analyze the local behavior of the components independently, thus enhancing the expressiveness of the TLTS (and icTA). We introduce Multi-Timed Labelled Transition Systems (MLTS), an extension of classical TLTS in order to cope with the notion of multiple local times, and we propose efficient algorithms using refinement techniques [17].\n\nContributions. One of our main contributions is to incorporate a alternative semantics over sequential semantics for TLTS and icTA. Also, we extend the classical theory of timed bisimulation with the notion multi-timed bisimulation and their corresponding decision algorithms. We also present two algorithms: (i) a forward reachability algorithm for the parallel composition of two icTA, which will help us to minimize the state space exploration by our second algorithm, and (ii) a decision algorithms for multi-timed bisimulation using the zone-based technique [5]. Multi-timed bisimulation is a relation over local clocks (and processes), and cannot be computed with the standard partition refinement algorithm [17]. Instead, our algorithm successively refines a set of zones such that ultimately each zone contains only multi-timed bisimilar pairs of states. Furthermore, we show that our algorithm is EXPTIME-complete. Since TA are a special variant of icTA, our work conservatively extends the expressiveness of TA and TLTS; and since timed bisimulation over TA [19, 20] can be regarded as a special case of multi-timed bisimulation, our decision algorithms could potentially be used to analyze complex DTS.\n\nStructure of the Paper. After recalling preliminary notions in Sect. 2, we introduce our alternative semantics for icTA in Sect. 3, based on multi-timed words consumed by MLTS. Section 4 deals with bisimulation: we first define multi-timed bisimulation, by adapting the classical definition to MLTS, then show its decidability by exhibiting an EXPTIME algorithm. Finally, Sect. 5 compares our work with existing contributions, and Sect. 6 concludes. Due to space constraints, some proofs are not given here, but stay available in a Technical Report available online [15].\n\n## 2 Preliminaries\n\nWe describe in this section the notations needed for formally defining Timed Labelled Transition Systems (TLTS) and Timed Automata TA.\n\nTimed Words. The set of all finite words over a finite alphabet of actions is denoted by . Let , and respectively denote the sets of natural, real and nonnegative real numbers. A timed word [2] over is a finite sequence of actions paired with nonnegative real numbers (i.e., ) such that the timestamped sequence is nondecreasing (i.e., ). We sometimes define as the pair with and t a sequence of timestamps with the same length.\n\nClocks. A clock is a real positive variable that increases with time. Let be a finite set of clock names. A clock constraint is a conjunction of comparisons of a clock with a natural constant c: with , , and , is defined by\n\nA clock valuation over is a mapping . For a time value , we note the valuation defined by . Given a clock subset , we note the valuation defined as follows: if and otherwise. The projection of on , written , is the valuation over containing only the values in of clocks in .\n\nTimed Automata (TA). A TA is a tuple where is a finite alphabet, X a clock set, S a set of locations with the initial location and the set of (sink) final states, is the automaton's transition relation, associates to each location a clock constraint as invariant. For a transition , we classically write and call s and the source and target location, is the guard, a the action or label, Y the set of clocks to be reset. During the execution of a TA , a state is a pair , where s denotes the current state with its accompanying clock valuation , starting at where maps each clock to 0. We only consider legal states, i.e. states that satisfy (i.e. valuations that map clocks to values that satisfy the current state's invariant).\n\nTimed Transition System ( ). The transition system TLTS generated by is defined by TLTS , where Q is a set of legal states over with initial state , a finite alphabet and is the TLTS transition relation defined by: (a) Delay transition: for some , iff , (b) Discrete transition: , iff , , and .\n\n## 3 An Alternative Semantics for DTA\n\nIn this section, we define an alternative semantics (which we will call multi-timed semantics) for icTA as opposed to the mono-timed semantics of [1]. The main problem with the semantics of [1] is that they use the reference time. The benefits of this new definition are threefold. First, the multi-timed semantics preserves the untimed language of the icTA. Second, the multi-timed semantics can work with multi-timed words. Third, the region equivalence defined in [1] could form a finite time-abstract bisimulation on the multi-timed semantics. Hence, the multi-timed semantics allows to build a region automaton that accepts exactly Untime for all icTA [1]. Thus, we extend TLTS and icTA to their multi-timed version.\n\n### 3.1 Multi-timed Actions\n\nLet Proc be a non-empty set of processes, then, we denote by the set of functions from Proc to , that we call tuples. A tuple is smaller that , noted, iff and . A Monotone Sequence of Tuples (MST) is a sequence = of tuples of where: , . A multi-timed word on is a pair where is a finite word , and is a MST of the same length. This is the analog of a timed word (or multi-timed action) [2]. A multi-timed word can equivalently be seen as a sequence of pairs in .\n\n### 3.2 Multi-timed Labeled Transition Systems\n\nOur multi-timed semantics is defined in terms of runs that record the state and clock values at each transition points traversed during the consumption of a multi-timed word. Instead of observing actions at a global time, a multi-timed word allows to synchronise processes on a common action that may occur at a specific process time.\n\nDefinition 1\n\n(Multi-timed Labelled Transition System). A Multi-Timed Labelled Transition System (MLTS) over a set of processes Proc is a tuple such that: (i) is a set of states. (ii) is the initial state. (iii) is a finite alphabet. (v) is a set of transitions.\n\nThe transitions from state to state of a MLTS are noted in the following way: (i) A transition is denoted and is called a , if a and , (ii) A transition is denoted and is called a , if and .\n\nA run of can be defined as a finite sequence of moves, where discrete and continuous transitions alternate: = , where and . The multi-timed word of is , where . A multi-timed word is accepted by iff there is a maximal initial run whose multi-timed word is . The language of , denoted , is defined as the set of multi-timed words accepted by some run of . Note that MLTS are a proper generalisation of TLTS: each TLTS can be seen as a MLTS with a single process and conversely.\n\nFor example, consider the two transition systems in Fig. 1: a MLTS on the left ( ) and two TLTS on the right ( and ) with the finite input alphabet . In brief, and could be considered as the projection of on the case of process 1 and 2.\n\nFig. 1.\n\nMulti-timed and Timed Labelled Transition Systems\n\n### 3.3 A Multi-timed Semantics for icTA\n\nDTA [1, 11] consist of a number of local timed automata. In [1], DTA are not much studied. Instead, their product is first computed, giving rise to the class of icTA ( , where is a TA and is a function maps each clock to a process).\n\nGiven , a clock valuation and : the valuation is defined by = for all . A Rate is a tuple = of local time functions. Each local time function maps the reference time to the time of process , i.e., . The functions must be continuous, strictly increasing, divergent, and satisfy . The set of all these tuples is denoted by .\n\nThe operational semantics of an icTA has been associated to a sequential semantics. A run of an icTA for with a sequential semantics as a sequence where , and , and . Here, we want to associate operational semantics of a icTA to a MLTS.\n\nDefinition 2\n\nLet be an icTA and . Our multi-timed semantics of the icTA is given by a MLTS over , denoted by MLTS( ). The set of states Q consists of triples composed of a location, a clock valuation and lastly the reference time: . The starting state is , where is the valuation that assigns 0 to all the clocks. is the alphabet of . The transition relation is defined by:\n\n 1. (i)\n\nA transition is denoted , and is called a , where , , and .\n\n 2. (ii)\n\nA transition is denoted , and is called a , where , , , there exists a transition , such that , = , , .\n\nIn Definition 2, we have introduced a multi-timed semantics for icTA, following ideas of [1]. A run of an icTA for Rates with our multi-timed semantics is an initial path in MLTS where discrete and continuous transition alternate. A multi-timed word is accepted by for iff it is accepted by MLTS .\n\nExample 1\n\nThe Fig. 2(a) shows an icTA with the finite input alphabet , the set of processes Proc = , the set of clocks and = (2t, t) i.e. = 2t and = t. A run of on multi-timed word = ((a, (2.0, 1.0))(b, (3.0, 1.5))(c, (4.2, 2.1)) (d, (6.0, 3.0))) is given by .\n\nFig. 2.\n\n(a) An icTA , (b) An counter example of Multi-timed bisimulation\n\n## 4 Multi-timed Bisimulation\n\nFrom a distributed approach, a DTS consist of several processes with their associated local clocks that are not running at the same rate. Thus, in order to formalize preservation of distributed timed behavior, we extend the classical definition of timed bisimulation [9] towards a multi-timed semantics. Our motivation for extending the classical definition of timed bisimulation is twofold: first, efficient algorithms checking for timed and time-abstract bisimulation have been discovered [12, 19]. Nonetheless, these algorithms are based on sequential semantics (i.e., TLTS and TA). Second, verifying the preservation of distributed timed behavior in DTS could be used to master the combinatorial explosion of the size of the model due to the composition of the processes.\n\n### 4.1 Strong Multi-timed Bisimulation\n\nLet and be two MLTS over the same set of actions and processes Proc. Let (resp., ) be the set of states of (resp., ). Let be a binary relation over . We say that is a strong multi-timed bisimulation whenever the following transfer property holds (note that technically this is simply strong bisimulation over ):\n\nDefinition 3\n\nA strong multi-timed bisimulation over MLTS , is a binary relation such that, for all , the following holds:\n\n 1. (i)\n\nFor every and for every discrete transition , there exists a matching discrete transition such that and symmetrically.\n\n 2. (ii)\n\nFor every , for every delay transition , there exists a matching delay transition such that and symmetrically.\n\nTwo states and are multi-timed bisimilar, written , iff there is a multi-timed bisimulation that relates them. and are multi-timed bisimilar, written , if there exists a multi-timed bisimulation relation over and containing the pair of initial states.\n\nAs a consequence of Definition 3, the notion of multi-timed bisimulation extends to icTA and we have the following definition:\n\nDefinition 4\n\nLet and be two icTA. We say the automata and are multi-timed bisimilar, denoted , iff Rates MLTS( ) MLTS( ).\n\nWhen there is only one process, the multi-timed bisimulation is the usual timed bisimulation. Consider the two icTA (top) and (bottom) in Fig. 2(b) with the alphabet , the set of processes Proc = , the set of clocks and = i.e. = and = 3t. and in Fig. 2(b) depicts an icTA. performs nondeterministically the transition with the guard , the action a, resets clock to 0 and enters location . Similarly, performs nondeterministically the transitions with the guard , the action a, resets clock to 0 and enters location . We will show that these icTA are not multi-timed bisimilar (Definition 3) ever if their underling TA are bisimilar (and ever isomorphic): We have in and since can run the delay transition and in . We have can only match this transition with . From these states can fire a while cannot.\n\n### 4.2 Decidability\n\nInspired by [12], we show that for given icTA , , checking whether is decidable via a suitable zone graph [12]. In order to define the notion of clock zone over a set of clocks , we need to consider the set of extended clock constraints.\n\nDefinition 5\n\nA clock constraint is a conjunction of comparisons of a clock with a constant c, given by the following grammar, where ranges over , , , and :\n\nA clock constraint of the form is called diagonal constraint and , must belong to the same process. The notion of satisfaction of a clock constraint by a valuation is given by the clause c iff c.\n\nInformally, a clock zone is a conjunction of extended clock constraints with inequalities of clock differences and its semantics is the set of clock valuations that satisfy it = . We omit the semantics brackets ( ) when obvious. For any clock zones , and finite set of clocks X, the semantics of the intersection, clock reset, inverse clock reset, time successor and time predecessor events on clock zone can be defined as: (i) , (ii) , (iii) , (iv) , (v) .\n\nA zone graph [12] is similar to a region graph [2] with the difference that each node consists of pair (called a zone) of a location s and a clock zone . For , we write q if and , indicating that a state is included in a zone. Analogously, we can write to indicate that and . We will use the notation to denote the action a of the edge e. Furthermore, we extend the zone operations for an icTA in the following way:\n\nDefinition 6\n\nLet be a zone and be a transition of , then = is the set of valuations that q can reach by taking the transition e.\n\nDefinition 7\n\nLet be a zone and be a transition of , then = is the set of valuations that q can reach by executing the transition e.\n\nIntuitively, the zone describes the discrete successor of the zone under the transition e, and the zone describes the discrete predecessor of the zone under the transition e.\n\nDefinition 8\n\n(Multi-timed Zone Graph). Given an icTA , its symbolic multi-timed zone graph (ZG( )) is a transition system ZG( ) = , where: (i) Q consists of pairs where s , and is a clock zone with . (ii) is the initial zone with = . (iii) is the set of labels of . (iv) is a set of transitions, where each transition in ZG( ) is a labelled by a transition , where s and are the source and target locations, is a clock constraint defining the guard of the transition, a is the action of the edge and Y is the set of clocks to be reset by the transition in the icTA . For each , transitions are defined by the rules:\n\n 1. (i)\n\nFor every e = and clock zone , there exists a discrete transition , where if .\n\n 2. (ii)\n\nFor a clock zone , there exists a delay transition , where and I(s).\n\nNote that is used here as a symbol to represent symbolic positive delay transitions. Only the reachable part is constructed.\n\nLemma 1\n\nLet be a zone and be a transition of an icTA , then , , , and are also zones.\n\nMulti-timed Zone Graph Algorithm: In Algorithm 1, we build a reachable multi-timed zone graph (ZG( )) for the parallel composition of two icTA ( and ). Algorithm 1 build a multi-timed zone graph, starting with the pair ( initial location of the automaton with = represents the initial zone). However, the multi-timed zone graph can be infinite, because constants used in zones may grow for ever. Therefore, we use a technique called extrapolation abstraction ( (LU-bound)) [4, 7], where L is the maximal lower bound and U is the maximal upper bounds. For every location s of a ZG( ), there are bound functions LU and the symbolic zone graph using . Then, we build zones of the form .\n\nLemma 2\n\n(Completeness). Let = be a run of , for some Rates. Then, for any state where , there exists a symbolic zone added in Q such that .\n\nThe above lemma tells that the Algorithm 1 over-approximates reachability. Now, we can establish the termination of the Algorithm 1, because there are finitely many zones. Here, we will use Algorithm 1 to over-approximate the co-reachable state space of the two icTA and , on the strongly synchronized product of and . The time complexity of this algorithm is given in terms of the number of clocks, the number of clocks and the number of transitions of the icTA: where |S| represent the number of states in the icTA , |X| the number of clocks in and the number of transitions in .\n\nRefinement Algorithm: Now, we describe a refinement algorithm with signature to compute the multi-timed bisimulation from their zone graph of their strong product ZG(ZG( )). The passage of arbitrary local times are abstracted by time elapse transitions from a zone to successor zones, and discrete transitions. Essentially, our algorithm is based on the refinement technique [6, 17, 19]. The state space Q of ZG( ) is divided in zones that initially over-approximate the co-reachable states of and . Algorithm 2 starts from an initial set of zones and successively refines these sets such that ultimately each zone contains only bisimilar state pairs.\n\nThe runs of a zone graph involve a sequence of moves with discrete and time-elapse transitions. The refinement algorithm has thus to deal with the following difficulties: when taking a transition, where the clocks in different processes are not perfectly synchronous, it should take into consideration that the time elapse traverses continuously diagonal, almost vertical and horizontal time successor zones. Conversely, when the clocks belonging to the same process (i.e., perfectly synchronous), the time elapsing traverses only continuously diagonal time successor zones. Thus, the time refinement operator presented in [19] is not applicable within our Algorithm 2. Figure 3 presents an example: (a) a time elapsing traversing the clock regions 1 to 3 for synchronous clocks, (b) a time elapsing traversing continuously diagonal, almost horizontal and vertical time successor zones for asynchronous clocks.\n\nFig. 3.\n\n(a) A time elapsing traversing 0 to 3, (b) Multi-timed time successors.\n\nThe discrete refinement operator presented in [19] is also not applicable within our Algorithm 2. Therefore, our algorithm adopts the idea of the signature-based technique [6], which assigns states to equivalence blocks according to a characterizing signature. In each refinement iteration, the set of zones are refined according to a signature. The algorithm in [6], cannot be applied in our setting in a straightforward way, due to its untimed characteristic, while in our case, the time and discrete characteristics should be considered. Based on [6], we introduce a signature refinement operator which refine the set of zones until a fixed point is reached, which is the complete multi-timed bisimulation. Thus, we introduce the timed and discrete predecessor operators.\n\nDefinition 9\n\nLet q = and = be two zones, then: = is the set of valuations in the zone from which a valuation of can be reached through the elapsing of time, without entering any other zones besides and (i.e., ).\n\nThe operator refines selecting the states that can reach .\n\nLemma 3\n\nLet , Q be two zones, then is a clock zone.\n\nWe use as signature of a state the set of outgoing transitions from . Then, a refinement of a zone can be computed by grouping states that have the same signature. The resulting set of zones then represents the multi-timed bisimulation relation: two states and are multi-timed bisimilar iff they are in the same zone with similar outgoing transitions. Formally, this is captured in the following definition:\n\nDefinition 10\n\nLet q = be a zone, then the signature of a state q formed by the set of labels of all the edges starting from is defined as:\n\n = . Also, the signature of the zone q is defined as: = .\n\n operator is used to compute the signatures of a state into a zone. Our Algorithm 2 consists of two steps: The initial phase, is responsible for keeping a pair of states in q into zones so that every pair of states from the same zone q have the same signature . The refinement phase, consists of computing the timed predecessors (see Definition 11 below) and the discrete signature predecessors (see Definition 12 below) until a stable set of zones is reached. Stable zone are a multi-timed bisimulation relation if every pair of states of every zone in the set have the same signature with respect to every computed refinement. A detailed explication about building a stable zones follows:\n\n * Initial phase: Let = Q be the initial set of zones, where Q is given by Algorithm 1. After the initial phase, the set contains zones consisting of states with unique signatures, .\n\n * Refinement phase: An existing set of zones are iteratively refined until all zones becomes stable simultaneously with respect to all their timed predecessors and discrete predecessors. For simplicity, we will write to denote the pairs .\n\nDefinition 11\n\nLet be a set of zones and q = , = be two zones in . Then for the delay transitions, the refinement function is defined as follows:\n\n =\n\nDefinition 12\n\nLet be a set of zones and q = , = be two zones in . Let q = be the currently examined zone and be the signatures of the set of states into the zone q. Let and be the transitions of the icTAs and . Then the refinement of a zone q is defined as follows:\n\nLemma 4\n\nLet be a class of and let e be an edge of the , then each of and forms a partition of in zones.\n\nThe correctness of the Algorithm 2 follows from the algorithm in [6, 17]. The definition above to generate a finer set of zones, which deals with delay transitions. The definition of , generate also a finer set of zones and distinguishes the states with discrete transitions. Termination is ensured by Lemma 4. Algorithm 2 describes the main steps of the decision procedure for multi-timed bisimulation checking. It is based on the function BuildSymbZoneGraph (i.e., Algorithm 1). The function PartitionZoneGraph returns stable set of zones . Given a set of zones , the Algorithm 2 computes the states from that are bisimilar up to the desired initial state .\n\nProposition 1\n\nLet q = be a zone. Let and be two states in q, then iff .\n\nTheorem 1\n\nDeciding multi-timed bisimulation between two icTA is EXPTIME-complete.\n\nAn example of the zone graph, partition and multi-timed bisimulation computed by our algorithms can be found in Fig. 4. The Fig. 4(a) shows two icTA and with the finite input alphabet , the set of processes Proc = , the set of clocks and > . The Fig. 4(b) shows the zone graph computed by Algorithm 1. The Fig. 4(c) shows the multi-timed bisimulation for and .\n\nFig. 4.\n\n(a) Composition of icTAs; (b) Zone graph; (c) bisimulation\n\n## 5 Related Work\n\nBecause TA are a general-purpose formalism, several implementations and extensions have been considered. For example, Puri [18] studied the semantics of robustness timed automata where clocks can drift in a bounded way, i.e. clocks may grow at independent rates in the interval . Krishnan [11] considered asynchronous distributed timed automata, where clocks evolve independently in each component. Akshay et al. concentrate on the untimed language of DTA. In a previous work [16], we suggested a model that has the same expressive power as event clock automata [2], but without studied possible simulation algorithms.\n\nThe notion of bisimulation for TA is studied in various contributions [4, 8, 9, 19, 20]. Cerans [9] gives a proof of decidability for timed bisimulation. Several techniques are used in the literature for providing algorithms capable of checking (bi-)simulation: Weise and Lenzkes [20] rely on a zone-based algorithm for weak bisimulation over TA, but no implementation is provided; Bulychev et al. [8] study timed simulation for simulation-checking games, for which an implementation is available from [4]; region construction for timed bisimulation was also considered by Akshay et al. [1], but never implemented; and more closely to our work, Tripakis and Yovine proposed a time-abstract bisimulation over TA in [19]. Krishnan [11] and our previous work [16] manipulated clock drifts as well for manipulating DTA, but without considering bisimulation.\n\n## 6 Conclusions\n\nBisimulation is a common technique to reduce the state space explosion issue encountered during model-checking of real-time systems. To enable the application of this technique for DTS modelled by icTA, we proposed an alternative semantics for capturing the execution of icTA, based on multi-timed words running over Multi-Timed Labelled Transition Systems. We extended the notion of bisimulation to such structures, and proposed an EXPTIME algorithm for checking decidability. We are now studying how to efficiently implement such structures and decidability algorithm, and plan to compare their performance against classical work as proposed in [4, 19].\n\nReferences\n\n1.\n\nAkshay, S., Bollig, B., Gastin, P., Mukund, M., Narayan Kumar, K.: Distributed timed automata with independently evolving clocks. In: Breugel, F., Chechik, M. (eds.) CONCUR 2008. LNCS, vol. 5201, pp. 82\u201397. Springer, Heidelberg (2008). doi:10.\u200b1007\/\u200b978-3-540-85361-9_\u200b10 CrossRef\n\n2.\n\nAlur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183\u2013235 (1994)MathSciNetCrossRef90010-8)MATH\n\n3.\n\nBalaguer, S., Chatain, T.: Avoiding shared clocks in networks of timed automata. In: Koutny, M., Ulidowski, I. (eds.) CONCUR 2012. LNCS, vol. 7454, pp. 100\u2013114. Springer, Heidelberg (2012). doi:10.\u200b1007\/\u200b978-3-642-32940-1_\u200b9 CrossRef\n\n4.\n\nBehrmann, G., Bouyer, P., Larsen, K.G., Pel\u00e1nek, R.: Lower and upper bounds in zone-based abstractions of timed automata. STTT 8(3), 204\u2013215 (2006)CrossRefMATH\n\n5.\n\nBengtsson, J., Yi, W.: Timed automata: semantics, algorithms and tools. In: Desel, J., Reisig, W., Rozenberg, G. (eds.) ACPN 2003. LNCS, vol. 3098, pp. 87\u2013124. Springer, Heidelberg (2004). doi:10.\u200b1007\/\u200b978-3-540-27755-2_\u200b3 CrossRef\n\n6.\n\nBlom, S., Orzan, S.: A distributed algorithm for strong bisimulation reduction of state spaces. Electr. Notes Theor. Comput. Sci. 68(4), 523\u2013538 (2002)CrossRef80390-1)MATH\n\n7.\n\nBouyer, P.: Forward analysis of updatable timed automata. Form. Methods Syst. Des. 24(3), 281\u2013320 (2004)MathSciNetCrossRefMATH\n\n8.\n\nBulychev, P., Chatain, T., David, A., Larsen, K.G.: Efficient on-the-fly algorithm for checking alternating timed simulation. In: Ouaknine, J., Vaandrager, F.W. (eds.) FORMATS 2009. LNCS, vol. 5813, pp. 73\u201387. Springer, Heidelberg (2009). doi:10.\u200b1007\/\u200b978-3-642-04368-0_\u200b8 CrossRef\n\n9.\n\n\u010cer\u0101ns, K.: Decidability of bisimulation equivalences for parallel timer processes. In: Bochmann, G., Probst, D.K. (eds.) CAV 1992. LNCS, vol. 663, pp. 302\u2013315. Springer, Heidelberg (1993). doi:10.\u200b1007\/\u200b3-540-56496-9_\u200b24 CrossRef\n\n10.\n\nDe Biasi, M., Snickars, C., Landern\u00e4s, K., Isaksson, A.: Simulation of process control with WirelessHART networks subject to clock drift. In: COMPSAC (2008)\n\n11.\n\nKrishnan, P.: Distributed timed automata. In: Workshop on Distributed Systems (1999)\n\n12.\n\nLaroussinie, F., Larsen, K.G., Weise, C.: From timed automata to logic \u2014 and back. In: Wiedermann, J., H\u00e1jek, P. (eds.) MFCS 1995. LNCS, vol. 969, pp. 529\u2013539. Springer, Heidelberg (1995). doi:10.\u200b1007\/\u200b3-540-60246-1_\u200b158 CrossRef\n\n13.\n\nMilner, R.: Communication and Concurrency. Prentice Hall, Upper Saddle River (1989)MATH\n\n14.\n\nMonot, A., Navet, N., Bavoux, B.: Impact of clock drifts on CAN frame response time distributions. In: ETFA, Toulouse, France (2011)\n\n15.\n\nOrtiz, J., Schobbens, P.-Y.: Extending timed bisimulation for distributed timed systems. Technical report, University of Namur (2016). http:\/\/\u200bwww.\u200binfo.\u200bfundp.\u200bac.\u200bbe\/\u200b~jor\/\u200bMulti-TimedReport\/\u200b\n\n16.\n\nOrtiz, J., Legay, A., Schobbens, P.-Y.: Distributed event clock automata. In: Bouchou-Markhoff, B., Caron, P., Champarnaud, J.-M., Maurel, D. (eds.) CIAA 2011. LNCS, vol. 6807, pp. 250\u2013263. Springer, Heidelberg (2011). doi:10.\u200b1007\/\u200b978-3-642-22256-6_\u200b23 CrossRef\n\n17.\n\nPaige, R., Tarjan, R.E.: Three partition refinement algorithms. SIAM J. Comput. 16(6), 973\u2013989 (1987)MathSciNetCrossRefMATH\n\n18.\n\nPuri, A.: Dynamical properties of timed automata. In: Ravn, A.P., Rischel, H. (eds.) FTRTFT 1998. LNCS, vol. 1486, pp. 210\u2013227. Springer, Heidelberg (1998). doi:10.\u200b1007\/\u200bBFb0055349 CrossRef\n\n19.\n\nTripakis, S., Yovine, S.: Analysis of timed systems using time-abstracting bisimulations. Form. Methods Syst. Des. 18(1), 25\u201368 (2001)CrossRefMATH\n\n20.\n\nWeise, C., Lenzkes, D.: Efficient scaling-invariant checking of timed bisimulation. In: Reischuk, R., Morvan, M. (eds.) STACS 1997. LNCS, vol. 1200, pp. 177\u2013188. Springer, Heidelberg (1997). doi:10.\u200b1007\/\u200bBFb0023458 CrossRef\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_5\n\n# Auto-Active Proof of Red-Black Trees in SPARK\n\nClaire Dross1 and Yannick Moy1\n\n(1)\n\nAdaCore, 75009 Paris, France\n\nClaire Dross\n\nEmail: dross@adacore.com\n\nAbstract\n\nFormal program verification can guarantee that a program is free from broad classes of errors (like reads of uninitialized data and run-time errors) and that it complies with its specification. Tools such as SPARK make it cost effective to target the former in an industrial context, but the latter is much less common in industry, owing to the cost of specifying the behavior of programs and even more the cost of achieving proof of such specifications. We have chosen in SPARK to rely on the techniques of auto-active verification for providing cost effective formal verification of functional properties. These techniques consist in providing annotations in the source code that will be used by automatic provers to complete the proof. To demonstrate the potential of this approach, we have chosen to formally specify a library of red-black trees in SPARK, and to prove its functionality using auto-active verification. To the best of our knowledge, this is the most complex use of auto-active verification so far.\n\nWork partly supported by the Joint Laboratory ProofInUse (ANR-13-LAB3-0007, http:\/\/\u200bwww.\u200bspark-2014.\u200borg\/\u200bproofinuse) and project VECOLIB (ANR-14-CE28-0018) of the French national research organization.\n\n## 1 Introduction\n\nFormal program verification allows programmers to guarantee that the programs they write have some desired properties. These properties may simply be that the program does not crash or behave erratically, or more complex critical properties related to safety or security. Being able to guarantee such properties will be essential for high assurance software as requirements are increasingly complex and security attacks more pervasive.\n\nSPARK is a subset of the Ada programming language targeted at safety- and security-critical applications. GNATprove is a tool that analyzes SPARK code and can prove absence of run-time errors and user-specified properties expressed as contracts. GNATprove is based on modular deductive verification of programs, analyzing each function in isolation based on its contract and the contracts of the functions it calls. The main benefit of this approach is that it allows using very precise semantics of programming constructs and powerful automatic provers. The main drawback is that top-level specifications are not sufficient. Programmers need to provide many intermediate specifications in the form of additional contracts, loop invariants and assertions.\n\nProviding the right intermediate specifications is a difficult art, but progress has been achieved in recent years through a method known as auto-active verification. Various languages and tools now provide features for effective auto-active verification. SPARK is among these. In this paper, we explore the capabilities of auto-active verification for automatically proving complex algorithms. We have chosen to target red-black trees because they are well-known, commonly used in practice, and yet sufficiently complex that no implementation of imperative red-black trees has been formally verified using auto-active verification. Our implementation of red-black trees, with all the code for auto-active verification, is publicly available in the repository of SPARK.1\n\n## 2 Preliminaries\n\n### 2.1 SPARK 2014\n\nSPARK is a subset of the Ada programming language targeted at safety- and security-critical applications. SPARK builds on the strengths of Ada for creating highly reliable and long-lived software. SPARK restrictions ensure that the behavior of a SPARK program is unambiguously defined, and simple enough that formal verification tools can perform an automatic diagnosis of conformance between a program specification and its implementation. The SPARK language and toolset for formal verification have been applied over many years to on-board aircraft systems, control systems, cryptographic systems, and rail systems [18].\n\nIn the versions of SPARK up to SPARK 2005, specifications are written as special annotations in comments. Since version SPARK 2014 [17], specifications are written as special Ada constructs attached to declarations. In particular, various contracts can be attached to subprograms: data flow contracts, information flow contracts, and functional contracts (preconditions and postconditions, introduced respectively by Pre and Post). An important difference between SPARK 2005 and SPARK 2014 is that functional contracts are executable in SPARK 2014, which greatly facilitates the combination of test and proof. The definition of the language subset is motivated by the simplicity and feasibility of formal analysis and the need for an unambiguous semantics. Tools are available that provide flow analysis and proof of SPARK programs.\n\nFlow analysis checks correct access to data in the program: correct access to global variables (as specified in data and information flow contracts) and correct access to initialized data. Proof is used to demonstrate that the program is free from run-time errors such as arithmetic overflow, buffer overflow and division-by-zero, and that the functional contracts are correctly implemented. GNATprove is the tool implementing both flow analysis and proof of SPARK code.\n\n### 2.2 Auto-Active Verification\n\nThe term auto-active verification was coined in 2010 by researcher Rustan Leino [15] to characterise tools where user input is supplied before VC generation [and] therefore lie between automatic and interactive verification (hence the name auto-active). This is in contrast to fully automatic verifiers for which the specification is fixed and interactive verifiers for which the user input is supplied after VC generation, which is the typical case when the reasoning engine is an interactive proof assistant. Auto-active verification is at the center of the academic formal program verification toolsets Dafny [14], the Eiffel Verification Environment (EVE) [9], Why3 [8] as well as the industrial formal program verification toolsets Frama-C2 and SPARK3.\n\nIn all these toolsets, auto-active verification consists in a set of specification features at the level of the source language, and a set of tool capabilities to interact with users at the level of the source code. The specification features consist at least in constructs to specify function contracts (preconditions and postconditions) and data invariants, as well as specialized forms of assertions (loop invariants and loop variants, assumptions and assertions). All the toolsets mentioned above also support ghost code, a feature to instrument code for verification. Ghost functions are also called lemmas when their main purpose is to support the proof of a property that is later used at the point where the function is called. See [12] for a comparison of how ghost code differs between Why3, Frama-C and SPARK. Various tool capabilities facilitate user interaction at source level: fast running time that exploits multiprocessor architectures and minimizes rework between runs, the ability to trade running time for more verification power, feedback from the toolset when verification is unsuccessful (counterexamples in particular).\n\nAuto-active verification in the above toolsets has been used to fully verify algorithms, libraries and even full applications: examples include a container library in Eiffel [19], distributed systems in Dafny [10], secure execution of apps in Dafny [11], binary heaps in Why3 [21], allocators in SPARK [5].\n\n### 2.3 Red-Black Trees\n\nRed-black trees are a kind of self-balancing binary search trees. Nodes in the tree are colored red or black, and balance is maintained by ensuring that two properties are preserved: (1) a red node can only have black children, and (2) every path from the root to a leaf has the same number of black nodes. The consequence of these two properties is that the path from the root to a leaf can be at most twice as long as the path from the root to another leaf.\n\nImplementations of red-black trees are used in the Linux kernel (in C) and standard container libraries for various languages (C++ STL, Java.util, Ada). The insertion and deletion algorithms work by inserting or deleting the node as in a binary search tree, which may violate properties (1) and (2) above, and then restoring the balance by working their way up on the path from the root to the point of insertion or deletion. At every node on this path, the algorithms may rotate the subtree, which consists in a local rearrangement of nodes to restore properties (1) and (2). These algorithms are sufficiently complex that no implementation of imperative red-black trees has been formally verified in Dafny, Eiffel or Why3. See Sect. 5 for a list of the closest works, including some using auto-active verification. We are following the algorithm from Cormen et al. [4] for insertion in a red-black tree. We did not implement the deletion algorithm, which would be very similar to insertion. In the same way, we did not verify that every branch in a red-black tree contains the same number of black nodes.\n\n## 3 Red-Black Trees in SPARK\n\n### 3.1 Invariants and Models\n\nImplementing red-black trees correctly from the pseudo-code algorithm in a textbook is straightforward, but understanding why the algorithm is correct is tricky, and thus the implementation is hard to verify formally. The main point of complexity is that it forces one to reason about different levels of properties all at once. Instead, we have divided the implementation into three distinct parts, each one concerned with one property level: binary trees, search trees and red-black trees. Binary trees maintain a tree structure on the underlying memory. Search trees build on binary trees by associating values to tree nodes and maintain the order of values in the tree. Red-black trees build on search trees and enforce balancing using the classical red-black tree coloring mechanism.\n\nThe property enforced at each level is expressed in a type invariant. In SPARK, the invariant may be temporarily violated inside the implementation of the functions that operate on the type, but are guaranteed to hold for external users of objects of that type. More precisely, functions that operate on a type can assume the invariant on entry and must restore it on exit (which leads to verification conditions in SPARK).\n\nBinary Trees: As explained in Sect. 3.2, binary trees are implemented as arrays, using the representation described in Fig. 1. Each node contains a reference to its left and right children, if any, as well as a reference to its parent and a position, which may be Top for the root, Right or Left otherwise depending on the node position with respect to its parent. The invariant of binary trees states that values of these fields are consistent across the tree. For example, the left child of a node has position Left and the node as parent.\n\nTo reason about the tree structure at a higher level, we provide a model (an abstract representation) of binary trees which makes explicit the access paths from the root to every node in the tree. It associates a sequence of directions, namely Right or Left, with each node in the binary tree, corresponding to the path from the root to the node. As the underlying array also contains unused cells that do not correspond to tree nodes, an additional boolean encodes whether the node belongs to the tree. Figure 2 gives the model of the binary tree presented in Fig. 1. In this example, all the nodes belong to the tree except the last one. The access paths written below each node can be used to reconstruct easily the high level view of the tree.\n\nFig. 1.\n\n(from left to right) Representation of nodes in binary trees. Example of a binary tree, for readability, parents and positions are not represented. A higher level view of the same binary tree.\n\nFig. 2.\n\nExample of model of a binary tree.\n\nFig. 3.\n\nType invariant of search trees. For a search tree T, Model (T) returns the model of the underlying binary tree of T. For each index I in the underlying array, if Model (T) (I).Reachable is true then I is reachable in T and Model (T) (I).Path is the sequence of directions corresponding to the path from the root of T to I. < stands for prefix order on paths.\n\nSearch Trees: The invariant of search trees states that the value stored in each node of the tree is larger than all the values stored in the subtree rooted at its left child and smaller than all the values stored in the subtree rooted at its right child. It is given in Fig. 3, together with an example of values that would fit the tree from Fig. 1. To express this invariant, we use the model of the underlying binary tree. The value stored at node J belonging to the subtree rooted at node I (where path inclusion from the root is used to determine that J belongs to the subtree rooted at node I) is smaller (resp. greater) than the value stored at node I if J belongs to the subtree rooted at the left (resp. right) child of I.\n\nRed-Black Trees: The invariant of red-black trees states that a red node can only have black children. It is given in Fig. 4. An example of colors that would fit the tree from Fig. 3 is also given in Fig. 4. This corresponds to property (1) of red-black trees as presented in Sect. 2.3. Verifying property (2) would require implementing a new inductive model function over binary trees, like the one we defined for reachability. As it would be very similar to the work presented here, and would essentially double the effort, we did not attempt it.\n\nFig. 4.\n\nType invariant of red-black trees. (Color figure online)\n\n### 3.2 Implementation\n\nOur implementation of red-black trees differs on two accounts from the straighforward implementation of the algorithm. First, as stated above, we used an array as the underlying memory for trees, instead of dynamically allocating nodes. This is to comply with a restriction of SPARK which does not allow pointers, but only references and addresses. The rationale for this restriction is that pointers make automatic proof very difficult due to possible aliasing. Hence trees are bounded by the size of the underlying array. As the algorithm for balancing red-black trees requires splitting and merging trees, we had the choice of either copying arrays for generating new trees, or sharing the same array between disjoint trees (coming from the splitting of a unique tree). For obvious efficiency reasons, we chose the latter. Hence we are defining a type Forest for possibly representing disjoint binary trees sharing the same underlying array.\n\nThe other distinguishing feature of our implementation is the layered design. Each module defining a type with an invariant also needs to provide functions for manipulating objects of the type while preserving their invariant. As an example, binary trees are not updated by direct assignments in the implementation of search trees, but using two new functions, Extract and Plug, which split and merge disjoint trees while preserving the forest invariant.\n\nAt the next layer, search trees are defined as records with two components: a binary tree along with an additional array of values. For search trees, we only need to consider forests that hold one tree identified through its root. Only intermediate values will hold true forests with multiple roots, while the tree is being rotated. The module defining search trees provides basic set functions, namely inserting a value into the tree and testing a value for membership in the tree. It also provides balancing functions for the upper layer of red-black trees. They allow rotating nodes of a search tree to the left or to the right while preserving the order between values. An example of such a rotation is given in Fig. 5. Defining these balancing functions inside the implementation of search trees rather than inside the implementation of red-black trees allows keeping all order-related concerns in the search tree layer. Indeed, balancing functions do not preserve balance, as they are to be called on unbalanced trees, but they do preserve order. Note that implementing the balancing functions at this level avoids the need for lifting low-level tree handling functions such as Plug and Extract at the next layer. All the functions defined on search trees are implemented using functions over binary trees.\n\nFig. 5.\n\nExample of application of Right_Rotate.\n\nRed-black trees are implemented in the same way as search trees by adding an array of colors to a search tree and using balancing functions to rebalance the tree after an insertion.\n\n### 3.3 Specification\n\nFunctional specifications of the insertion and membership functions that operate on red-black trees consist in simple contracts (preconditions and postconditions) presented in Fig. 6. These contracts use a model function Values that returns the set of values in the tree. Mem returns true if and only if the element is in the tree and Insert adds a new element in the tree.\n\nFig. 6.\n\nSpecification of red-black trees.\n\nThe most complex specifications have to do with the four properties to maintain over red-black trees:\n\n 1. 1.\n\nA red-black tree is always a valid binary tree (we can navigate it from the root in the expected way).\n\n 2. 2.\n\nThere is no memory leak (if we have inserted fewer than Max elements, there is still room enough in the data structure to insert a new element).\n\n 3. 3.\n\nThe values stored in the tree are ordered (it is a valid search tree).\n\n 4. 4.\n\nThe tree stays balanced (we only verify this property partially, that is, that red nodes can only have black children).\n\nAs already discussed, each property is specified at the most appropriate layer. The first property is enforced at the level of binary trees. The invariant on binary trees (see Sect. 3.1) ensures that the fields of a node (Parent, Position, Left, and Right) are consistent. This is not enough to ensure that all the allocated nodes in the forest belong to well-formed binary trees though, as it does not rule out degenerate, root-less, cyclic structures that would arise from linking the root of a binary tree as the child of one of its leafs. Still, this is enough to ensure that red-black trees are always well formed, as red-black trees always have a root. Note that the fact that every node in the forest is part of a well formed binary tree is ensured at the level of binary trees by enforcing that such degenerate structures can never be created in the contracts of functions operating on binary trees.\n\nThe second property is enforced at the level of search trees. It is specified as a postcondition of every function operating on search trees. Figure 7 shows the part of the postcondition of Right_Rotate ensuring that it has not introduced any dangling node. It uses the function Model described in Sect. 3.1 to reason about node reachability.\n\nFig. 7.\n\nPostcondition of Right_Rotate dealing with absence of memory leaks.\n\nThe third and fourth properties are expressed in the type invariant of respectively search trees and red-black trees as explained in Sect. 3.1.\n\nApart from these top-level specifications, many more specifications are needed on subprograms at lower layers (binary trees and search trees) in order to be able to prove the properties at higher layers (respectively search trees and red-black trees). This is inherent to the modular style of verification supported by GNATprove. For example, as Right_Rotate on search trees calls Plug and Extract on binary trees, the contracts for these functions need to provide enough information to verify both the absence of memory leaks as stated in the postcondition of Right_Rotate and the preservation of the order of values as stated in the invariant of search trees.\n\n### 3.4 Proof Principles\n\nVerifying our implementation of red-black trees has proved to be challenging, and above the purely automatic proving capabilities of GNATprove. There are several reasons for this:\n\n * The imperative, pointer-based implementation of red-black trees makes it difficult to reason about disjointness of different trees\/subtrees in the forest.\n\n * Reasoning about reachability in the tree structure involves inductive proofs, which automatic provers are notoriously bad at.\n\n * Reasoning about value ordering involves using transitivity relations, to deduce that ordering for two pairs of values (X, Y) and (Y, Z) can be extended to the pair (X, Z). This requires in general to find a suitable intermediate value Y, which usually eludes automatic provers.\n\n * The size of the formulas to verify, number of verification conditions, and number of paths in the program are large enough to defy provers scalability.\n\nTo work around these limitations, we used auto-active verification techniques, which, as described in Sect. 2.2, can guide automatic provers without requiring a proof assistant. We explain some of these techniques in this section.\n\nFig. 8.\n\nIntermediate lemma stating disjointness of trees in a forest.\n\nIntermediate Lemmas: One of the classical techniques in manual proof consists in factoring some useful part of a proof in an intermediate lemma so that it can be verified independently and used as many times as necessary. In auto-active verification, this can be done by introducing a procedure with no output, which, when called, will cause the deductive engine to verify its precondition and assume its postcondition. In Fig. 8, we show an intermediate lemma which can be used to verify that two trees of a single forest with different roots are disjoint. A caller of this function will have to verify that T1 and T2 are different valid roots in F and as a consequence we know that there can be no node reachable from both roots in F. Naturally, the lemma is not assumed, its actual proof is performed when verifying the procedure Prove_Model_Distinct.\n\nReasoning by Induction: Though some automatic provers are able to discharge simple inductive proofs, inductive reasoning still requires manual interaction in most cases. In auto-active style, an inductive proof can be done using loop invariants. GNATprove splits the verification of a loop invariant in two parts. First, it verifies that the invariant holds in the first iteration of the loop and then that it holds in any following iteration knowing that it held in the previous one. This behavior is exactly what we want for a proof by induction. For example, Fig. 9 demonstrates how the intermediate lemma presented in Fig. 8 can be verified using a loop to perform an induction over the size of the path from the root T1 to any node reachable from T1 in F. The loop goes from 1 to the maximum size of any branch in the forest F. We have written the property we wanted to prove as a loop invariant. To verify this procedure, GNATprove will first check that the invariant holds in the first iteration of the loop, that is, that T1 itself cannot be reached from T2. Then, it will proceed by induction to show that this holds for any node reachable from T1 in F.\n\nFig. 9.\n\nProof by induction over the path length from the root to a node in the tree.\n\nProviding Witnesses: When reasoning about value ordering, it is common to use transitivity. For example, when searching for a value in a search tree, we only compare the requested value with values stored along a single path in the tree, that is, the path where it was expected to be stored. All other values are ruled out by transitivity of the order relation: if value X is not found on this path, it cannot be equal to another value Z in the tree, as X and Z are on two opposite sides of the value Y at the root of the subtree containing both X and Z. Unfortunately, due to how they handle universal quantification, automatic provers used in GNATprove are usually unable to come up with the appropriate intermediate value to use in the transitivity relation. To achieve the proofs, we provided provers with the appropriate term whenever necessary. For example, function Find_Root in Fig. 10 computes the first common ancestor of two nodes in a search tree.\n\nFig. 10.\n\nFunction that computes a witness for transitivity applications.\n\n### 3.5 Ghost Code\n\nIn this experiment, we made an extensive use of ghost code, that is, code meant only for verification, that has no effect on the program behavior. We used it for two different purposes. The first use of ghost code is for specifying complex properties about our algorithms, in particular through model functions. As ghost code can be executed in SPARK, these ghost model functions can be used to produce complex test oracles that can be exercised in the test campaign.\n\nThe second use of ghost code in our experiment is for auto-active verification. In particular, the procedures used to encode intermediate lemmas are ghost, as they have no effect. What is more, we strived to keep all verification-only code inside ghost procedures so that it can be removed by the compiler and will not slow down the execution of the program. It is all the more important since the code is very inefficient, involving multiple loops and model constructions. As functional behaviors are complex, coming up with contracts for these ghost procedures can be painful, and produce huge, hard to read specifications. To alleviate this problem, we can benefit from a feature of GNATprove which inlines local subprograms with no contracts, allowing the proof to go through with less annotation burden. In this way, we can choose, on a case-by-case basis, if it is worthwhile to turn a chunk of auto-active proof into an intermediate lemma with its own contract, allowing for a modular verification, or if we prefer to have the tool automatically inline the proof wherever we call the ghost procedure.\n\n## 4 Development and Verification Data\n\nAll the execution times and verification times reported in this section were obtained on a Core i7 processor with 2,8 GHz and 16 GB RAM.\n\nThe code implementing the core algorithm for red-black trees, even when split in three modules for binary trees, search trees and red-black trees, is quite small, only 286 lines overall. But this code only accounts for 14% of the total lines of code, when taking into account contracts (22%) and more importantly ghost code (64%). Table 1 summarizes the logical lines of code as counted by the tool GNATmetric. It took roughly two weeks to develop all the code, contracts and ghost code to reach 100% automatic proof.\n\nTable 1.\n\nNumber of lines of code for operational code, contracts and ghost code. | Code | Contracts | Ghost | Total\n\n---|---|---|---|---\n\nBinary trees | 92 (10%) | 250 (28%) | 548 (62%) | 890\n\nSearch trees | 127 (12%) | 188 (17%) | 780 (71%) | 1095\n\nRed-black trees | 67 (52%) | 18 (14%) | 45 (35%) | 130\n\nTotal | 286 (14%) | 456 (22%) | 1373 (64%) | 2115\n\nThere are few simple top-level contracts for red-black trees (see Table 2). Many more contracts and assertions are needed for auto-active verification, in the form of subprogram contracts, type invariants, type default initial conditions, loop invariants and intermediate assertions which split the work between automatic provers and facilitate work of individual provers.\n\nTable 2.\n\nNumber of conjuncts (and-ed subexpressions) in contracts on types, on subprograms, in loop invariants and in assertions. Numbers in parentheses correspond to conjuncts for contracts on externally visible subprograms. | On types | On subprograms | On loops | Assertions | Total\n\n---|---|---|---|---|---\n\nBinary trees | 10 | 155 (73) | 42 | 12 | 219\n\nSearch trees | 2 | 138 (60) | 20 | 68 | 228\n\nRed-black trees | 2 | 4 (4) | 8 | 10 | 24\n\nTotal | 14 | 297 (177) | 70 | 90 | 471\n\nTaking both tables into account, it is clear that verification of search trees was the most costly in terms of overall efforts, with a large part of ghost code (71%) and many intermediate assertions needed (68 conjuncts). Verification of red-black trees on the contrary was relatively straighforward, with less ghost code than operational code (35% compared to 52%) and few intermediate assertions needed (10 conjuncts). This matches well the cognitive effort required to understand the correction of search trees compared to red-black trees. Note that the verification of red-black trees would probably have needed roughtly the same effort as binary trees if the second propery of red-black trees had been considered. Overall, ghost code accounts for a majority (64%) of the code, which can be explained by the various uses of ghost code to support automatic proof as described in Sect. 3.4.\n\nThe automatic verification that the code (including ghost code) is free of run-time errors and that it respects its contracts takes less than 30 min, using 4 cores and two successive runs of GNATprove at proof levels 2 and 3. As automatic provers CVC4, Z3 and Alt-Ergo are called in sequence on unproved Verification Conditions (VCs), it is not surprising that CVC4 proves a majority of VCs (3763), while Z3 proves 103 VCs left unproved by CVC4 and Alt-Ergo proves the last 3 remaining VCs, for a total of 3869 VCs issued from 2414 source code checks (1185 run-time checks, 231 assertions and 998 functional contracts).\n\nAs the code has been fully proved to be free of run-time errors and that all contracts have been proved, it is safe to compile it with no run-time checks, and only the precondition on insertion in red-black trees activated (since this might be violated by an external call). Disabling run-time checks is done through a compiler switch (-gnatp) and only enabling preconditions in red-black trees is done through a configuration pragma in the unit. Inserting one million integers in a red-black tree from 1 to 1 million leads to a violation of the balancing in 999,998 cases, which requires 999,963 left rotations and no right rotations. The running time for performing these 1 million insertions is 0.65 s without run-time checks, and 0.70 s with run-time checks (which are few due to the use of Ada range types for array indexes), or 0.65 s (respectively 0.70 s) per insertion.\n\nEnabling all contracts and assertions at run-time is also possible during tests. Here, ghost code is particularly expensive to run, as constructing the model for a binary tree is at worst quadratic in the size of the tree, and contracts contain quantifications on the maximal size of the tree that call functions which themselves quantify over the same size in their own contracts or code. In addition, the expensive operation of constructing the model is performed repeatedly in contracts, as SPARK does not yet provide a let-expression form. As a result, inserting one element in a tree of size one takes 2 min.\n\n## 5 Related Work\n\nThere have been several previous attempts at verifying red-black trees implementations. In particular, red-black trees are used in the implementation of ordered sets and maps in the standard library of the Coq proof assistant [1, 7]. As part of these libraries, the implementations have been proven correct using interactive proofs in Coq. These implementations notably differ from our work because they are written in a functional style, using recursive data types instead of pointers and recursive functions instead of loops. Similar libraries are provided for the Isabelle proof assistant [13]. Functional implementations of red-black trees have also been verified outside of proof assistants, using characteristic formulas [3], or in the Why3 programming language as part of VACID-0 competition [16]. This last implementation differs from the previous ones in that it is mostly auto-active, even if it uses Coq for a few verification conditions.\n\nVerifying imperative implementations of red-black trees is more challenging as it involves reasoning about the well-formedness of the tree structure, which comes for free in the functional implementations. As part of VACID-0, attempts have been made at verifying red-black trees in C using VCC and in Java using KeY [2]. Both attempts seem to have been left in preliminary stages though.\n\nMore recently, imperative implementations of red-black trees in C and Java have been verified using more specialized logics. Enea et al. obtained an automatic verification of a C implementation of red-black trees using separation logic, a logic specialized for the verification of heap manipulating programs [6]. In the same way, Stef\u0103nescu et al. were able to verify several implementations of red-black trees in particular in Java and C using matching logic [20]. As used in this work, matching logic provides a very precise, low-level view of the heap structure, allowing for powerful proofs on this kind of programs. Both works use specialized tools, which are specifically designed for verifying low-level, heap manipulating programs but which have never been used, to the best of our knowledge, to verify higher-level software.\n\n## 6 Conclusion\n\nIn this article, we have explained how, using auto-active techniques, we could achieve formal verification of key functional properties of an imperative implementation of red-black trees in SPARK. This is not an example of what should be a regular use of the SPARK toolset but rather a successful demonstration of how far we can go using such technology.\n\nHowever, the techniques presented on this example can be reused with significant benefits on a much smaller scale. In particular, we have shown that inductive proofs can be achieved rather straightforwardly using auto-active reasoning. The multi-layered approach, using type invariants and model functions to separate concerns, can also be reused to reason about complex data structures.\n\nTo popularize the use of auto-active techniques, we are also working on integrating simple interactive proof capabilities in GNATprove. This would allow applying the same techniques in a simpler, more straightforward way, and also to avoid polluting the program space with ghost code which is never meant to be executed.\n\nAcknowledgements\n\nWe would like to thank our colleague Ben Brosgol and the anonymous reviewers for their useful comments.\n\nReferences\n\n1.\n\nAppel, A.W.: Efficient verified red-black trees (2011). https:\/\/\u200bwww.\u200bcs.\u200bprinceton.\u200bedu\/\u200b~appel\/\u200bpapers\/\u200bredblack.\u200bpdf\n\n2.\n\nBruns, D.: Specification of red-black trees: showcasing dynamic frames, model fields and sequences. In: Wolfgang, A., Richard, B. (eds.) 10th KeY Symposium (2011)\n\n3.\n\nChargu\u00e9raud, A.: Program verification through characteristic formulae. ACM Sigplan Not. 45(9), 321\u2013332 (2010)CrossRefMATH\n\n4.\n\nCormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. The MIT Press, Cambridege (2009)MATH\n\n5.\n\nDross, C., Moy, Y.: Abstract software specifications and automatic proof of refinement. In: Lecomte, T., Pinger, R., Romanovsky, A. (eds.) RSSRail 2016. LNCS, vol. 9707, pp. 215\u2013230. Springer, Cham (2016). doi:10.\u200b1007\/\u200b978-3-319-33951-1_\u200b16\n\n6.\n\nEnea, C., Sighireanu, M., Wu, Z.: On automated lemma generation for separation logic with inductive definitions. In: Finkbeiner, B., Pu, G., Zhang, L. (eds.) ATVA 2015. LNCS, vol. 9364, pp. 80\u201396. Springer, Cham (2015). doi:10.\u200b1007\/\u200b978-3-319-24953-7_\u200b7 CrossRef\n\n7.\n\nFilli\u00e2tre, J.-C., Letouzey, P.: Functors for proofs and programs. In: Schmidt, D. (ed.) ESOP 2004. LNCS, vol. 2986, pp. 370\u2013384. Springer, Heidelberg (2004). doi:10.\u200b1007\/\u200b978-3-540-24725-8_\u200b26 CrossRef\n\n8.\n\nFilli\u00e2tre, J.-C., Paskevich, A.: Why3 \u2014 where programs meet provers. In: Felleisen, M., Gardner, P. (eds.) ESOP 2013. LNCS, vol. 7792, pp. 125\u2013128. Springer, Heidelberg (2013). doi:10.\u200b1007\/\u200b978-3-642-37036-6_\u200b8. https:\/\/\u200bhal.\u200binria.\u200bfr\/\u200bhal-00789533 CrossRef\n\n9.\n\nFuria, C.A., Nordio, M., Polikarpova, N., Tschannen, J.: AutoProof: auto-active functional verification of object-oriented programs. Int. J. Softw. Tools Technol. Transfer 1\u201320 (2016). http:\/\/\u200bdx.\u200bdoi.\u200borg\/\u200b10.\u200b1007\/\u200bs10009-016-0419-0\n\n10.\n\nHawblitzel, C., Howell, J., Kapritsos, M., Lorch, J.R., Parno, B., Roberts, M.L., Setty, S., Zill, B.: IronFleet: proving practical distributed systems correct. In: Proceedings of the 25th Symposium on Operating Systems Principles, SOSP 2015, pp. 1\u201317. ACM, New York (2015). http:\/\/\u200bdoi.\u200bacm.\u200borg\/\u200b10.\u200b1145\/\u200b2815400.\u200b2815428\n\n11.\n\nHawblitzel, C., Howell, J., Lorch, J.R., Narayan, A., Parno, B., Zhang, D., Zill, B.: Ironclad apps: end-to-end security via automated full-system verification. In: Proceedings of the 11th USENIX Conference on Operating Systems Design and Implementation, OSDI 2014, pp. 165\u2013181. USENIX Association, Berkeley (2014). http:\/\/\u200bdl.\u200bacm.\u200borg\/\u200bcitation.\u200bcfm?\u200bid=\u200b2685048.\u200b2685062\n\n12.\n\nKosmatov, N., March\u00e9, C., Moy, Y., Signoles, J.: Static versus dynamic verification in Why3, Frama-C and SPARK 2014. In: Margaria, T., Steffen, B. (eds.) ISoLA 2016. LNCS, vol. 9952, pp. 461\u2013478. Springer, Cham (2016). doi:10.\u200b1007\/\u200b978-3-319-47166-2_\u200b32. https:\/\/\u200bhal.\u200binria.\u200bfr\/\u200bhal-01344110 CrossRef\n\n13.\n\nLammich, P., Lochbihler, A.: The isabelle collections framework. In: Kaufmann, M., Paulson, L.C. (eds.) ITP 2010. LNCS, vol. 6172, pp. 339\u2013354. Springer, Heidelberg (2010). doi:10.\u200b1007\/\u200b978-3-642-14052-5_\u200b24 CrossRef\n\n14.\n\nLeino, K.R.M.: Dafny: an automatic program verifier for functional correctness. In: Clarke, E.M., Voronkov, A. (eds.) LPAR 2010. LNCS (LNAI), vol. 6355, pp. 348\u2013370. Springer, Heidelberg (2010). doi:10.\u200b1007\/\u200b978-3-642-17511-4_\u200b20. http:\/\/\u200bdl.\u200bacm.\u200borg\/\u200bcitation.\u200bcfm?\u200bid=\u200b1939141.\u200b1939161 CrossRef\n\n15.\n\nLeino, K.R.M., Moskal, M.: Usable auto-active verification. In: Usable Verification Workshop (2010). http:\/\/\u200bfm.\u200bcsl.\u200bsri.\u200bcom\/\u200bUV10\/\u200b\n\n16.\n\nLeino, K.R.M., Moskal, M.: VACID-0: verification of ample correctness of invariants of data-structures, edition 0 (2010)\n\n17.\n\nMcCormick, J.W., Chapin, P.C.: Building High Integrity Applications with SPARK. Cambridge University Press, Cambridge (2015)CrossRefMATH\n\n18.\n\nO'Neill, I.: SPARK - a language and tool-set for high-integrity software development. In: Boulanger, J.L. (ed.) Industrial Use of Formal Methods: Formal Verification. Wiley, Hoboken (2012)\n\n19.\n\nPolikarpova, N., Tschannen, J., Furia, C.A.: A fully verified container library. In: Bj\u00f8rner, N., de Boer, F. (eds.) FM 2015. LNCS, vol. 9109, pp. 414\u2013434. Springer, Cham (2015). doi:10.\u200b1007\/\u200b978-3-319-19249-9_\u200b26 CrossRef\n\n20.\n\nStef\u0103nescu, A., Park, D., Yuwen, S., Li, Y., Ro\u015fu, G.: Semantics-based program verifiers for all languages. In: Proceedings of the 2016 ACM SIGPLAN International Conference on Object-Oriented Programming, Systems, Languages, and Applications, pp. 74\u201391. ACM (2016)\n\n21.\n\nTafat, A., March\u00e9, C.: Binary heaps formally verified in Why3. Research report 7780, INRIA, October 2011. http:\/\/\u200bhal.\u200binria.\u200bfr\/\u200binria-00636083\/\u200ben\/\u200b\n\nFootnotes\n\n1\n\nhttps:\/\/\u200bgithub.\u200bcom\/\u200bAdaCore\/\u200bspark2014\/\u200btree\/\u200bmaster\/\u200btestsuite\/\u200bgnatprove\/\u200btests\/\u200bred_\u200bblack_\u200btrees.\n\n2\n\nhttp:\/\/\u200bframa-c.\u200bcom\/\u200b.\n\n3\n\nhttp:\/\/\u200bwww.\u200badacore.\u200bcom\/\u200bsparkpro\/\u200b.\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_6\n\n# Analysing Security Protocols Using Refinement in iUML-B\n\nColin Snook1 , Thai Son Hoang1 and Michael Butler1\n\n(1)\n\nECS, University of Southampton, Southampton, U.K.\n\nColin Snook (Corresponding author)\n\nEmail: cfs@ecs.soton.ac.uk\n\nThai Son Hoang\n\nEmail: t.s.hoang@ecs.soton.ac.uk\n\nMichael Butler\n\nEmail: mjb@ecs.soton.ac.uk\n\nAbstract\n\nWe propose a general approach based on abstraction and refinement for constructing and analysing security protocols using formal specification and verification. We use class diagrams to specify conceptual system entities and their relationships. We use state-machines to model the protocol execution involving the entities' interactions. Features of our approach include specifying security principles as invariants of some abstract model of the overall system. The specification is then refined to introduce implementable mechanisms for the protocol. A gluing invariant specifies why the protocol achieves the security principle. Security breaches arise as violations of the gluing invariant. We make use of both theorem proving and model checking techniques to analyse our formal model, in particular, to explore the source and consequence of the security attack. To demonstrate the use of our approach we explore the mechanism of a security attack in a network protocol.\n\nKeywords\n\nVirtual LANSecurityEvent-BiUML-B\n\n## 1 Introduction\n\nEnsuring security of protocols is a significant and challenging task in the context of autonomous cyber-physical systems. In this paper, we investigate the use of formal models of protocols in order to discover and analyse possible security threats. In particular, we are interested in the role of formal models in identifying security flaws, exploring the nature of attacks that exploit these flaws and proposing measures to counter flaws in systems that are already deployed.\n\nOur contribution is a general approach based on abstraction and refinement for constructing and analysing security protocols. The approach is suitable for systems containing multiple conceptual entities (for example, data packets, devices, information tags, etc.). We use class diagrams to specify the relationships between entities and state-machines to specify protocols involved in their interactions. Security principles are defined as constraints on the system entities and their relationships. We use refinements of these models, to gradually introduce implementation details of the protocols that are supposed to achieve these security properties. The use of abstract specification and refinement allows us to separate the security properties from the protocol implementation. In particular, possible security flaws are detected as violations of the gluing invariants that link the abstract and concrete models. Further analysis helps to pinpoint the origin and nature of attacks that could exploit these flaws. The approach has been developed within the Enable-S3 project [4] which aims to provide cost-efficient cross-domain verification and validation methods for autonomous cyber-physical systems. Within Enable-S3, we are applying the approach on case studies in the avionics and maritime domains. The case-studies involve secure authentication and communications protocols as part of larger autonomous systems.\n\nWe illustrate our approach with an analysis of Virtual Local Area Network (VLAN) operation including the principle of tagging packets. We explore a known security flaw of these systems, namely double tagging. We use the Event-B method and iUML-B class diagrams and state-machines as the modelling tool.\n\nThe rest of the paper is structured as follows. Section 2 gives some background on the case study, the methods and tools that we use. The main content of the paper is in Sect. 3 describing the development using iUML-B and analysis of the VLAN model. Finally, we summarise our approach in Sect. 4 and conclude in Sect. 5. For more information and resources, we refer the reader to our website: http:\/\/\u200beprints.\u200bsoton.\u200bac.\u200buk\/\u200bid\/\u200beprint\/\u200b403533. The website contains the Event-B model of the VLAN.\n\n## 2 Background\n\n### 2.1 VLAN Tagging\n\nA Local Area Network (LAN) consists of devices that communicate over physical data connections that consist of multiple steps forming routes via intermediate network routing devices called switches. The 'trunk' connections between switches are used by multiple routes. A VLAN restricts communication so that only devices that share the same VLAN as the sender, can receive the communication thus providing a way to group devices irrespective of physical topology. In order to achieve this, switches attach a tag to message packets in order to identify the sender's VLAN. The tag is removed before being sent to the receiving device. Typically, a system uses one VLAN identity to represent a default VLAN. This is known as the native VLAN. A packet intended for the native VLAN does not require tagging. The IEEE 802.1Q standard [6] is the most common protocol for ethernet-based LANs and includes a system for VLAN tagging and associated handling procedures. The standard permits multiple VLAN tags to be inserted so that the network infrastructure can use VLANs internally as well as supporting client VLAN tagging. A well-known security attack exploits double tagging by hiding a tag for a supposedly inaccessible VLAN behind a tag for the native VLAN. The receiving switch sees the unnecessary native VLAN tag and removes it before sending the packet on to the next switch. This switch then sees the tag for the inaccessible VLAN and routes the packet accordingly so that the packet infiltrates the targeted VLAN. Double tagging attacks can be avoided by not using (i.e. de-configuring) the native VLAN.\n\n### 2.2 Event-B\n\nEvent-B [1] is a formal method for system development. Main features of Event-B include the use of refinement to introduce system details gradually into the formal model. An Event-B model contains two parts: contexts and machines. Contexts contain carrier sets, constants, and axioms constraining the carrier sets and constants. Machines contain variables , invariants constraining the variables, and events. An event comprises a guard denoting its enabled-condition and an action describing how the variables are modified when the event is executed. In general, an event has the following form, where are the event parameters, is the guard of the event, and is the action of the event1.\n\n(1)\n\nA machine in Event-B corresponds to a transition system where variables represent the states and events specify the transitions. Contexts can be extended by adding new carrier sets, constants, axioms, and theorems. Machine M can be refined by machine N (we call M the abstract machine and N the concrete machine). The state of M and N are related by a gluing invariant where are variables of M and N, respectively. Intuitively, any \"behaviour\" exhibited by N can be simulated by M, with respect to the gluing invariant J. Refinement in Event-B is reasoned event-wise. Consider an abstract event and the corresponding concrete event . Somewhat simplifying, we say that is refined by if guard is stronger than that of and action can be simulated by action, taking into account the gluing invariant J. More information about Event-B can be found in [5]. Event-B is supported by the Rodin platform (Rodin) [2], an extensible toolkit which includes facilities for modelling, verifying the consistency of models using theorem proving and model checking techniques, and validating models with simulation-based approaches.\n\n### 2.3 iUML-B\n\niUML-B [8\u201310] provides a diagrammatic modelling notation for Event-B in the form of state-machines and class diagrams. The diagrammatic models are contained within an Event-B machine and generate or contribute to parts of it. For example a state-machine will automatically generate the Event-B data elements (sets, constants, axioms, variables, and invariants) to implement the states while Event-B events are expected to already exist to represent the transitions. Transitions contribute further guards and actions representing their state change, to the events that they elaborate. An existing Event-B set may be associated with the state-machine to define its instances. In this case the state-machine is 'lifted' so that it has a value for every instance of the associated set. State-machines are typically refined by adding nested state-machines to states.\n\nClass diagrams provide a way to visually model data relationships. Classes, attributes and associations are linked to Event-B data elements (carrier set, constant, or variable) and generate constraints on those elements. For the VLAN we use class diagrams extensively to model the sets of entities and their relationships and we use state-machines to constrain the sequences of events and to declare state dependant invariant properties.\n\nFig. 1.\n\nExample iUML-B diagrams\n\nFigure 1 shows an abstract example of an iUML-B model to illustrate the features we have used in the VLAN. We give the corresponding translation into Event-B in Fig. 2. In Fig. 1a, there are three classes; which elaborate carrier sets, and , which is a sub-class of and elaborates a variable. An attribute or association of a class can have a combination of the following properties: surjective, injective, total, and functional. Attributes of and of are total and functional, while of is functional. An injective association defined between and elaborates a constant. Figure 1b shows an example of a state-machine, which is lifted to the carrier set for its instances. This is also the instances set for the class and a state of the state-machine is named after its variable sub-class, . Further sub-states and are modelled as variable subsets of . The state of an instance is represented by its membership of these sets. The state-machine transitions are linked to the same events as the methods of . Hence the state-machine constrains the invocation of class methods for a particular instance of the class. The contextual instance is modelled as a parameter which can be used in additional guards and actions in both the class diagram and the state-machine.\n\nFig. 2.\n\nEvent-B translation of the iUML-B example\n\nThe transition , from the initial state to also enters parent state and therefore represents a constructor for the class . The class method is also defined as a constructor and automatically generates an action to initialise the instance of with its defined initial value. The same event is also given as a method of class in order to generate a contextual instance which is used in an additional (manually entered) guard to define a value for the association of the super-class. The transition and method is a normal method of class , which is available when the contextual instance exists in and , and changes state by moving the instance from to . The other guards and actions shown in this event concerning parameter and attribute , have been added as additional guards and actions of the transition or method. These are not shown in the diagram as they are entered using the diagram's properties view. The state invariant shown in state applies to any instance while it is in that state. The Event-B version of the invariant is quantified over all instances and an antecedent added to represent the membership of . In the rest of this paper we do not explain the translation to Event-B.\n\n### 2.4 Validation and Verification\n\nConsistency of Event-B models is provided via means of proof obligations, e.g., invariant preservation by all events. Proof obligations can be discharged automatically or manually using the theorem provers of Rodin. Another important tool for validation and verification of our model is ProB [7]. ProB provides model checking facility to complement the theorem proving technique for verifying Event-B models. Features of the ProB model checker include finding invariant violations and deadlock for multiple refinement levels simultaneously. Furthermore, ProB also offers an animator enabling users to validate the behaviour of the models by exploring execution traces. The traces can be constructed interactively by manual selection of events or automatically as counter-examples from the model checker. Here, an animation trace is a sequence of event execution with parameters' value. The animator shows the state of the model after each event execution in the trace.\n\n## 3 Development\n\nIn this section, we discuss the development of the model. The model consists of three refinement levels. The abstract level captures the essence of the security property which is proven for the abstract representation of events that make new packets and move them around the network. The first refinement introduces some further detail of the network system and is proven to be a valid refinement of the first model. That is, it maintains the security property. Both of these first levels are un-implementable because they refer directly to a conceptual property of a packet which is the VLAN that the packet was intended for. In reality it is not possible to tell from a raw packet, which VLAN it was originally created for. The second refinement introduces tagging as a means to implement a record of this conceptual property. The refinement models nested tagging and the behaviour of a typical switch which, apart from tagging packets depending on their source, also removes tags for the native LAN. The automatic provers are unable to prove that removing tags satisfies the gluing invariant. This is the well-known security vulnerability to double tagging attacks. Adding a constraint to, effectively, disallow the native LAN from being configured as a VLAN, allows the provers to discharge this proof obligation. This corresponds to the usual protective measure against double tagging attacks.\n\n### 3.1 M0: An Abstract Model of VLAN Security\n\nWe aim to make the first model minimally simple while describing the essential security property. We use a class diagram (Fig. 3) to introduce some 'given' sets for data packets (class ) and VLANs (class ). The constant association describes the that each packet is intended for. (Note that this is a conceptual relationship representing an intention and hence the implementation cannot access it). We abstract away from switches and devices and introduce a set of nodes, class , to represent both. The communications topology is given by the constant association, , which maps nodes to nodes in a many to many relationship.\n\nFig. 3.\n\nAbstract model of VLAN security requirement\n\nThe set of VLANs that a particular node is allowed to see, is given by the constant association . For now this is a many to many relationship but in later refinements we will find that, while switches are allowed to see all VLANs, devices may only access the packets of one VLAN.\n\nThe class represents the subset of packets that currently exist (whereas, represented all possible packets that might exist currently or in the past or future). A packet that exists, always has exactly one owner node. The method takes a non-existing packet from and adds it to and initialises the new packet's to the contextual node instance. The method changes the of an existing packet to a new node that is non-deterministically selected from the nodes that the current owner node is directly linked to via .\n\nThe class invariant, , in class describes the security property2:\n\n(2)\n\ni.e., the VLAN for which this packet is intended, belongs to the VLANs that its owner is allowed to see. For this invariant to hold we need to restrict the method so that it only moves packets to a new owner that is allowed to see the VLAN of the packet. For now we do this with a guard, , where is the packet and is the destination node. However, this guard must be replaced in later refinements because it refers directly to the conceptual property and is therefore not implementable. We also ensure that only creates packets with a value that its maker node is allowed to see.\n\nWe use a state-machine (Fig. 3) to constrain the sequence of events that can be performed on a packet. The state-machine is lifted to the set of all packets, At this stage we only require that is the initial event that brings a packet into existence, and this can be followed by any number of events.\n\nFig. 4.\n\nFirst refinement of VLAN introducing switches and devices\n\n### 3.2 M1: Introducing Switches and Devices\n\nIn M0, to keep things simple we did not distinguish between switches and devices. However, they have an important distinction since switches are allowed to see all VLAN packets. The design will utilise this distinction so we need to introduce it early on. In M1 (Fig. 4) we introduce two new classes, and , as subtypes of .\n\nSince switches are implicitly associated with all VLANS (i.e. trusted), we do not need to model which VLANs they are allowed to access. Therefore, we replace with a functional association whose domain (source) is restricted to . It is a total function, rather than a relation, because a device has access to exactly one VLAN and again we model this as a constant function since we do not require it to vary.\n\nSwitches are not allowed to create new packets so we move to . Since, when moving a packet, the destination kind affects the security checks, we split into two alternatives: which does not need any guard concerning and where we replace the guard, , with to reflect the data refinement. Note however, that the new guard still refers to .\n\nThe refinement introduces the need for some further constraints on the sequence of events for a particular package. We introduce sub-states and (Fig. 4) to show that a packet can only be moved to a device from a switch. Note that these states could be derived from (hence the invariants in states and ) however, the state diagram helps visualise the process relative to a packet which will become more significant in the next refinement level.\n\nFig. 5.\n\nSecond refinement of VLAN introducing tagging\n\n### 3.3 M2: Introducing Tagging\n\nWe can now introduce the tagging mechanism that allows switches to know which VLAN a packet is intended for. Our aim is that, in this refined model, switches should not use the relationship other than for proving that the tag mechanism achieves an equivalent result. We introduce a new given set, (Fig. 5) which has a total functional association with . This function represents the VLAN identifier within a tag, which is part of the implementation, i.e., guards that reference are implementable. We add a variable partial function association, , from to , which represents the tagging of a packet.\n\nIn typical LAN protocols, already tagged packets can be tagged again to allow switches to use VLANs for internal system purposes. Although, for simplification, we omit this internal tagging, we allow tags to be nested so that we can model a double tagging attack by a device. Therefore we model nested tags with a variable partial functional association, from to itself. When a packet arrives at a switch from a device, the switch can tell which VLAN it belongs to from the port that it arrived on. However, for simplicity, we avoid introducing ports in this refinement. Instead we model this information via a variable functional association from to . Hence a switch can determine which VLAN a packet, p, is for via . Port configuration could easily be introduced in a subsequent refinement without altering the main points of this article. A significant behaviour of switches that relates to security is how they deal with packets for the native VLAN. Therefore, in the Event-B context for M2, we introduce a specific instance of called .\n\nThe behaviour (Fig. 5) is refined to add procedures for handling tagged packets. State is split into three sub-states, for packets that have just been received from a device, for packets from a device that have been successfully processed and for packets that are found to be invalid. A device may now send an untagged packet to a switch (transition and allow the switch to determine appropriate tagging, or it may tag the packet itself (transition in which case the switch will check the tag. In the latter case the tag may be valid or invalid and may have nested tags.\n\nAfter receiving a packet, , at the state , the new owner switch processes it by taking one of the following transitions:\n\n * : if is not already tagged, a tag, , such that , is added and the packet is accepted by moving it to state .\n\n * : if is already tagged correctly (i.e., ) and not tagged as the native VLAN (i.e. ) the packet is accepted as is.\n\n * : if is correctly tagged for the native VLAN (i.e., ), the tag is removed and the packet is accepted. The tag is removed in such as way as to leave tagged with a nested tag if any.\n\n * : if is incorrectly tagged (i.e., ), it is rejected by moving it to state which has no outgoing transitions.\n\nAfter processing packet, , the switch can either pass it on to another switch or, if available, pass it to a device via one of the following transitions:\n\n * : if is not tagged, and the switch is connected to a device, , on the native VLAN (i.e. ),\n\n * : if is tagged and the switch is connected to a device, , which is on the VLAN indicated by the tag (i.e. ).\n\nIt is these two transitions that refine , which need to establish the security invariant using tags rather than the unimplementable guard concerning . This has been done as indicated above by the conditions on . It can been seen by simple substitution, that the state invariants of enable the prover to establish that the new guards are at least as strong as the abstract one ( ). We also need to prove that these state invariants are satisfied by the incoming transitions of state . A state invariant is added to in order to allow the prover to establish this. Again, this can be checked using simple substitutions of the guards of , and using this state invariant. The other two state invariants for are merely to establish well-definedness of the function applications. The state invariants of state are clearly established by the actions of incoming transitions and .\n\n### 3.4 Analysis\n\nWe analyse the protocol using both theorem proving and model checking techniques. Given the model in Sect. 3.3, the automatic provers discharge all proof obligations except for one. The prover cannot establish that the transition establishes the state-invariant\n\n(3)\n\nof state . In general, a failed invariant preservation proof identifies the property (the invariant) that may be at risk and the transition (event) that may violate it. We say 'may' because lack of proof does not necessarily indicate a problem. It can be a result of insufficient prover power. We therefore use the ProB model checker to confirm the problem.\n\nFig. 6.\n\nNetwork topology for analysis\n\nAs with any model checker, we instantiate the context of the system, in this case, the network topology. The network topology under consideration can be seen in Fig. 6. The switches, i.e., and have access to all VLANs, namely, , and . The native VLAN is defined to be . Devices belong to and devices and both belong to We define two packets and where is intended for and is for , i.e.,\n\nFinally, we define two tags and corresponding to and , respectively. A tag with nested tag is numbered accordingly, for example, is for and has an inner tag for . Our subsequent analysis is based on this particular setting.\n\nFirstly, we want to identify whether the state-invariant (3) can indeed be violated. We model check the whole refinement-chain from M0 to M2. ProB indeed identifies a counter-example trace which leads to the violation of the invariant as follow.\n\n(4)\n\n(5)\n\n(6)\n\nIn the trace, creates (4) before moving it to with tag (5). When removes the native tag from (6), resulting in the state-invariant (3) becomes invalid since is intended for , but it is now tagged with , which is identified for\n\nHowever, the violation could be caused by an unnecessarily strong gluing invariant. To verify whether the security invariant (2) is indeed violated in M2, we model check M2 without M0 and M1 but with the security invariant copied from M0 to M2 in place of the gluing invariant. Once again, ProB returns a counter-example trace which is an extension of the previous trace, i.e.,\n\n(7)\n\n(8)\n\n(9)\n\n(10)\n\nAfter removing the native tag of (9), the packet is moved from to (10). At this time, has arrived to a device which does not have permission to receive any packet for .\n\nNote that there are three different points in the process leading to the security breach:\n\n * the point where the security attack is initiated (8),\n\n * the point where the design assumptions are violated and (9),\n\n * the point where the security is breached (10).\n\nComing back to the original failed invariant preservation proof obligation, we can now confirm that it is indeed possible for the invariant to be violated3. Examination of the pending goal that the prover is attempting to prove reveals more detail about the problem.\n\nIt shows that the prover has replaced the packet's tag with its nested tag in the design property, and is attempting to show that the VLAN of the nested tag is also for the correct VLAN for the packet. From the theorem prover, therefore, we know that\n\n * the switch's procedure of removing the native tag causes a problem,\n\n * the problem is that the nested tag becomes the packets main tag and does not necessarily indicate the correct VLAN.\n\nWhen a constraint, , i.e., no device can be configured to use the native VLAN, is added to the model the proof obligation is immediately discharged since the guard of the transition can easily be shown to be false. This constraint corresponds to the recommended protective action to prevent double tagging attacks.\n\nOverall, the theorem provers can identify the security flaw in a design or protocol. They do not need to find an example attack but can pinpoint the exact nature of the flaw directly. This is because proof obligations are generated from the actions of individual events. While the provers indicates the nature of the violation of the design assumption, they do not reveal the complete sequence from attack to security breach. The model-checker, while being restricted to example instantiations, is able to illustrate the process from initial attack through to security breach.\n\n## 4 Summary of Approach\n\nTo summarise, our approach is as follows:\n\n 1. 1.\n\nCreate an iUML-B Class diagram model of the entities and relationships that are essential concepts of the system. Add a state-machine to model the required behaviour of the system. Only model sufficient concepts to express the security property. Do not model the mechanism that implements the security.\n\n 2. 2.\n\nExpress the security property as an invariant over the entities in the model. Make sure that the model preserves the invariant.\n\n 3. 3.\n\nRefine the iUML-B model (possibly over several iterations) to introduce the mechanism that will ensure the system is secure. Do not constrain the behaviour of elements unless the security system has control over this behaviour. That is, allow attacks to occur within the model.\n\n 4. 4.\n\nAnimate each refinement level to ensure that the model behaves in a useful way. This is important to validate that our formal model captures the behaviour of the real system.\n\n 5. 5.\n\nIf any POs are not proven check the type of PO and the goal to see whether there is a mistake in the model. Correct the model as necessary.\n\n 6. 6.\n\nIf unproven POs remain for the gluing invariant, this may mean that the security mechanism has a flaw. Analyse the problem as follows:\n\n * Examine the PO. Note the event that it relates to and examine the goal of the prover. This can often be used to interpret what is going wrong or whether a manual proof is possible.\n\n * Run the model-checker to establish that there really is a problem. If the model checker can not find a trace to the violation, a manual proof may be possible.\n\n * Remove the gluing invariant and copy the security property invariant from the abstract model and run the model checker (without previous refinement levels). If it does not find a trace that violates the security property, the gluing invariant may be too strong.\n\n * If a trace to the security property is found there is a flaw in the protocol. The trace can be examined to analyse the nature of the attack, the flaw in the security mechanism and how it leads to the security violation.\n\nIn the example presented in this paper, the abstract model (step 1) M0 was developed in Sect. 3.1, and the security invariant (step 2) was introduced in the same section. The refinement process (step 3) involved an intermediate refinement M1 in Sect. 3.2 and a final refinement M2 in Sect. 3.3. At each refinement level, animation with ProB (step 4) and examination of unproven POs (step 5), helped us to arrive at a correct and useful model. A security flaw was detected and analysed (step 6) as described in Sect. 3.4.\n\n## 5 Conclusion\n\nOur investigation into a known example of a security vulnerability indicates that formal modelling with strong verification tools can be extremely beneficial in understanding security problems. The tools at our disposal include an automatic theorem prover as well as a model checker. In our previous work on safety-critical systems we have found that these tools exhibit great synergy and this is also the case when analysing security protocols.\n\nWe use iUML-B class diagrams and state-machines as a diagrammatic representation of the Event-B formalism. The diagrams help us create, visualise and communicate the models leading to a better understanding of the systems.\n\nAlthough we use animation to informally validate system behaviour, we have not yet done any rigorous analysis of liveness properties. A future aim of our research is to incorporate liveness reasoning into our approach.\n\nThis refinement-based approach can be applied to any problem that involves sets of entities that are interacting in some way via a procedure or protocol. For example, an authentication protocol such as Needham-Schroder could be modelled abstractly as a class of agents sending messages and receiving them with property perceived sender based on an actualSender. This could then be refined to replace direct references to the actual sender, with encrypted nonces.\n\nFinally, we envisage that without refinement, formulating the gluing invariant that links the specification to the implementation would, in general, be challenging. Here the role of the gluing invariant is essential as its violation helps the designer to identify the point where the design assumptions are offended, causing the actual security breach. A similar observation has been made in [3].\n\nAcknowledgement\n\nThis work is funded by the Enable-S3 Project, http:\/\/\u200bwww.\u200benable-s3.\u200beu.\n\nReferences\n\n1.\n\nAbrial, J.-R.: Modeling in Event-B: System and Software Engineering. Cambridge University Press, Cambridge (2010)CrossRefMATH\n\n2.\n\nAbrial, J.-R., Butler, M., Hallerstede, S., Hoang, T.S., Mehta, F., Voisin, L.: Rodin: an open toolset for modelling and reasoning in Event-B. Softw. Tools Technol. Transf. 12(6), 447\u2013466 (2010)CrossRef\n\n3.\n\nButler, M.: On the use of data refinement in the development of secure communications systems. Form. Asp. Comput. 14(1), 2\u201334 (2002)CrossRefMATH\n\n4.\n\nEnable-S3 consortium. Enable-S3 project website. http:\/\/\u200bwww.\u200benable-s3.\u200beu. Accessed 04 Dec 2016\n\n5.\n\nHoang, T.S.: An introduction to the Event-B modelling method. In: Romanovsky, A., Thomas, M. (eds.) Industrial Deployment of System Engineering Methods, pp. 211\u2013236. Springer, Heidelberg (2013)\n\n6.\n\nIEEE. 802.1Q-2014 - Bridges and Bridged Networks. http:\/\/\u200bwww.\u200bieee802.\u200borg\/\u200b1\/\u200bpages\/\u200b802.\u200b1Q-2014.\u200bhtml. Accessed 02 Dec 2016\n\n7.\n\nLeuschel, M., Butler, M.: ProB: an automated analysis toolset for the B method. Softw. Tools Technol. Transf. (STTT) 10(2), 185\u2013203 (2008)CrossRef\n\n8.\n\nSaid, M.Y., Butler, M., Snook, C.: A method of refinement in UML-B. Softw. Syst. Model. 14(4), 1557\u20131580 (2015)CrossRef\n\n9.\n\nColin, S.: iUML-B statemachines. In: Proceedings of the Rodin Workshop 2014, pp. 29\u201330, Toulouse, France (2014). http:\/\/\u200beprints.\u200bsoton.\u200bac.\u200buk\/\u200b365301\/\u200b\n\n10.\n\nSnook, C., Butler, M.: UML-B: Formal modeling and design aided by UML. ACM Trans. Softw. Eng. Methodol. 15(1), 92\u2013122 (2006)CrossRef\n\nFootnotes\n\n1\n\nActions in Event-B are, in the most general cases, non-deterministic [5].\n\n2\n\nA concise summary of the Event-B mathematical notation can be found at http:\/\/\u200bwiki.\u200bevent-b.\u200borg\/\u200bimages\/\u200bEventB-Summary.\u200bpdf.\n\n3\n\nThis is because removing the native tag may reveal an invalid nested tag (the known security flaw exploited by double tagging attacks).\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_7\n\n# On Learning Sparse Boolean Formulae for Explaining AI Decisions\n\nSusmit Jha1 , Vasumathi Raman1, Alessandro Pinto1 , Tuhin Sahai1 and Michael Francis1\n\n(1)\n\nUnited Technologies Research Center, Berkeley, USA\n\nSusmit Jha (Corresponding author)\n\nEmail: jha@csl.sri.com\n\nAlessandro Pinto\n\nEmail: pintoa@utrc.utc.com\n\nTuhin Sahai\n\nEmail: sahait@utrc.utc.com\n\nMichael Francis\n\nEmail: francism@utrc.utc.com\n\nAbstract\n\nIn this paper, we consider the problem of learning Boolean formulae from examples obtained by actively querying an oracle that can label these examplesz as either positive or negative. This problem has received attention in both machine learning as well as formal methods communities, and it has been shown to have exponential worst-case complexity in the general case as well as for many restrictions. In this paper, we focus on learning sparse Boolean formulae which depend on only a small (but unknown) subset of the overall vocabulary of atomic propositions. We propose an efficient algorithm to learn these sparse Boolean formulae with a given confidence. This assumption of sparsity is motivated by the problem of mining explanations for decisions made by artificially intelligent (AI) algorithms, where the explanation of individual decisions may depend on a small but unknown subset of all the inputs to the algorithm. We demonstrate the use of our algorithm in automatically generating explanations of these decisions. These explanations will make intelligent systems more understandable and accountable to human users, facilitate easier audits and provide diagnostic information in the case of failure. The proposed approach treats the AI algorithm as a black-box oracle; hence, it is broadly applicable and agnostic to the specific AI algorithm. We illustrate the practical effectiveness of our approach on a diverse set of case studies.\n\nS. Jha\u2014The author is currently at SRI International.\n\n## 1 Introduction\n\nThe rapid integration of robots and other intelligent agents into our industrial and social infrastructure has created an immediate need for establishing trust between these agents and their human users. The long-term acceptance of AI will depend critically on its ability to explain its actions, provide reasoning behind its decisions, and furnish diagnostic information in case of failures. This is particularly true for systems with close human-machine coordination such as self-driving cars, care-giving and surgical robots. Decision-making and planning algorithms central to the operation of these systems currently lack the ability to explain the choices and decisions that they make. It is important that intelligent agents become capable of responding to inquiries from human users. For example, when riding in an autonomous taxi, we might expect to query the AI driver using questions similar to those we would ask a human driver, such as \"why did we not take the Bay Bridge\", and receive a response such as \"there is too much traffic on the bridge\" or \"there is an accident on the ramp leading to the bridge or in the middle lane of the bridge.\" These explanations are essentially propositional formulae formed by combining the user-observable system and the environment states using Boolean connectives.\n\nEven though the decisions of intelligent agents are the consequence of algorithmic processing of perceived system and environment states [24, 30], the straight-forward approach of reviewing this processing is not practical. First, AI algorithms use internal states and intermediate variables to make decisions which may not be observable or interpretable by a typical user. For example, reviewing decisions made by the A* planning algorithm [20] could reveal that a particular state was never considered in the priority queue. But this is not human-interpretable, because a user may not be familiar with the details of how A* works. Second, the efficiency and effectiveness of many AI algorithms relies on their ability to intelligently search for optimal decisions without deducing information not needed to accomplish the task, but some user inquiries may require information that was not inferred during the original execution of the algorithm. Third, artificial intelligence is often a composition of numerous machine learning and decision-making algorithms, and explicitly modelling each one of these algorithms is not practical. Instead, we need a technique which can treat these algorithms as black-box oracles, and obtain explanations by observing their output on selected inputs. These observations motivate us to formulate the problem of generating explanations as an oracle-guided learning of Boolean formula where the AI algorithm is queried multiple times on carefully selected inputs to generate examples, which in turn are used to learn the explanation.\n\nGiven the observable system and environment states, S and E respectively, typical explanations depend on only a small subset of elements in the overall vocabulary , that is, if the set of state variables on which the explanation depends is denoted by , then . This support or its exact size is not known a priori. Thus, the explanations are sparse formulae over the vocabulary V. The number of examples needed to learn a Boolean formula is exponential in the size of the vocabulary in the general case [8, 18, 19]. Motivated by the problem of learning explanations, we propose an efficient algorithm that exploits sparsity to efficiently learn sparse Boolean formula. Our approach builds on recent advances in oracle-guided inductive formal synthesis [16, 17]. We make the following three contributions:\n\n * We formulate the problem of finding explanations for decision-making AI algorithms as the problem of learning sparse Boolean formulae.\n\n * We present an efficient algorithm to learn sparse Boolean formula where the size of required examples grows logarithmically (in contrast to exponentially in the general case) with the size of the overall vocabulary.\n\n * We illustrate the effectiveness of our approach on a set of case-studies.\n\n## 2 Motivating Example\n\nWe now describe a motivating example to illustrate the problem of providing human-interpretable explanations for the results of an AI algorithm. We consider the A* planning algorithm [20], which enjoys widespread use in path and motion planning due to its optimality and efficiency. Given a description of the state space and transitions between states as a weighted graph where weights are used to encode costs such as distance and time, A* starts from a specific node in the graph and constructs a tree of paths starting from that node, expanding paths in a best-first fashion until one of them reaches the predetermined goal node. At each iteration, A* determines which of its partial paths is most promising and should be expanded. This decision is based on the estimate of the cost-to-go to the goal node. We refer readers to [20] for a detailed description of A*. Typical implementations of A* use a priority queue to perform the repeated selection of intermediate nodes. The algorithm continues until some goal node has the minimum cost value in the queue, or until the queue is empty (in which case no plan exists). Figure 1 depicts the result of running A* on a 50 50 grid, where cells that form part of an obstacle are colored red. The input map (Fig. 1(a)) shows the obstacles and free space. A* is run to find a path from lower right corner to upper left corner. On the output map (Fig. 1(b)), cells on the returned optimal path are colored dark blue. Cells which ever entered A*'s priority queue are colored light cyan, and those that never entered the queue are colored yellow.\n\nFig. 1.\n\n(a) Input map to A* (b) Output showing final path and internal states of A* (Color figure online)\n\nConsider the three cells X, Y, Z marked in the output of A* in Fig. 1(b). An observer might want to enquire why points X, Y or Z were not selected for the optimal path generated by A*. Given the output and logged internal states of the A* algorithm, we know that Y was considered as a candidate cell and discarded due to non-optimal cost whereas X was never even considered as a candidate. But, this is not a useful explanation because a non-expert observing the behavior of a robot cannot be expected to understand the concept of a priority queue, or the details of how A* works. Looking at point Z, we notice that neither X nor Z was ever inserted into the priority queue; hence, both were never considered as candidate cells on the optimal path. When responding to a user query about why X and Z were not selected in the optimal path, we cannot differentiate between the two even if all internal decisions and states of the A* algorithm were logged. So, we cannot provide the intuitively expected explanation that Z is not reachable due to certain obstacles, while X is reachable but has higher cost than the cells that were considered. This is an example of a scenario where providing explanation requires new information that the AI algorithm might not have deduced while solving the original decision making problem.\n\n## 3 Problem Definition\n\nThe class of AI algorithms used in autonomous systems include path planning algorithms, discrete and continuous control, computer vision and image recognition algorithms. All of these algorithms would be rendered more useful by the ability to explain themselves. Our goal is to eventually develop an approach to generate explanations for the overall system, but we focus on individual components in this paper rather than the overall system. For example, the path planner for a self-driving car takes inputs from machine learning and sensor-fusion algorithms, which in turn receive data from camera, LIDAR and other sensors. The processed sensor data often has semantic meaning attached to it, such as detection of pedestrians on the road, presence of other cars, traffic distribution in a road network, and so on. Given this semantic information, the reason for a particular path being selected by the path planner is often not obvious: this is the sort of explanation we target to generate automatically.\n\nA decision-making AI algorithm can be modelled as a function that computes values of output variables given input variables , that is,\n\nThe outputs are decision variables, while the inputs include environment and system states as observed by the system through the perception pipeline. While the decision and state variables can be continuous and real valued, the inquiries and explanations are framed using predicates over these variables, such as comparison of a variable to some threshold. Let the vocabulary of atomic predicates used in the inquiry from the user and the provided explanation from the system be denoted by . We can separate the vocabulary into two subsets: used to formulate the user inquiry and used to provide explanations.\n\nIntuitively, is the shared vocabulary that describes the interface of the AI algorithm and is understood by the human-user. For example, the inquiry vocabulary for a planning agent may include propositions denoting selection of a waypoint in the path, and the explanation vocabulary may include propositions denoting presence of obstacles on a map. An inquiry from the user is an observation about the output (decision) of the algorithm, and can be formulated as a Boolean combination of predicates in the vocabulary . Hence, we can denote it as where the predicates in are over the set , and the corresponding grammar is:\n\nSimilarly, the response is a Boolean combination of the predicates in the vocabulary where the predicates in are over the set , and the corresponding grammar is:\n\nDefinition 1\n\nGiven an AI algorithm and an inquiry , is a necessary and sufficient explanation when where are predicates over as explained earlier, and . is a sufficient explanation when .\n\nIf the algorithm could be modelled explicitly in appropriate logic, then the above definition could be used to generate explanations for a given inquiry using techniques such as satisfiability solving. However, such an explicit modelling of these algorithms is currently outside the scope of existing logical deduction frameworks, and is impractical for large and complicated AI systems even from the standpoint of the associated modelling effort. The AI algorithm is available as an executable function; hence, it can be used as an oracle that can provide an outputs for any given input. This motivates oracle-guided learning of the explanation from examples using the notion of confidence associated with it.\n\nDefinition 2\n\nGiven an AI algorithm and an inquiry , is a necessary and sufficient explanation with confidence when where are predicates over as explained earlier, and . is a sufficient explanation with confidence when .\n\nThe oracle used to learn the explanation is implemented using the AI algorithm. It runs the AI algorithm on a given input to generate the decision output , and then marks the input as a positive example if is true, that is, the inquiry property holds on the output. It marks the input as a negative example if is not true. We call this an introspection oracle, and it marks each input as either positive or negative.\n\nDefinition 3\n\nAn introspection oracle for a given algorithm and inquiry takes an input and maps it to a positive or negative label, that is, .\n\nWe now formally define the problem of learning Boolean formula with specified confidence given an oracle to label examples.\n\nDefinition 4\n\nThe problem of oracle-guided learning of Boolean formula from examples is to identify (with confidence ) the target Boolean function over a set of atomic propositions by querying an oracle that labels each input (which is an assignment to all variables in ) as positive or negative depending on whether holds or not, respectively.\n\nWe make the following observations which relates the problem of finding explanations for decisions made by AI algorithms to the problem of learning Boolean formula.\n\nObservation 1\n\nThe problem of generating explanation for the AI algorithm and an inquiry is equivalent to the problem of oracle-guided learning of Boolean formula using oracle as described in Definition 4.\n\n denotes the restriction of the Boolean formula by setting to in and denotes the restriction of by setting to . A predicate is in the support of the Boolean formula , that is, if and only if .\n\nObservation 2\n\nThe explanation over a vocabulary of atoms for the AI algorithm and a user inquiry is a sparse Boolean formula, that is, .\n\nThese observations motivate the following problem definition for learning sparse Boolean formula.\n\nDefinition 5\n\nBoolean function is called k-sparse if . The problem of oracle-guided learning of k-sparse Boolean formula from examples is to identify (with confidence ) the target k-sparse Boolean function over a set of atomic propositions by querying an oracle that labels each input (which is an assignment to all variables in ) as positive or negative depending on whether holds or not, respectively.\n\nFurther, the explanation of decisions made by an AI algorithm can be generated by solving the problem of oracle-guided learning of k-sparse Boolean formula. In the following section, we present a novel approach to efficiently solve this problem.\n\n## 4 Learning Explanations as Sparse Boolean Formula\n\nOur proposed approach to solve the k-sparse Boolean formula learning problem has two steps:\n\n 1. 1.\n\nIn the first step, we find the support of the explanation, that is, . This is accomplished using a novel approach which requires a small number of runs (logarithmic in ) of the AI algorithm .\n\n 2. 2.\n\nIn the second step, we find the Boolean combination of the atoms in which forms the explanation . This is accomplished by distinguishing input guided learning of propositional logic formula which we have earlier used for the synthesis of programs [16].\n\nBefore delving into details of the above two steps, we introduce additional relevant notations. Recall that the vocabulary of explanation is . Given any two inputs and , we define the difference between them as follows.\n\nNext, we define a distance metric d on inputs as the size of the difference set, that is,\n\nIntuitively, is the Hamming distance between the n-length vectors that record the evaluation of the atomic predicates in . We say that two inputs are neighbours if and only if . We also define a partial order on inputs as follows:\n\nGiven an input and a set , a random J-preserving mutation of , denoted , is defined as:\n\nFinding the Support: We begin with two random inputs on which the oracle returns different labels, say it returns positive on and negative on without loss of generality. Finding such can be done by sampling the inputs and querying the oracle until two inputs disagree on the outputs. The more samples we find without getting a pair that disagree on the label, the more likely it is that the Boolean formula being used by the oracle to label inputs is a constant (either or ). We later formalize this as a probabilistic confidence. Given the inputs , we find on which the inputs differ with respect to the vocabulary . We partition J into two subsets and . The two sets and differ in size by at most 1. The set of inputs that are halfway between the two inputs w.r.t the Hamming distance metric d defined earlier is given by the set defined as:\n\nSatisfiability solvers can be used to generate an input from . The oracle is run on to produce the corresponding label. This label will match either the label for the input or that of the input . We discard the input whose label matches to produce the next pair of inputs, that is,\n\nStarting from an initial pair of inputs on which produces different labels, we repeat the above process, considering a new pair of inputs at each iteration until we have two inputs that are neighbours, with . Hence, is in the support of the explanation . We add this to the set of variables . We repeat the above process to find the next variable to add to the support set. For example, consider a 2-sparse Boolean formula over the vocabulary set . Given two random samples and \\- the first is labelled positive by oracle and the second is negative. The set is and the produces a new example which is labelled positive. So, the next pair is and . The now produces new example which is labelled positive. Now, the set is a singleton set . So, is in the support set of . This is repeated to find the full support . The efficiency of the introspection process to obtain each variable is summarized in Lemma 1.\n\nLemma 1\n\nThe introspective search for each new variable takes at most queries to .\n\nProof\n\nThe size of the difference set for any inputs is at most n for a vocabulary of size n. The i-th call to reduces the size of the difference set as follows: . Thus, the number of calls to before the difference set is singleton and the two inputs are neighbours, obtained by solving the above recurrence equation, is .\n\nThis introspective search for variables in the support set is repeated till we cannot find a pair of inputs on which the oracle produces different outputs. We check this condition probabilistically using Lemma 2.\n\nLemma 2\n\nIf m random samples from produce the same output as input ' ' for the oracle where is k-sparse, then the probability that all mutations produce the same output is at least , where .\n\nProof\n\nIf all the mutations do not produce the same output, then the probability of the Oracle differing from the output of for any random sample is at least since the size of the set is at most . So,\n\nWe can now define that samples inputs from the set and generates two inputs on which the oracle disagrees and produces different outputs. If it cannot find such a pair of inputs, it returns . The overall algorithm for finding the support of the explanations with probability is presented in Algorithm 1.1 using the oracle . It is a recursive algorithm which is initially called with a randomly generated input and an empty set J. Notice that the support of a sufficient explanation can be found by making the recursive call on only one of the two inputs, that is, or instead of both.\n\nTheorem 1\n\nThe introspective computation of the support set of variables of the k-sparse Boolean formula defined over the vocabulary of size n using at most examples.\n\nProof\n\nEach variable in can be found using an introspective search that needs at most examples according to Lemma 1. So, the loop in Algorithm 1.1 makes at most queries. In Lemma 2, we showed that the maximum number of examples needed for is . The recursion is repeated at most times. Thus, the overall algorithms needs at most , that is, examples.\n\nLearning Boolean Formula : Learning a Boolean formula that forms the explanation for the given query is relatively straight-forward once the variables which form the support of the Boolean formula have been identified. Efficient techniques have been developed to solve this problem in the context of program synthesis, and we adopt a technique based on the use of distinguishing inputs proposed by us in [16]. The algorithm starts with a single random input . The oracle is queried with the example and it is marked positive or negative depending on the label returned by the oracle. A candidate explanation is generated which is consistent with the positive and negative examples seen so far. Then, the algorithm tries to find an alternative consistent explanation . If such an alternate explanation cannot be found, the algorithm terminates with as the final explanation. If is found, we find an input which distinguishes and and query the oracle with this new input in order to mark it as positive or negative. This refutes one of the two explanation formulae and . We keep repeating the process until we converge to a single Boolean formula. Algorithm 1.2 summarizes this learning procedure.\n\nTheorem 2\n\nThe overall algorithm to generate k-sparse explanation for a given query takes queries to the oracle, that is, the number of examples needed to learn the Boolean formula grows logarithmically with the size of the vocabulary n.\n\nProof\n\nThe first-step to compute the support set of the explanation takes queries and after that, the learning of explanation takes queries. So, the total number of queries needed is .\n\nThus, our algorithm adopts a binary search like procedure using the Hamming distance metric d to find the support of the Boolean formula over a vocabulary of size n using a number of examples that grow logarithmically in n. After the support has been found, learning the Boolean formula can be accomplished using the formal synthesis based approach that depends only on the size of the support set and not on the vocabulary size n. Algorithms that do not exploit sparsity have been previously shown to need examples that grow exponentially in n [18, 19] in contrast to the logarithmic dependence on n of the algorithm proposed here. The proposed algorithm is very effective for sparse Boolean formula, that is, , which is often the case with explanations.\n\n## 5 Experiments\n\nWe begin by describing the results on the motivating example of A* presented in Sect. 2. The vocabulary is for each cell i, j in the grid where denotes the decision that i, j-th cell was selected to be on the final path, and denotes the decision that the i, j-th cell was not selected to be on the final path. The vocabulary for each cell i, j in the grid where denotes that the cell i, j has an obstacle and denote that the cell i, j is free. The explanation query is: \"Why were no points in (around z) not considered on the generated path?\" The inquiry framed using is . A sufficient explanation for this inquiry is with set to 0.9. This is obtained in 2 min 4 s (48 examples). The second query is for the area around x: and the sufficient explanation obtained is in 2 min 44 s (57 examples). The third query for area around y is and the corresponding explanation is which was obtained in 1 min 48 s (45 examples). Given the 177 obstacles, a naive approach of enumerating all possible explanations would require runs of A* which is clearly infeasible in each of these three cases. Even if we assumed that the number of explanations is 2 (but did not know which two variables are in the support set), there are more than 15, 000 cases to be considered.\n\nFig. 2.\n\nExecution of reactive strategy for particular sequence of door closings. Each Robot i is initially assigned to goal Area i, but they can swap if needed to achieve the global goal (each marked Area must eventually get one robot). Brown lines indicate closed doors preventing the robots' motion. Time steps depicted are 0, 3, 4 and 24. (Color figure online)\n\nExplaining Reactive Strategy [26]: We also applied our approach to a reactive switching protocol for multi-robot systems generated according to the approach described in [26]. The task involves 4 robots operating in the workspace depicted in Fig. 2. In the beginning, each robot is assigned the corresponding area to surveil (i.e. Robot i is assigned to Area i). Starting from their initial positions, they must reach this region. However, in response to the opening and closing of doors in the environment at each time step, they are allowed to swap goals. As can be seen from the Fig. 2, robots 1 and 2 swap goals because the top door closes, and robots 3 and 4 swap goals because the bottom door is closed. They stand by these decisions even though the doors later reopen. The simulation takes 24 time steps for all the robots to reach their final goals. The vocabulary is , where denotes that robot i ended up in area j. The vocabulary , where denotes that the door between the top and middle row of areas is closed at time t, denotes that the door between the left and middle column of areas is closed at time t, etc. We pose the query,\"Why did Robot 1 end up in Area 2?\", i.e. . Starting with the original input sequence and one in which no door-related events occur, the generated explanation is , which is obtained in 0.76 s, and 7 introspective runs of the protocol on mutated inputs (door activity sequences). The second query was, \"Why did Robot 3 not end up in Area 3?\", or . This took 0.61 s and 6 runs to generate\", . Given that there are 4 doors and 24 time steps, a naive approach of enumerating all possible explanations would require runs of the reactive protocol.\n\nExplaining Classification Error in MNIST [21]: MNIST database of scanned images of digits is a common benchmark used in literature to evaluate image classification techniques. MNIST images were obtained by normalization of original images into greyscale 28 28 pixel image. We consider a k-NN classifier for k = 9 as the machine learning technique. Some of the test images are incorrectly identified by this technique and we show one of these images in Fig. 3 where 4 is misidentified as 9. We deploy our technique to find explanations for this error. The k-NN classifier uses voting among the k-nearest neighbours to label test data. We show the nearest neighbour with label '9' to the misclassified image in the figure below. This image of 4 had 6 neighbours which were labelled '9'. The oracle for generating explanations works as follows: If the number of neighbours of the image labelled '9' decreases from 6 (even if the final label from the k-NN classifier does not change), the oracle marks the image as positive, and negative, otherwise. The vocabulary of explanation is formed by 4 4 pixel blocks (similar to superpixels in [29]) being marked completely dark or clear (this corresponds to predicate abstraction of greyscale pixels). The set of atomic propositions in the support of the explanation is illustrated in the third figure by manually picking assignment values to support variables for purpose of illustration. The last two figures show images which are filtered by two conjunctions in the generated explanation. The generation of the explanation took 3 min 48 s and required 58 examples where we initialized the algorithm with the images of 4 and 9 in the figure below.\n\nFig. 3.\n\nLeft to right: Misclassified image of '4', closest image of '9', changing all pixels corresponding to support of explanations, changing pixels for one of the sufficient explanation, changing pixels for another sufficient explanation\n\n## 6 Related Work\n\nOur approach relies on learning logical explanations in the form of sparse Boolean formula from examples that are obtained by carefully selected introspective simulations of the decision-making algorithm. The area of active learning Boolean formula from positive and negative examples has been studied in literature [1, 18] in both exact and probably approximately correct (PAC) setting. Exact learning Boolean formula [3, 19] requires a number of examples exponential in the size of the vocabulary. Under the PAC setting, learning is guaranteed to find an approximately correct concept given enough independent samples [2, 23, 25]. It is known that k-clause conjunctive normal form Boolean formula are not PAC learnable with polynomial sample-size, even though monomials and disjunctive normal form representations are PAC learnable [8, 25]. Changing the representation from CNF to DNF form can lead to exponential blow-up. In contrast, we consider only sparse Boolean formula and our goal is to learn the exact Boolean formula with probabilistic confidence, and not its approximation. Efficient learning techniques exist for particular classes of Boolean formulae such as monotonic and read-one formulae [12, 15], but explanations do not always take these restricted forms, and hence, our focus on sparse Boolean formulae is better suited for this context.\n\nAnother related research area is the newly emerged field of formal synthesis, which combines induction and deduction for automatic synthesis of systems from logical or black-box oracle specifications [16]. Unlike active learning, formal synthesis is also concerned with defining techniques for the generation of interesting examples and not just its inductive generalization, much like our approach. While existing formal synthesis techniques have considered completion of templates by inferring parameters [4, 28, 32], composition of component Boolean functions or uplifting to bitvector form [7, 13, 16, 35], inferring transducers and finite state-machines [5, 6, 11], and synthesis of invariants [31, 33], our work is the first to consider sparsity as a structural assumption for learning Boolean formulae.\n\nThe need for explanations of AI decisions to increase trust of decision-making systems has been noted in the literature [22]. Specific approaches have been introduced to discover explanations in specific domains such as MDPs [9], HTNs [14] and Bayesian networks [36]. Explanation of failure in robotic systems by detecting problems in the temporal logic specification using formal requirement analysis was shown to be practically useful in [27]. Inductive logic programming [10] has also been used to model domain-specific explanation generation rules. In contrast, we propose a domain-independent approach to generate explanations by treating the decision-making AI algorithm as an oracle. Domain-independent approaches have also been proposed in the AI literature for detecting sensitive input components that determine the decision in a classification problem [29, 34]. While these approaches work in a quantitative setting, such as measuring sensitivity from the gradient of a neural network classifier's ouput, our approach is restricted to the discrete, qualitative setting. Further, we not only detect sensitive inputs (support of Boolean formulae) but also generate the explanation.\n\n## 7 Conclusion and Future Work\n\nWe proposed a novel algorithm that uses a binary-search like approach to first find the support of any sparse Boolean formula followed by a formal synthesis approach to learn the target formula from examples. We demonstrate how this method can be used to learn Boolean formulae corresponding to the explanation of decisions made by an AI algorithm. This capability of self-explanation would make AI agents more human-interpretable and decrease the barriers towards their adoption in safety-critical applications of autonomy. We identify two dimensions along which our work can be extended. First, our approach currently uses a predicate abstraction to Boolean variables for learning explanations. We plan to extend our technique to a richer logical language such as signal temporal logic for explanations involving real values. Second, we need to extend our approach to infer multiple valid explanations in response to an inquiry. This work is a first step towards using formal methods, particularly, formal synthesis to aid artificial intelligence by automatically generating explanations of decisions made by AI algorithms.\n\nReferences\n\n1.\n\nAbouzied, A., Angluin, D., Papadimitriou, C., Hellerstein, J.M., Silberschatz, A.: Learning and verifying quantified boolean queries by example. In: ACM Symposium on Principles of Database Systems, pp. 49\u201360. ACM (2013)\n\n2.\n\nAngluin, D., Computational learning theory: survey and selected bibliography. In: ACM Symposium on Theory of Computing, pp. 351\u2013369. ACM (1992)\n\n3.\n\nAngluin, D., Kharitonov, M.: When won't membership queries help? In: ACM Symposium on Theory of Computing, pp. 444\u2013454. ACM (1991)\n\n4.\n\nBittner, B., Bozzano, M., Cimatti, A., Gario, M., Griggio, A.: Towards pareto-optimal parameter synthesis for monotonie cost functions. In: FMCAD, pp. 23\u201330, October 2014\n\n5.\n\nBoigelot, B., Godefroid, P.: Automatic synthesis of specifications from the dynamic observation of reactive programs. In: Brinksma, E. (ed.) TACAS 1997. LNCS, vol. 1217, pp. 321\u2013333. Springer, Heidelberg (1997). doi:10.\u200b1007\/\u200bBFb0035397 CrossRef\n\n6.\n\nBotin\u010dan, M., Babi\u0107, D., Sigma*: Symbolic learning of input-output specifications. In: POPL, pp. 443\u2013456 (2013)\n\n7.\n\nCook, B., Kroening, D., R\u00fcmmer, P., Wintersteiger, C.M.: Ranking function synthesis for bit-vector relations. FMSD 43(1), 93\u2013120 (2013)MATH\n\n8.\n\nEhrenfeucht, A., Haussler, D., Kearns, M., Valiant, L.: A general lower bound on the number of examples needed for learning. Inf. Comput. 82(3), 247\u2013261 (1989)MathSciNetCrossRef90002-3)MATH\n\n9.\n\nElizalde, F., Sucar, E., Noguez, J., Reyes, A.: Generating explanations based on Markov decision processes. In: Aguirre, A.H., Borja, R.M., Garci\u00e1, C.A.R. (eds.) MICAI 2009. LNCS (LNAI), vol. 5845, pp. 51\u201362. Springer, Heidelberg (2009). doi:10.\u200b1007\/\u200b978-3-642-05258-3_\u200b5 CrossRef\n\n10.\n\nFeng, C., Muggleton, S.: Towards inductive generalisation in higher order logic. In: 9th International Workshop on Machine learning, pp. 154\u2013162 D (2014)\n\n11.\n\nGodefroid, P., Taly, A.: Automated synthesis of symbolic instruction encodings from i\/o samples. SIGPLAN Not. 47(6), 441\u2013452 (2012)CrossRef\n\n12.\n\nGoldsmith, J., Sloan, R.H., Sz\u00f6r\u00e9nyi, B., Tur\u00e1n, G.: Theory revision with queries: Horn, read-once, and parity formulas. Artif. Intell. 156(2), 139\u2013176 (2004)MathSciNetCrossRefMATH\n\n13.\n\nGurfinkel, A., Belov, A., Marques-Silva, J.: Synthesizing safe bit-precise invariants. In: \u00c1brah\u00e1m, E., Havelund, K. (eds.) TACAS 2014. LNCS, vol. 8413, pp. 93\u2013108. Springer, Heidelberg (2014). doi:10.\u200b1007\/\u200b978-3-642-54862-8_\u200b7 CrossRef\n\n14.\n\nHarbers, M., Meyer, J.-J., van den Bosch, K.: Explaining simulations through self explaining agents. J. Artif. Soc. Soc. Simul. 13, 10 (2010)\n\n15.\n\nHellerstein, L., Servedio, R.A.: On PAC learning algorithms for rich boolean function classes. Theoret. Comput. Sci. 384(1), 66\u201376 (2007)MathSciNetCrossRefMATH\n\n16.\n\nJha, S., Seshia, S.A.: A theory of formal synthesis via inductive learning. Acta Informatica, pp. 1\u201334 (2017)\n\n17.\n\nJha, S., A. Seshia, and A. Tiwari. Synthesis of optimal switching logic for hybrid systems. In: EMSOFT, pp. 107\u2013116. ACM (2011)\n\n18.\n\nKearns, M., Li, M., Valiant, L.: Learning boolean formulas. J. ACM 41(6), 1298\u20131328 (1994)MathSciNetCrossRefMATH\n\n19.\n\nKearns, M., Valiant, L.: Cryptographic limitations on learning boolean formulae and finite automata. Journal of the ACM (JACM) 41(1), 67\u201395 (1994)MathSciNetCrossRefMATH\n\n20.\n\nLaValle, S.M.: Planning Algorithms. Cambridge University Press, Cambridge (2006)CrossRefMATH\n\n21.\n\nLecun, Y., Cortes, C.: The MNIST database of handwritten digits. http:\/\/\u200byann.\u200blecun.\u200bcom\/\u200bexdb\/\u200bmnist\/\u200b\n\n22.\n\nLee, J., Moray, N.: Trust, control strategies and allocation of function in human-machine systems. Ergonomics 35(10), 1243\u20131270 (1992)CrossRef\n\n23.\n\nMansour, Y.: Learning boolean functions via the fourier transform. In: Theoretical Advances in Neural Computation and Learning, pp. 391\u2013424 (1994)\n\n24.\n\nNau, D., Ghallab, M., Traverso, P.: Automated Planning: Theory and Practice. Morgan Kaufmann Publishers Inc., San Francisco (2004)MATH\n\n25.\n\nPitt, L., Valiant, L.G.: Computational limitations on learning from examples. J. ACM (JACM) 35(4), 965\u2013984 (1988)MathSciNetCrossRefMATH\n\n26.\n\nRaman, V.: Reactive switching protocols for multi-robot high-level tasks. In: IEEE\/RSJ, pp. 336\u2013341 (2014)\n\n27.\n\nRaman, V., Lignos, C., Finucane, C., Lee, K.C.T., Marcus, M.P., Kress-Gazit, H.: Sorry Dave, I'm afraid i can't do that: explaining unachievable robot tasks using natural language. In: Robotics: Science and Systems (2013)\n\n28.\n\nReynolds, A., Deters, M., Kuncak, V., Tinelli, C., Barrett, C.: Counterexample-guided quantifier instantiation for synthesis in SMT. In: Kroening, D., P\u0103s\u0103reanu, C.S. (eds.) CAV 2015. LNCS, vol. 9207, pp. 198\u2013216. Springer, Cham (2015). doi:10.\u200b1007\/\u200b978-3-319-21668-3_\u200b12 CrossRef\n\n29.\n\nRibeiro, M.T., Singh, S., Guestrin, C.: Why Should I Trust You?: Explaining the predictions of any classifier. In: KDD, pp. 1135\u20131144 (2016)\n\n30.\n\nRussell, J., Cohn, R.: OODA Loop. Book on Demand, Norderstedt (2012)\n\n31.\n\nSankaranarayanan, S.: Automatic invariant generation for hybrid systems using ideal fixed points. In: HSCC, pp. 221\u2013230 (2010)\n\n32.\n\nSankaranarayanan, S., Miller, C., Raghunathan, R., Ravanbakhsh, H., Fainekos, G.: A model-based approach to synthesizing insulin infusion pump usage parameters for diabetic patients. In: Annual Allerton Conference on Communication, Control, and Computing, pp. 1610\u20131617, October 2012\n\n33.\n\nSankaranarayanan, S., Sipma, H.B., Manna, Z.: Constructing invariants for hybrid systems. FMSD 32(1), 25\u201355 (2008)MATH\n\n34.\n\n\u0160trumbelj, E., Kononenko, I.: Explaining prediction models and individual predictions with feature contributions. KIS 41(3), 647\u2013665 (2014)\n\n35.\n\nUrban, C., Gurfinkel, A., Kahsai, T.: Synthesizing ranking functions from bits and pieces. In: Chechik, M., Raskin, J.-F. (eds.) TACAS 2016. LNCS, vol. 9636, pp. 54\u201370. Springer, Heidelberg (2016). doi:10.\u200b1007\/\u200b978-3-662-49674-9_\u200b4 CrossRef\n\n36.\n\nYuan, C., Lim, H., Lu, T.-C.: Most relevant explanation in bayesian networks. J. Artif. Intell. Res. (JAIR) 42, 309\u2013352 (2011)MathSciNetMATH\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_8\n\n# Event-Based Runtime Verification of Temporal Properties Using Time Basic Petri Nets\n\nMatteo Camilli1 , Angelo Gargantini2 , Patrizia Scandurra2 and Carlo Bellettini1\n\n(1)\n\nDepartment of Computer Science, Universit\u00e0 degli Studi di Milano, Milan, Italy\n\n(2)\n\nDepartment of Management, Information and Production Engineering (DIGIP), Universit\u00e0 degli Studi di Bergamo, Bergamo, Italy\n\nMatteo Camilli (Corresponding author)\n\nEmail: camilli@di.unimi.it\n\nAngelo Gargantini\n\nEmail: angelo.gargantini@unibg.it\n\nPatrizia Scandurra\n\nEmail: patrizia.scandurra@unibg.it\n\nCarlo Bellettini\n\nEmail: bellettini@di.unimi.it\n\nAbstract\n\nWe introduce a formal framework to provide an efficient event-based monitoring technique, and we describe its current implementation as the MahaRAJA software tool. The framework enables the quantitative runtime verification of temporal properties extracted from occurring events on Java programs. The monitor continuously evaluates the conformance of the concrete implementation with respect to its formal specification given in terms of Time Basic Petri nets, a particular timed extension of Petri nets. The system under test is instrumented by using simple Java annotations on methods to link the implementation to its formal model. This allows a separation between implementation and specification that can be used for other purposes such as formal verification, simulation, and model-based testing. The tool has been successfully used to monitor at runtime and test a number of benchmarking case-studies. Experiments show that our approach introduces bounded overhead and effectively reduces the involvement of the monitor at run time by using negligible auxiliary memory. A comparison with a number of state-of-the-art runtime verification tools is also presented.\n\nKeywords\n\nRuntime verificationFormal methods @ runtimeTiming analysisTemporal propertiesPetri nets\n\n## 1 Introduction\n\nSoftware systems are increasingly employed in most domains and activities, including safety critical ones. Therefore, the society increasingly relies on software, and unreliable or unpredictable behavior is becoming less and less tolerated. As a consequence, over the past years, the validation of software systems has become an increasingly important and active research area.\n\nEvent-based runtime verification [1] is the monitoring of running programs to verify the occurring events against the requirements. A particularly challenging aspect is the monitoring of temporal properties in the presence of strict time constraints. In fact, monitoring at runtime introduces overheads on the System Under Test (SUT) that may affect the correctness of the verified properties.\n\nIn this paper, we introduce a formal event-based runtime verification framework and we describe its current implementation as a Java software tool, so called MahaRAJA 1. This framework enables the monitoring of Java programs, by evaluating the conformance of the concrete implementation with respect to its formal specification given in terms of Time Basic (TB) Petri nets [2] (or simply TB nets), a powerful temporal extension of Petri nets (PNs) for modeling concurrent\/distributed systems with real-time constraints.\n\nAlthough descriptive formalisms are very popular in runtime verification [3], the adoption of operational specifications, like in our approach, offers some advantages with respect to declarative specifications [4, 5]. They are usually easier to write, visualize, understand, and allow for step-wise model refinement [6]. Moreover, although other operational formalisms such as timed-automata [7] or finite-state-machines [8] support the modeling of temporal or behavioral aspects, PNs-based approaches can be more concise and easier to use [9]. Furthermore, aspects such as messaging, communication protocols, which are commonly used in concurrent or distributed systems, can be difficult to model with the language primitives of timed-automata [10, 11]. Finally, despite several state-based, logic-based, and event-based notations have been used for runtime verification [1], our work is the first attempt (to the best of our knowledge) exploiting the expressiveness of the TB nets for verifying temporal properties at runtime.\n\nThe MahaRAJA framework requires the SUT to be instrumented by using simple Java annotations on methods, in order to link the implementation to its formal model. Then, at runtime, the execution of the events of interest triggers the conformance verification of temporal properties. Rather than using heavy offline computation to predict the generation rate of possibly invalid events to estimate the maximum detection latency [12], we use an online approach that focuses on maintaining the analysis as lightweight as possible. MahaRAJA operates on and in conjunction with the SUT and it performs data collection and processing asynchronously with the SUT execution. The monitor and the SUT run concurrently on separated CPU cores using a buffer-based mechanism for communication. Our approach tries to bound the cost of executing the SUT instrumentation by having a bounded number of instructions executed upon the generation of possible invalid events. This runtime verification procedure is highly scalable because it does not depend on the size of the entire state space (often far larger than the model size [13]). It operates using just an occurring event and the 1-step reachability set of the current model's state, thus using limited extra memory.\n\nThe tool has been applied to a number of benchmarking case studies [14] and we experimentally evaluated the runtime overhead, making it possible for a system designer to reason about the timing constraints of the SUT. The experiments show that MahaRAJA introduces limited monitoring overhead and limited detection latency, thereby opening up the possibility to adopt a fast failing approach or implement a self-healing procedure [15] in a latency-aware adaptation setting.\n\nThe paper is organized as follows. Section 2 introduces the proper background on TB nets. Section 3 introduces the formalization of our technique and Sect. 4 describes our current software implementation. Section 5 introduces our experimental evaluation of the runtime overhead, making it possible for a system designer to reason about the timing constraints of the SUT. Section 6 compares our monitoring framework with a number of state-of-the-art runtime verification tools, thus showing both advantages and disadvantages of our framework. Finally, Sect. 7 presents our conclusion and future directions of our work.\n\n## 2 Background on Time Basic Nets\n\nThis section briefly introduces the TB nets formalism by means of a running example, i.e., the timed producer\/consumer (P\/C) model reported in Fig. 1.\n\nTB nets are a formal model for distributed systems with real-time constraints. This modeling formalism is more expressive then other temporal extensions of PNs and it supports both time and functional extensions in a semantically clear and rigorous way [2]. Thus it represents an effective formal model to deal with specification of highly concurrent systems with real-time constraints.\n\nThe structure of a TB net [2, 16] is a bipartite graph , where P is the finite set of places (i.e., system state variables), T is the finite set of transitions (i.e., events causing state changes), is the flow relation. The pre\/post-sets of are = and = , respectively.\n\nFig. 1.\n\nProducer-consumer TB net model.\n\nThe P\/C example describes two processes that asynchronously interact through the place . After producing (respectively, consuming), the two processes perform some local activity (i.e., and ).\n\nIn TB nets, tokens are enriched by timestamps recording their creation time. Each place can contain a multiset (bag) of tokens2. A marking (i.e., a representation of the system state) is a mapping , that associates time-stamps to tokens in places (e.g., in Fig. 1).\n\nTime constraints are associated with transitions: two (linear or linearizable) functions associated to each transition t define the lower and the upper bounds ( ) of the interval of real values representing its possible firing times (e.g., [ ] associated with ). Tokens produced by the atomic firing of a transition are time-stamped with the same value. The actions of removing and creating tokens are performed instantaneously.\n\nA binding of t is a function that represents a set of time-stamps possibly causing t to be fired. The numerical interval holds the possible firing times for and it is evaluated by replacing each occurrence of a place p (free variable) with .\n\nFor instance, consider the transition and the following binding: : . According to the time function of , the firing times range over [3500, 8500].\n\nStarting from the marking m, a binding is enabled if and only if . A firing instance of t is a pair composed of an enabled binding and a real value . The firing of t results in a new marking :\n\nwhere is if , the null bag otherwise, is if , the null bag otherwise, and operators are extended to bags. This is denoted .\n\nFor instance, the binding : is enabled in the marking . Thus, the firing instance is valid. The firing process produces a new marking . In particular, it withdraws the token from place and it puts a fresh new token, time-stamped with the value 450, into .\n\nThe interval can be interpreted in two different ways. The weak semantics states that t can fire at any instant in . The strong semantics instead states that t must fire at any instant in , unless it is disabled by a conflicting transition fired before the upper bound of (refer to [2] for the details). Our running example adopts a strong semantics.\n\nThe marking is reachable from if and only if there exists a path (sequence of firing instances and markings) such that:\n\nThe transitions associated with the enabled bindings in m are called enabled transitions and they are denoted by enab(m).\n\n## 3 Event-Based Runtime Verification\n\nThis section introduces the formalization of our event-based monitoring approach. In order to abstract the behavior of a running program , let us introduce the observable components of , so called action methods.\n\nDefinition 1\n\n(Action method). Given a program , an action method is a subroutine performing a specific task, such that its execution is observed at runtime.\n\nThe action methods are the events of interest that we want to observe and verify with respect to the expected behavior provided in terms of a TB net formal specification. During the execution of , we extract temporal information from the action methods depending on their own action time.\n\nDefinition 2\n\n(Action time). Given a program and a set of action methods A, the action time function maps action methods in A to a non empty set of elements in .\n\nIntuitively, the action time determines the moment (i.e., time instant) at which we want to observe the action methods. , implies that a is observed at its own invocation time. The temporal information extracted from the execution of a is a timestamp representing the initial time. Similarly, if , a is observed at its own final time; if , a is observed both at invocation and termination time.\n\nGiven the observable components and the action time function, we use the notion of timed trace to abstract the behavior of a running real-time system.\n\nDefinition 3\n\n(Timed trace). Given a program and a set of action methods , a timed trace is a finite sequence of events , such that each event is a triplet , where:\n\n * is the action method that triggers the event. We denote it with .\n\n * is the moment associated with the event. We denote it with .\n\n * is the timestamp associated with the event. We denote it with .\n\nAs an example, consider the code excerpts reported in Fig. 2. They represent a Java implementation of the and the , respectively, in a simple producer-consumer program. The calls the method that retrieves and removes a object from the , waiting if necessary until an element becomes available. Then it performs some additional tasks using the new element through the method. The creates a new object through the method and then it pushes the element into the .\n\nThe set of action methods is defined as produce, producerTask, consume, consumerTask , while the action type function is : {produce { }, producerTask { }, consumerTask { }, consume { , }}.\n\nFig. 2.\n\nJava implementation of the Producer and Consumer.\n\nThe rationale behind the function is explained by means of the following example. Both the produce (Fig. 2, line 8) and the producerTask (line 12) action methods maps to } action time. In fact, the two action methods affect the behavior of the program at the end of their own execution: the producerTask method creates a new data element that becomes available at the end of the method execution; the produce puts the new data element into the buffer data structure and then terminates itself. Therefore, we want to observe only the final time of these action methods. Instead, the consumerTask action method (Fig. 2, line 13) processes the new data by launching an external asynchronous task. In this case we are just interested in knowing whether the external task is called in due time. Therefore, the consumerTask maps to { } action time. Finally, the execution of the consume action method (Fig. 2, line 8) causes the program to wait until a new element becomes available, which is consumed and returned at the end of the method execution. Hence, for each (multiple) execution of the consume action method, we want to observe both the initial and the final time. In fact, we may want to check that the consumer does not wait for available data more than a specific time limit.\n\nThe execution of the producer-consumer program can generate, for instance, the timed trace reported in (1).\n\n(1)\n\nIt is worth noting that consume occurs twice in . In fact, the function maps the consume action method both to and , thus its own execution generates two different events timestamped with the initial and the final time, respectively.\n\nAnother important observation is that the program can perform inside the action methods different nested methods calls not belonging to A, therefore these are not observed at runtime. This allows us to build timed traces with different levels of granularity.\n\nThe construction of a timed trace is formalized as follows.\n\nDefinition 4\n\n(Timed trace construction). Given a running program , the set of action methods A and the action time function , the timed trace is constructed from the execution of each such that:\n\nwhere v is the timestamp associated with the moment g.\n\nThe timed trace constructed following Definition 4 includes only the events of interest defined by the action methods and the action time function.\n\nTo formalize the conformance relation between a running program and its formal specification, let us introduce first the notion of action method mapping.\n\nDefinition 5\n\n(Action method mapping function). Given a TB net structure (P, T, E) and the set of action methods A associated with the program , the action method mapping function associates each element and each moment to a transition .\n\nWe use this mechanism to bind action methods in the implementation to transitions in the model. This way, the conformance verification can be performed by checking that all the events of a timed trace correspond to feasible firing transitions in the formal specification. The formalization is reported below:\n\nDefinition 6\n\n(Path Conformance). Given a timed trace and an execution path of a TB net model, there exists a conformance relation between and iff. for each , there exists such that:\n\n 1. (i)\n\n (i.e., is mapped to transition )\n\n 2. (ii)\n\n (i.e., the timestamp of belongs to the firing times of )\n\nDefinition 7\n\n(Model Conformance). Given a timed trace and a TB net model N and the function, there is a conformance relation between and N iff. there exists a feasible execution path of N, such that conforms to , according to .\n\nFor example consider the timed trace introduced in (1) and the following definition of the mapping function\n\nIn this case, there exists a conformance relation between and the producer-consumer TB net reported in Fig. 1. In fact, from the initial marking the transition is enabled with the following binding : . The timestamp belongs to : [0, 1000], thus we observe a valid event, and we can compute the next marking , reachable from by firing the transition at time 450.\n\nThe transition is enabled from by the binding : . The timestamp 1100, associated with the second event belongs to : [1000, 2500], thus we observe a valid event, and we can compute the next marking , reachable from by firing the transition at time 1100.\n\nAnd so forth, until we process the last action method. The complete path , such that conforms to is:\n\n## 4 The MahaRAJA Framework\n\nWe implemented the runtime verification technique presented in the previous section as a Java library3. The main component of the library is the Monitor, i.e., a system that observes and analyzes an executing SUT (Java program) in order to verify its correctness by comparing the observed behavior (i.e., ordered timed trace) with an expected behavior (i.e., feasible execution path) of the TB model given in input as a PNML file [18]. The model can be easily generated using a graphical user interface that allows the user to create and edit arbitrary complex TB net models through simple drag and drop gestures.\n\nThe input program is linked to the formal specification exploiting the mechanism of Java annotations to map action methods to corresponding transitions (i.e., the mapping function introduced in Definition 5). The Monitor is executed in a separated thread and is composed of the following modules: the Observer, the Analyzer and the Executor.\n\nThe Observer module makes use of AspectJ [19] to observe code execution and trigger the verification of the conformance relation, performed by the Analyzer component. The framework defines a set of annotations4 used to define the action type function and the action methods mapping function. The following annotations were inserted into the producer-consumer program:\n\nAs an example, the annotation maps the consume action method to { , } action times, thus observable both before and after its own execution. For each invocation we observe two events: the first event is bound to the transition; the second event is bound to the transition.\n\nThe execution of the methods annotated by , and are handled by , and AspectJ advice types [19], respectively, to generate the proper and\/or observable events. The Observer module inspects the execution of the SUT by using the facilities of AspectJ and generate observable events into the event queue by injecting additional code upon the execution of the action methods.\n\nThe Analyzer module incrementally builds the timed trace through the verification procedure reported in Algorithm 1. For each occurring event e, extracted from the event queue, the Analyzer launches the verification procedure, passing as argument the current marking and the current event e. Thus, it verifies that in the input model, the transition t, retrieved by applying the function, is enabled from the current marking m (line 3) and the time belongs to (line 6). If this condition holds, the Executor component updates the trace (line 7) creating a new reachable marking with the proper timestamp .\n\nIt is worth noting that, given an event e and a reachable marking m, there can be multiple enabled bindings for the transition t (line 5). In this case, for each binding, we compute a new reachable marking and we put it into the reachability set (line 8) representing all the valid next steps of . During the construction of the path, for each event e it is fundamental to maintain the entire 1-step reachability set for the transition t (instead of a single reachable marking), in order to avoid false alarms (i.e., unreal inconsistencies between the code and its specification) during the conformance checking. The Verify function is executed for each marking in the reachability set. If there does not exist any marking in the reachability set such that the verification procedure is successful, the Analyzer does not verify the conformance relation between and , thus a conformance failure exception is thrown. This exception contains useful information about the throwing action method, along with the timestamp associated to this event and the set of enabled bindings (i.e., the expected events). The Analyzer module do not need to store the full history of both and , thus it requires limited extra memory. Moreover, the verification procedure is scalable with respect to the SUT size, in fact its own time complexity (i.e., ) does not depend on either the model size or the entire state space, but just on the number of enabled bindings in the current marking.\n\nTo alleviate possible burst of the monitoring overhead, our framework makes use of the Java Thread Affinity [20] library to separate the execution of the SUT and the Monitor into different isolated CPU cores, decreasing the latency caused by suspending and resuming important running tasks. Moreover, MahaRAJA let the user define a tolerance that should be set to the expected monitor invocation overhead. The tolerance allows two levels of risk to be defined: warning and error corresponding to a timing constraint violation respectively in- and outside the tolerance range. By default the tolerance is disabled, in fact, its definition involves the evaluation of the monitor invocation overhead, which is not an easy task and it strictly depends on the underlying hardware\/software environment.\n\nIn order to help the user to increase the confidence about the correctness of the SUT, the MahaRAJA software tool can be used in conjunction with JUnit to generate different monitored test cases. This way, the user can integrate our runtime verification technique with assertions on variables and on specific goal conditions, given in terms of time constraint (i.e., a logical predicate formed by linear inequalities involving timestamps) on the observed timed trace [17].\n\nThe next section introduces our experimental results that could also be used as a guide to evaluate the runtime overhead in order to reason about the timing constraints of the SUT.\n\n## 5 Experimental Validation\n\nWe validated the MahaRAJA framework by collecting data at runtime and performing a testing activity on a number of real-time benchmarking examples [14] summarized in Table 1: a simple producer-consumer (P\/C) application, a cruise-control (CC) system, an automated teller machine (ATM) software system, an elevator (EL) controller and a factory (FA) automation distributed system.\n\nTable 1.\n\nCase studies.\n\nCase study | |P| | |T| | SLOC | Tasks | Frequency\n\n---|---|---|---|---|---\n\nP\/C | 5 | 4 | 208 | 3 | 4,19\n\nCC | 11 | 16 | 1185 | 4 | 2,65\n\nATM | 12 | 25 | 1409 | 3 | 1,57\n\nEL | 18 | 24 | 1231 | 5 | 1,12\n\nFA | 14 | 12 | 996 | 10 | 1,09\n\nThe model size is reported in terms of number of places (|P|) and number of transitions (|T|). The SLOC column reflects the source lines of code number in the corresponding Java SUT. The tasks column contains the number of parallel threads (or process in case of distributed computing) composing the SUT. The frequency column reports the average number of monitor invocations per second.\n\nThe monitoring process ran in parallel with the SUT in a machine equipped with a Intel Xeon E5-2630 at 2.30 GHz CPU, 32 GB of RAM, the Ubuntu 14.04.3 LTS (GNU\/Linux 3.13.0-39-generic x86_64) operating system with a completely fair scheduler [21], and the Java HotSpot 1.8 64-Bit Server virtual machine using the Garbage-First (G1) collector tuned to avoid full runs5. Data about runtime overhead is reported in this section. They were extracted from program executions monitoring events. The runtime overhead has been assessed considering the following metrics.\n\n * Monitoring Overhead: The monitoring overhead is caused by the AspectJ instrumentation (AJO) and the monitor invocation overhead (MIO). Table 2 reports the average values (in s) of these two different components, for each running case study. The average AJO values, introduced by the invocation of AspectJ advices, strictly depend on the byte code generated from the annotated program by using the ajc compiler [19]. Generally, we observed a lower AJO within advices (i.e., events with action time) and a higher AJO within advices (i.e., events with both and action time). The order of magnitude of the measured AJO values is approximately 10 s (see Table 2).\n\nThe MIO (i.e., the time required to enqueue an occurring event into the event queue) does not depend on the action time. In general, both the MIO and the AJO have the same order of magnitude, but the average MIO is 50% lower. Thus, the overhead introduced by AspectJ dominates the overall monitoring overhead. Although the distribution of the MIO values for different programs are very similar, a different monitor invocation frequency (e.g., the CC frequency is 47% lower than the P\/C one) impacts on the average MIO. For instance, the average P\/C MIO is lower then the average CC MIO (approximately 16% lower).\n\n * Jitter: The Jitter represents the deviance between the monitoring overhead values. The results reported in Table 2 show that the order of magnitude of the AJO jitter and the MIO jitter is the same (approximately 10 s). We found that the AJO jitter, for all the action method types, is approximately 43% lower than the MIO jitter. While the AJO jitter strictly depends on the behavior of AspectJ at runtime, the MIO jitter depends on the state of the Monitor during the execution of the action methods. In fact, a suspended Monitor causes a burst of the MIO due to the time required by resuming it, during the enqueuing of an acton method into an empty event queue.\n\n * Detection latency: Bounding the detection latency (DL) makes it possible for the Monitor to quickly recognize a conformance failure, thus making the SUT able to promptly react to a degraded situation though a recovery procedure.\n\nTable 2 reports the average DL in s. Our experience indicates the following trend: the higher the frequency is, the lower the DL is. This behavior is caused by the overhead of resuming a suspended Monitor thread. In fact, a low frequency implies an empty event queue almost all the execution time long. In this case, it is very likely to observe the Monitor resumption upon an incoming event. Therefore, although different programs lead to similar DL distribution, lower monitor invocation frequency results in more scattered DL values. The results obtained from our experiments show that MahaRAJA reacts to a conformance failure with a DL of the order of 1 ms.\n\n * Memory Overhead: The memory overhead is the space used by the Java virtual machine to run and maintain the Monitor component. Table 2 shows that MahaRAJA requires negligible auxiliary memory (few KBytes on average). Gathered data shows that this value is related to the monitor invocation frequency: the higher is the frequency, the higher is the memory overhead. In fact, a high frequency implies the accumulation of events into the event queue.\n\nTable 2.\n\nMonitoring overhead experiments results.\n\nCase study | P\/C | CC | ATM | EL | FA\n\n---|---|---|---|---|---\n\nAJO ( s) | Before | 43.8 | 48.5 | 45.0 | 44.5 | 50.1\n\nAfter | 59.0 | 51.5 | 47.4 | 52.3 | 52.8\n\nAround | 53.4 | 53.8 | 53.1 | 61.4 | 58.3\n\nAJO Jitter ( s) | Before | 28.2 | 30.9 | 36.6 | 37.1 | 33.0\n\nAfter | 27.2 | 24.8 | 19.6 | 20.6 | 20.3\n\nAround | 22.8 | 12.5 | 26.2 | 27.6 | 34.5\n\nMIO ( s) | 28.0 | 23.6 | 24.0 | 23.0 | 24.1\n\nMIO Jitter ( s) | 45.5 | 45.4 | 44.8 | 50.4 | 45.7\n\nDL ( s) | 874.7 | 1221.9 | 1243.9 | 1274.4 | 1335.6\n\nMemory (KB) | 10838 | 5302 | 3503 | 2083 | 1734\n\n## 6 Related Work and Comparative Evaluation\n\nThis section mentions the main approaches in the field of event-based runtime verification, and reports also a qualitative comparative evaluation of these tools for the runtime verification of Java programs. A preliminary quantitative comparison is available at [17].\n\nCoMA [22] is a formal specification-based software tool that can continuously monitor the behaviors of a target Java program and recognize undesirable behaviors in the implementation with respect to its formal specification given in terms of Abstract State Machines (ASMs). Java PathExplorer (JPaX) [23] is a system for monitoring the execution of Java programs. The system extracts an execution trace (as a sequence of events) from a running program and verifies that the trace satisfies certain (past and future) LTL properties. Monitored bytecode is instrumented (by using JTrek) and an observer can check during runtime that the properties are never violated. The Java Monitoring and Checking (MaC) architecture [24] supplies two different specification languages: the Primitive Event Definition Language (PEDL) and Meta Event Definition Language (MEDL) allowing for a separation between the definition of the primitive events of a system and the system properties. Instrumented programs send an event stream to the event recognizer to identify higher-level activities, which are in turn processed to find property violations. HAWK [25] is a programming-oriented extension of the rule-based EAGLE logic [26] that has been shown capable of defining and implementing a range of finite trace monitoring logics, including future and past time temporal logic, extended regular expressions, and state machines. It is implemented as a Java library able to perform monitoring through a state-by-state comparison, avoiding to store the entire input trace.\n\nLarva [27] is an event-based runtime verification monitoring tool for temporal and contextual properties of Java programs. The technique implemented in Larva makes use of dynamic communicating automata with timers and events (DATE) to describe properties of systems.\n\nMonitored-oriented programming (MOP) [3] allows the source code of the SUT to be annotated with formal property specifications that can be written in any supported formalism. The formal specifications are translated in the target programming language. Thus, the obtained monitoring code can be used either at runtime or offline by checking traces recorded by probes. In this case, the violation handling mechanism is itself part of the design of the SUT, rather than an additional component on top of the system.\n\nThe analysis technique in [12] tries to estimate the rate of possible invalid occurring events and the maximum detection latency to realize predictable monitoring schemas. However, this is not always applicable due to different patterns in the occurrence of monitored events for different execution scenarios of the SUT [28]. An alternative approach used to decrease the monitoring overhead is time-triggered monitoring [28, 29] which makes use of periodic sampling of the SUT state and different strategies to reduce the monitoring overhead by dynamically adjusting the sampling period.\n\nTable 3 reports a comparative evaluation between MahaRAJA and some representative state-of-the-art runtime verification software tools. The following key features have been taken into account (for a more general comparison see [1]):\n\nTable 3.\n\nFeatures comparison of different Java runtime monitoring tools.\n\nTool | MahaRAJA | Coma | Larva | Java-MOP | Java-MaC | Hawk | JPaX\n\n---|---|---|---|---|---|---|---\n\nFormalism | TB nets | ASMs | DATEs | various | PEDL, MEDL | LTL, PLTL | LTL, PLTL\n\nO\/D | O | O | O | O, D | D | D | D\n\nS\/E | E | S | E | E | E | E | E\n\nExceptions | | | | | | |\n\nReal-time | | | | | | |\n\nVariables | | | | | | |\n\nSelf-awareness | | | | | | |\n\nTesting | | | | | | |\n\n Depending on the plug-in: Finite State Machines, Regular Expressions, Context Free Grammar, PLTL, LTL, String Rewriting Systems. Operational\/Descriptive formalism. State\/Event-based approach.\n\n * formalism: it represents the formalism used to specify the SUT;\n\n * operational\/descriptive: it represents whether the tool uses a operational or descriptive formalism;\n\n * state\/event-based: state-based monitoring approaches rely on a state-by-state comparison, where a state stores the relevant data about the SUT;\n\n * exceptions: it represents whether or not the user can express properties which include exception handling;\n\n * real-time: it refers to the ability to verify quantitative temporal properties;\n\n * variables: it refers to the ability of monitoring value changes of variables;\n\n * self-awareness: it refers to the capability of the monitoring system to return feedback to the SUT upon failure;\n\n * testing: it represents the possibility to use the facilities of the monitoring framework to write test cases.\n\nThe results of our comparative evaluation show for each selected monitoring tool, the explicit support for the considered features. As we can see, the MahaRAJA framework has some interesting features, not directly supported by other tools. For instance, it allows both the runtime verification and testing of quantitative temporal properties. MahaRAJA does not support the monitoring of variables (Coma, Larva, Java-MOP and Java-MaC have this feature).\n\n## 7 Conclusion\n\nWe presented an event-based runtime verification approach and its supporting tool MahaRAJA to verify temporal properties on Java programs. The proposed framework adopts TB nets to represent the desired behavior of the SUT, including real-time requirements. The designer annotates the source code to link Java methods to transitions of the model. Then, MahaRAJA exploits AspectJ to observe code execution and trigger the conformance verification at runtime. The usefulness of the approach has been assessed by monitoring a number of real-time benchmarking case-studies to discover both modeling and implementation faults. MahaRAJA focuses on the monitoring of timed events and its main limitation is that it does not support the monitoring of variables, although they can be easily checked during testing activity using MahaRAJA in conjunction with JUnit. Nonetheless, we believe that our approach represents a viable technique for checking temporal properties of Java programs with respect to their formal specifications. Our experience shows that the monitoring overhead can be numerically evaluated and we found AspectJ as the major bottleneck. For this reason, we plan to replace AspectJ with other efficient bytecode transformation techniques [30]. The auxiliary memory used by the instrumentation is negligible and a preliminary quantitative comparison with other representative state-of-the-art runtime verification software tools individuates MahaRAJA as the less invasive [17]. The detection latency is also limited, thus allowing for a prompt recover after a failure.\n\nThe quantitative evaluation lead us to consider MahaRAJA as a viable light-weight pluggable tool to support the verification at runtime of real-time self-adaptive systems [15, 31]. We will explore this last topic in our future work.\n\nReferences\n\n1.\n\nDelgado, N., Gates, A.Q., Roach, S.: A taxonomy and catalog of runtime software-fault monitoring tools. IEEE Trans. Softw. Eng. 30(12), 859\u2013872 (2004)CrossRef\n\n2.\n\nGhezzi, C., Mandrioli, D., Morasca, S., Pezz\u00e8, M.: A unified high-level Petri net formalism for time-critical systems. IEEE Trans. Softw. Eng. 17, 160\u2013172 (1991)CrossRef\n\n3.\n\nChen, F., D'Amorim, M., Ro\u015fu, G.: A formal monitoring-based framework for software development and analysis. In: Davies, J., Schulte, W., Barnett, M. (eds.) ICFEM 2004. LNCS, vol. 3308, pp. 357\u2013372. Springer, Heidelberg (2004). doi:10.\u200b1007\/\u200b978-3-540-30482-1_\u200b31 CrossRef\n\n4.\n\nArcaini, P., Gargantini, A., Riccobene, E.: Combining model-based testing and runtime monitoring for program testing in the presence of nondeterminism. In: 2013 IEEE Sixth International Conference on Software Testing, Verification and Validation Workshops (ICSTW), pp. 178\u2013187, March 2013\n\n5.\n\nLiang, H., Dong, J.S., Sun, J., Wong, W.E.: Software monitoring through formal specification animation. Innov. Syst. Softw. Eng. 5(4), 231\u2013241 (2009)CrossRef\n\n6.\n\nFelder, M., Gargantini, A., Morzenti, A.: A theory of implementation and refinement in timed Petri nets. Theoret. Comput. Sci. 202(12), 127\u2013161 (1998)MathSciNetCrossRef00078-9)MATH\n\n7.\n\nBengtsson, J., Yi, W.: Timed Automata: Semantics, Algorithms and Tools. Springer, Heidelberg (2004)MATH\n\n8.\n\nGurevich, Y.: Sequential abstract-state machines capture sequential algorithms. ACM Trans. Comput. Log. 1(1), 77\u2013111 (2000)MathSciNetCrossRef\n\n9.\n\nRamchandani, C.: Analysis of asynchronous concurrent systems by timed Petri nets. Technical report, Cambridge, MA, USA (1974)\n\n10.\n\nIglesia, D.G.D.L., Weyns, D.: MAPE-K formal templates to rigorously design behaviors for self-adaptive systems. ACM Trans. Auton. Adapt. Syst. 10(3), 15:1\u201315:31 (2015)CrossRef\n\n11.\n\nLee, W.J., Cha, S.D., Kwon, Y.R.: Integration and analysis of use cases using modular Petri nets in requirements engineering. IEEE Trans. Softw. Eng. 24(12), 1115\u20131130 (1998)CrossRef\n\n12.\n\nZhu, H., Dwyer, M.B., Goddard, S.: Predictable runtime monitoring. In: Proceedings of the 2009 21st Euromicro Conference on Real-Time Systems, ser. ECRTS 2009, pp. 173\u2013183. IEEE Computer Society, Washington, DC (2011)\n\n13.\n\nValmari, A.: The state explosion problem. In: Reisig, W., Rozenberg, G. (eds.) ACPN 1996. LNCS, vol. 1491, pp. 429\u2013528. Springer, Heidelberg (1998). doi:10.\u200b1007\/\u200b3-540-65306-6_\u200b21 CrossRef\n\n14.\n\nGomaa, H.: Designing Concurrent, Distributed, and Real-Time Applications with UML, 1st edn. Addison-Wesley Longman Publishing Co., Inc., Boston (2000)\n\n15.\n\nCamilli, M., Gargantini, A., Scandurra, P.: Specifying and verifying real-time self-adaptive systems. In: 2015 IEEE 26th International Symposium on Software Reliability Engineering (ISSRE), pp. 303\u2013313, November 2015\n\n16.\n\nBellettini, C., Capra, L.: Reachability analysis of time basic Petri nets: a time coverage approach. In: Proceedings of the 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, ser. SYNASC 2011, pp. 110\u2013117. IEEE Computer Society, Washington, DC (2011)\n\n17.\n\nMaharaja framework. http:\/\/\u200bcamilli.\u200bdi.\u200bunimi.\u200bit\/\u200bmaharaja\/\u200b. Accessed Dec 2016\n\n18.\n\nHillah, L.M., Kordon, F., Petrucci, L., Tr\u00e8ves, N.: PNML framework: an extendable reference implementation of the Petri net markup language. In: Lilius, J., Penczek, W. (eds.) PETRI NETS 2010. LNCS, vol. 6128, pp. 318\u2013327. Springer, Heidelberg (2010). doi:10.\u200b1007\/\u200b978-3-642-13675-7_\u200b20 CrossRef\n\n19.\n\nKiczales, G., Hilsdale, E., Hugunin, J., Kersten, M., Palm, J., Griswold, W.G.: An overview of AspectJ. In: Knudsen, J.L. (ed.) ECOOP 2001. LNCS, vol. 2072, pp. 327\u2013354. Springer, Heidelberg (2001). doi:10.\u200b1007\/\u200b3-540-45337-7_\u200b18 CrossRef\n\n20.\n\nChronicle Software: Java Thread Affinity Library (2016). http:\/\/\u200bchronicle.\u200bsoftware\/\u200bproducts\/\u200bthread-affinity\/\u200b. Accessed Jan 2016\n\n21.\n\nLi, T., Baumberger, D., Hahn, S.: Efficient and scalable multiprocessor fair scheduling using distributed weighted round-robin. SIGPLAN Not. 44(4), 65\u201374 (2009)CrossRef\n\n22.\n\nArcaini, P., Gargantini, A., Riccobene, E.: CoMA: conformance monitoring of Java programs by abstract state machines. In: Khurshid, S., Sen, K. (eds.) RV 2011. LNCS, vol. 7186, pp. 223\u2013238. Springer, Heidelberg (2012). doi:10.\u200b1007\/\u200b978-3-642-29860-8_\u200b17 CrossRef\n\n23.\n\nHavelund, K., Ro\u015fu, G.: An overview of the runtime verification tool Java PathExplorer. Formal Methods Syst. Des. 24(2), 189\u2013215 (2004)CrossRefMATH\n\n24.\n\nKim, M., Viswanathan, M., Kannan, S., Lee, I., Sokolsky, O.: Java-MaC: a run-time assurance approach for Java programs. Form. Methods Syst. Des. 24(2), 129\u2013155 (2004)CrossRefMATH\n\n25.\n\nd'Amorim, M., Havelund, K.: Event-based runtime verification of Java programs. SIGSOFT Softw. Eng. Notes 30(4), 1\u20137 (2005)CrossRef\n\n26.\n\nBarringer, H., Goldberg, A., Havelund, K., Sen, K.: Rule-based runtime verification. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 44\u201357. Springer, Heidelberg (2004). doi:10.\u200b1007\/\u200b978-3-540-24622-0_\u200b5 CrossRef\n\n27.\n\nColombo, C., Pace, G.J., Schneider, G.: Dynamic event-based runtime monitoring of real-time and contextual properties. In: Cofer, D., Fantechi, A. (eds.) FMICS 2008. LNCS, vol. 5596, pp. 135\u2013149. Springer, Heidelberg (2009). doi:10.\u200b1007\/\u200b978-3-642-03240-0_\u200b13 CrossRef\n\n28.\n\nBonakdarpour, B., Navabpour, S., Fischmeister, S.: Time-triggered runtime verification. Formal Methods Syst. Des. 43(1), 29\u201360 (2013)CrossRefMATH\n\n29.\n\nNavabpour, S., Bonakdarpour, B., Fischmeister, S.: Path-aware time-triggered runtime verification. In: Qadeer, S., Tasiran, S. (eds.) RV 2012. LNCS, vol. 7687, pp. 199\u2013213. Springer, Heidelberg (2013). doi:10.\u200b1007\/\u200b978-3-642-35632-2_\u200b21 CrossRef\n\n30.\n\nMastrangelo, L., Hauswirth, M.: JNIF: Java native instrumentation framework. In: Proceedings of the International Conference on Principles and Practices of Programming on the Java Platform: Virtual Machines, Languages, and Tools, ser. PPPJ 2014, pp. 194\u2013199. ACM, New York (2014)\n\n31.\n\nde Lemos, R., Garlan, D., Ghezzi, C., Giese, H.: Software engineering for self-adaptive systems: assurances (Dagstuhl Seminar 13511). Dagstuhl Rep. 3(12), 67\u201396 (2014). http:\/\/\u200bdrops.\u200bdagstuhl.\u200bde\/\u200bopus\/\u200bvolltexte\/\u200b2014\/\u200b4508\n\nFootnotes\n\n1\n\nMonitoring at Runtime of temporAl properties on Java Applications.\n\n2\n\n is a map , formally expressed as a weighted sum of X elements.\n\n3\n\nThe source code, binaries, and some runnable examples can be found at [17].\n\n4\n\nThey are recorded in class files by the compiler and retained by the virtual machine at run time, so they can be read reflectively by the Observer component.\n\n5\n\nAdditional information about the configurations of MahaRAJA and the JVM is available at [17].\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_9\n\n# Model-Counting Approaches for Nonlinear Numerical Constraints\n\nMateus Borges1 , Quoc-Sang Phan2, Antonio Filieri1 and Corina S. P\u0103s\u0103reanu2, 3\n\n(1)\n\nImperial College London, London, UK\n\n(2)\n\nCarnegie Mellon University Silicon Valley, Mountain View, USA\n\n(3)\n\nNASA Ames, Mountain View, USA\n\nMateus Borges\n\nEmail: m.borges@ic.ac.uk\n\nAbstract\n\nModel counting is of central importance in quantitative reasoning about systems. Examples include computing the probability that a system successfully accomplishes its task without errors, and measuring the number of bits leaked by a system to an adversary in Shannon entropy. Most previous work in those areas demonstrated their analysis on programs with linear constraints, in which cases model counting is polynomial time. Model counting for nonlinear constraints is notoriously hard, and thus programs with nonlinear constraints are not well-studied. This paper surveys state-of-the-art techniques and tools for model counting with respect to SMT constraints, modulo the bitvector theory, since this theory is decidable, and it can express nonlinear constraints that arise from the analysis of computer programs. We integrate these techniques within the Symbolic Pathfinder platform and evaluate them on difficult nonlinear constraints generated from the analysis of cryptographic functions.\n\nKeywords\n\nModel counting modulo theoriesBitvector arithmeticNonlinear constraintsCryptographic functions\n\n## 1 Introduction\n\nModel counting is of central importance in quantitative reasoning, with applications in probabilistic inference [7, 8], reliability analysis [11], and quantitative information flow [2, 3, 23, 24]. Most previous work in those areas was performed on programs with linear constraints, using model counting tools such as Latte [18]. Model counting for nonlinear constraints is notoriously hard, and thus programs with nonlinear constraints are not well-studied (with only limited support for floating-point values abstracted as real numbers [4]). In this paper we survey state-of-the-art model counting techniques and tools for SMT (satisfiability modulo theories) constraints modulo the bitvector theory, since this theory is decidable and it can express the nonlinear constraints that arise naturally from the analysis of computer programs. Our work is motivated by a security project [1] that aims to develop automated quantitative information flow analysis techniques for complex applications, including cryptographic functions that are very difficult to analyze. The bitvector theory is particularly useful for these functions which typically use operations on bitvector values.\n\nWe integrate the surveyed techniques within Symbolic PathFinder (SPF) [25] and evaluate them on difficult nonlinear constraints generated using symbolic execution. Although we restrict our evaluation to cryptographic functions, our study should be relevant to anybody interested in quantitative reasoning over complex, nonlinear systems.\n\n### 1.1 Symbolic Execution and SPF\n\nSPF performs symbolic execution over Java byte code programs. Symbolic execution [14] is a systematic analysis technique that executes a program on symbolic, rather than concrete, input values and computes the effects of the program as functions of these symbolic inputs. The result of symbolic execution is a set of symbolic paths, each with a path condition PC, which is a conjunction of constraints over the symbolic inputs that characterizes all the inputs that follow that path. All the PCs are disjoint by construction.\n\n### 1.2 Quantification of Information Leaks\n\nPerfect software security is hard to achieve. Systems often leak information to an adversary who can observe different aspects of program behavior. Research on quantitative information flow aims at quantifying (in number of bits) the expected leakage.\n\nA program can be viewed as a probabilistic function that maps a high security input h and a low security input l to an observable output o. An adversary tries to guess h by providing l and observing the output. The leakage of the program P is defined as the mutual information between the secret h and the public output o [19]: , where denotes the classical Shannon entropy of a random variable x, measuring the \"uncertainty\" about x. For a deterministic program P, there is no uncertainty about o when h is given. Therefore . The entropy can thus be computed as: .\n\nIntuitively, the leakage gives an estimate on the number of bits in the secret that an adversary can infer by observing the output of the program. If this estimate is small (or zero) then the program can be considered safe. In [2], Backes et al. combined model checking and model counting to compute the leakage when the observable is an output variable. In a similar setting, we used symbolic execution (SPF) combined with Latte to compute an upper bound on the leakage [23].\n\nMore recently [3, 24], we used SPF and Latte to compute the leakage when the observables are non-functional characteristics of program executions, i.e. side-channels, such as time consumed, number of memory accessed or packets transmitted over a network. In this model, a symbolic path identified by leads to a concrete observable . Assuming the secret input has uniform distribution, which means the adversary has no prior knowledge about it, the probability of observing can be computed using SPF and model counting as follows: , where is the number of solutions (computed with model counting) of constraint and is the size of the input domain D assumed to be (possibly very large but) finite.\n\nIn all the previous work mentioned above, Latte was used to perform model counting; it implements the polynomial time Barvinok algorithm to count models for a system of linear integer inequalities. However Latte cannot handle nonlinear constraints. In this paper we study approaches for the fixed-width bitvector theory, which can represent such constraints. In the following, we use the term \"bitvector\" and \"word\" interchangeably.\n\n## 2 Model Counting Techniques and Tools\n\nIn this section we evaluate several tool-supported approaches for counting the models of bitvector constraints. These approaches can be classified according to two orthogonal dimensions: exact vs approximate and bit-level vs word-level.\n\nExact techniques count the exact number of models for a given constraint. Approximate techniques only explore a portion of the solution space, carefully selected to provide probabilistic guarantees on the accuracy ( ) and confidence ( ) of the result. In particular, they guarantee that , where is the approximate result and c is the exact (unknown) count. Other randomized approaches not providing formal guarantees (e.g., [26, 31]) are not considered in this study.\n\nBit-level Approaches address the model counting problem for propositional (SAT) formulas, i.e., #SAT. Model counting for bit vector formulas can be performed as follows. A bitvector formula is first converted to a propositional formula using bit blasting to generate an equivalent Boolean circuit based on bit-level behavior of bitvector operations. This Boolean circuit is interpreted as a propositional logic problem and converted in conjunctive normal form (CNF); at this point #SAT approaches can be used to count the number of models. While the procedure is general, the conversion of Boolean circuits into CNF is usually based on the Tseitin transformation [30], which introduces additional Boolean variables in the process. While this transformation guarantees a model for the CNF form is also a model for the initial problem, the introduction of additional variables may lead to different model counts. For this reason, in this paper we use only #SAT tools supporting projection, i.e., able to project the solution space only on the variables appearing in the Boolean circuit, ignoring the ones introduced by Tseitin transformation.\n\nWe found five tools for #SAT that support projection and can thus be used in our setting for bitvector counting: SharpCDCL, All-SAT, SharpSAT and Dsharp, which compute exact solutions, and ApproxMC-p, which produces approximate solutions.\n\n * SharpCDCL [15] is an enumeration-based approach; it iteratively invokes the SAT solver to produce at each iteration a new model, keeping trace of the set of models and their number.\n\n * All-SAT [13] and SharpSAT [28] extend the DPLL algorithm to count the number of solutions of a SAT problem. They both use caching mechanisms and use constraint propagation for pruning the DPLL, which avoid the exhaustive exploration of subtrees containing no solutions.\n\n * Dsharp [20] reuses the algorithmic core of SharpSAT, adapting it to work with a deterministic Decomposable Negation Normal Form (d-DNNF) representation of the SAT problem. d-DNNF provides a more compact representation of the constraints in memory that, according to [20], may better support model counting.\n\n * ApproxMC-p [16] takes as input accuracy and confidence targets and produce an approximate count which deviates from the exact count by at most a factor with probability at least . The approach uses universal hash functions to perform a uniform sampling within the domain. The ratio between the number of models for this sample and the sample size is used as an estimate of the ratio of models over the entire problem domain. The samples is automatically decided to achieve and .\n\nWord-Level Approaches aim to avoid the cost of bit blasting by defining counting procedures that operate directly on SMT variables and operations. We investigate a recent tool that provides an approximate counting procedure for bitvectors: SMTApproxMC [7]. SMTApproxMC uses word-level hashing functions to sample a finite number of candidate models and then an SMT solver to check how many of these candidate models satisfy the constraint. The number of models found within the sample are used to build a robust statistical estimator achieving the desired probabilistic guarantees. SMTApproxMC can avoid bit blasting whenever the SMT solver can check a constraint without it (e.g., for linear constraints); however, for nonlinear constraints (all the subjects of this study), SMTApproxMC requires bit blasting.\n\nChistikov et al. [8] also extend the hashing-based approach used for #SAT (e.g., in [16]) to counting for SMT problems. Hashing functions allow to uniformly sample candidate solutions. Statistics on the sample are used to estimate the total number of models. However, no tool is available and, according to [7], SMTApproxMC is faster.\n\nA related approach is implemented in the MathSAT solver [9], which provides a functionality, called All-SMT, that given a set of Boolean variables , it can enumerate all the models of the problem projected on . The source code of the tool is not available, nor a technical description of the All-SMT feature, thus we do not know the details of the counting algorithm it implements but can only report its execution time. Our own All-SMT solver aZ3 [21, 22] is less efficient than MathSAT, so we do not include its experiment results here.\n\nOther Approaches. We have also investigated other techniques for model counting: blocking-clause enumeration, BDD-based enumerations, counting with Gr\u00f6bner bases and a brute-force enumeration that we use as baseline.\n\nBlocking clause enumeration make the solver find all the models for a problem by iteratively adding the negation of already found models to the initial problem. The iteration terminates when no more solutions can be found. Intuitively, this method can work only for complex problems with few models. We implemented it on top of Z3 SMT solver [10] to practically confirm this intuition.\n\nBDD-based enumeration represents a propositional formula as a binary decision diagram and then counts the paths from its root to the leaf representing the Boolean constant \"true\". We implemented a prototype based on the BDD library CUDD [27], which builds a BDD corresponding to a constraint bitblasted with Z3. Unfortunately, for all the subjects in this study the execution time exceeded the timeout of 1 h.\n\nGr\u00f6bner bases are used in computational algebra to reason about polynomials over finite fields. Boolean variables and and operators from propositional logic can be mapped into corresponding variables and functions over polynomials. Each zero of such polynomials corresponds to exactly one model of the initial propositional formula [12, 29]. Algebraic solvers can be used to find those zeroes. We implemented this technique using PolyBoRi [5], but its execution timed out for all the subjects.\n\nFinally, we also implemented as a reference a brute force approach which encodes the constraints as bitwise operations on unsigned integers in C. The mapping is straightforward from the smtlib representation. The program iterates over the entire domain and count the number of models for a constraint. We compiled the C sources using level 1 optimization in GCC.\n\n## 3 Evaluation\n\nSubjects. We study modular exponentiation ( ) and modular multiplication ( ) implementations. These are core routines for most public-key cryptographic systems, most notably RSA. In the past, some implementations have been found vulnerable to side channel attacks [6, 17], mostly as effect of optimizations. Our goal is to localize side channels by quantifying information leaks with symbolic execution and model counting (see Sect. 1).\n\nFor our experiments, we analyzed a set of randomly selected path conditions from two different implementations of the modular operations (the source code is given in the appendix). The first implementation (subjects a-* in the following), taken from [24], optimizes modPow with a reduction step at each iteration, but uses a naive implementation of modMul. We analyze the program with the same configurations from [24]: the modulus m can be either 1717, 834443, or 1964903306; both the base b and exponent e are symbolic, with and .\n\nThe second implementation (benchmarks b-*) is more realistic as it uses Java's BigInteger class to encode large messages and secrets (this example was provided to us by DARPA at a recent engagement) and uses fast multiplication. Here modulus m is fixed with a 1536-bit value; the base b is also a concrete 1532-bit value; the exponent e is symbolic BigInteger with 40 bits. We analyze both modPow and modMul, where both x and y are symbolic 24-bit BigInteger.\n\nFig. 1.\n\nExecution time comparison.\n\nExperimental Results. Figure 1 summarizes the performance of the different tools. The results indicate that enumeration-based techniques perform well for complex problem with few solutions (SharpCDCL, Z3-BC). Exact techniques based on DPLL (All-SAT and SharpSAT) scale better than enumeration, but fail for the subjects involving complex constraints over large domains, like a-6 and a-7 which have approximately 58k and 78k CNF clauses over a domain of 59B points. Notably, All-SAT produced the correct count only for the first three subjects. For all the others (marked with ), it significantly under-approximated the count. However, the most recent release dates back to 2004 and the tool is not maintained, making difficult to get the tool fixed.\n\nThe performance of approximate methods (ApproxMC and SMTApproxMC) depends on the required accuracy and confidence . The correct counts and the approximate ones are shown in a table in the appendix. We run the tools with two different settings: (f) , and (p) , . SMTApproxMC provides a bad performance on our subjects; this is however expected since its internal solver is required to bit blast our nonlinear constraints for each query. From our experience, low-accuracy approximate methods can be used for a preliminary assessment of the number of solutions: if the coarse approximate count is small, exact methods may then be used for an exact solution. Similarly, if the count is close to the domain size, it is possible to count exactly the models of the negation of the problem (which should be only a few). If the count is far from its extreme values (0 and domain size) or if the problem is particularly complex ( CNF clauses on our subjects), exact counters will probably fail if the domain is large and a more precise approximate solution can be pursued.\n\nNot surprisingly, the brute force approach is faster than model counting tools when the domain size is small enough ( ), but it is not a viable solution for larger problems.\n\n## 4 Conclusion\n\nWe surveyed model counting techniques that are applicable to complex nonlinear constraints. We restricted our study to techniques and tools that are capable of providing formal guarantees on the results. Our survey suggests that that the most promising techniques use approximate model counting and bit-level hashing, however the performance of the tools can degrade when increased precision is required. SMT-based model counting is still a very young research area, but its relevance for quantitative analysis can be an effective driver for its development, as program verification has effectively driven the development in SMT solving.\n\nAcknowledgement\n\nThis work was funded in part by the National Science Foundation (NSF Grant Nos. CCF-1319858, CCF-1549161) and also by DARPA under agreement number FA8750-15-2-0087. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. Mateus Borges is funded by an Imperial College PhD Scholarship.\n\nReferences\n\n1.\n\nISSTAC: Integrated Symbolic Execution for Space-Time Analysis of Code. http:\/\/\u200bwww.\u200bcmu.\u200bedu\/\u200bsilicon-valley\/\u200bresearch\/\u200bisstac\n\n2.\n\nBackes, M., Kopf, B., Rybalchenko, A.: Automatic discovery and quantification of information leaks. In: SP 2009, pp. 141\u2013153 (2009)\n\n3.\n\nBang, L., Aydin, A., Phan, Q.S., P\u0103s\u0103reanu, C.S., Bultan, T.: String analysis for side channels with segmented oracles. In: FSE 2016, pp. 193\u2013204. ACM (2016)\n\n4.\n\nBorges, M., Filieri, A., d'Amorim, M., P\u0103s\u0103reanu, C.S., Visser, W.: Compositional solution space quantification for probabilistic software analysis. In: PLDI, pp. 123\u2013132. ACM (2014)\n\n5.\n\nBrickenstein, M., Dreyer, A.: PolyBoRi: a framework for gr\u00f6bner-basis computations with boolean polynomials. J. Symb. Comput. 44(9), 1326\u20131345 (2009)CrossRefMATH\n\n6.\n\nBrumley, D., Boneh, D.: Remote timing attacks are practical. In: SSYM 2003, pp. 1\u20131. USENIX Association (2003)\n\n7.\n\nChakraborty, S., Meel, K.S., Mistry, R., Vardi, M.Y.: Approximate probabilistic inference via word-level counting. In: AAAI 2016, pp. 3218\u20133224 (2016)\n\n8.\n\nChistikov, D., Dimitrova, R., Majumdar, R.: Approximate counting in SMT and value estimation for probabilistic programs. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 320\u2013334. Springer, Heidelberg (2015). doi:10.\u200b1007\/\u200b978-3-662-46681-0_\u200b26\n\n9.\n\nCimatti, A., Griggio, A., Schaafsma, B.J., Sebastiani, R.: The MathSAT5 SMT solver. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013. LNCS, vol. 7795, pp. 93\u2013107. Springer, Heidelberg (2013). doi:10.\u200b1007\/\u200b978-3-642-36742-7_\u200b7 CrossRef\n\n10.\n\nMoura, L., Bj\u00f8rner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337\u2013340. Springer, Heidelberg (2008). doi:10.\u200b1007\/\u200b978-3-540-78800-3_\u200b24 CrossRef\n\n11.\n\nFilieri, A., P\u0103s\u0103reanu, C.S., Visser, W.: Reliability analysis in symbolic pathfinder. In: ICSE, pp. 622\u2013631. IEEE Press (2013)\n\n12.\n\nGao, S.: Counting zeros over finite fields using Gr\u00f6bner bases. Master's thesis, Carnegie Mellon University (2009)\n\n13.\n\nGrumberg, O., Schuster, A., Yadgar, A.: Memory efficient all-solutions SAT solver and its application for reachability analysis. In: Hu, A.J., Martin, A.K. (eds.) FMCAD 2004. LNCS, vol. 3312, pp. 275\u2013289. Springer, Heidelberg (2004). doi:10.\u200b1007\/\u200b978-3-540-30494-4_\u200b20 CrossRef\n\n14.\n\nKing, J.C.: Symbolic execution and program testing. Commun. ACM 19(7), 385\u2013394 (1976)MathSciNetCrossRefMATH\n\n15.\n\nKlebanov, V., Manthey, N., Muise, C.: SAT-based analysis and quantification of information flow in programs. In: Joshi, K., Siegle, M., Stoelinga, M., D'Argenio, P.R. (eds.) QEST 2013. LNCS, vol. 8054, pp. 177\u2013192. Springer, Heidelberg (2013). doi:10.\u200b1007\/\u200b978-3-642-40196-1_\u200b16 CrossRef\n\n16.\n\nKlebanov, V., Weigl, A., Weisbarth, J.: Sound probabilistic #SAT with projection. In: QAPL 2016, pp. 15\u201329 (2016)\n\n17.\n\nKocher, P.C.: Timing attacks on implementations of Diffie-Hellman, RSA, DSS, and other systems. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 104\u2013113. Springer, Heidelberg (1996). doi:10.\u200b1007\/\u200b3-540-68697-5_\u200b9\n\n18.\n\nLoera, J.A.D., Hemmecke, R., Tauzer, J., Yoshida, R.: Effective lattice point counting in rational convex polytopes. J. Symb. Comput. 38(4), 1273\u20131302 (2004)MathSciNetCrossRefMATH\n\n19.\n\nMalacaria, P.: Algebraic foundations for quantitative information flow. Math. Struct. Comput. Sci. 25, 404\u2013428 (2015)MathSciNetCrossRefMATH\n\n20.\n\nMuise, C., McIlraith, S.A., Beck, J.C., Hsu, E.I.: Dsharp: fast d-DNNF compilation with sharpSAT. In: Kosseim, L., Inkpen, D. (eds.) AI 2012. LNCS (LNAI), vol. 7310, pp. 356\u2013361. Springer, Heidelberg (2012). doi:10.\u200b1007\/\u200b978-3-642-30353-1_\u200b36 CrossRef\n\n21.\n\nPhan, Q.S.: Model counting modulo theories. Ph.D. thesis, Queen Mary University of London (2015)\n\n22.\n\nPhan, Q.S., Malacaria, P.: All-solution satisfiability modulo theories: applications, algorithms and benchmarks. In: ARES 2015, pp. 100\u2013109 (2015)\n\n23.\n\nPhan, Q.S., Malacaria, P., P\u0103s\u0103reanu, C.S., d'Amorim, M.: Quantifying information leaks using reliability analysis. In: SPIN 2014, pp. 105\u2013108. ACM (2014)\n\n24.\n\nP\u0103s\u0103reanu, C.S., Phan, Q.S., Malacaria, P.: Multi-run side-channel analysis using Symbolic Execution and Max-SMT. In: CSF 2016, pp. 387\u2013400, June 2016\n\n25.\n\nP\u0103s\u0103reanu, C.S., Visser, W., Bushnell, D., Geldenhuys, J., Mehlitz, P., Rungta, N.: Symbolic PathFinder: integrating symbolic execution with model checking for Java bytecode analysis. Autom. Softw. Eng. 20, 1\u201335 (2013)CrossRef\n\n26.\n\nRubinstein, R.: Stochastic enumeration method for counting NP-hard problems. Methodol. Comput. Appl. Probab. 15(2), 249\u2013291 (2013)MathSciNetCrossRefMATH\n\n27.\n\nSomenzi, F.: CUDD: CU decision diagram package release 3.0.0 (2015)\n\n28.\n\nThurley, M.: sharpSAT \u2013 Counting models with advanced component caching and implicit BCP. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 424\u2013429. Springer, Heidelberg (2006). doi:10.\u200b1007\/\u200b11814948_\u200b38 CrossRef\n\n29.\n\nTran, Q., Vardi, M.Y.: Groebner bases computation in boolean rings for symbolic model checking. In: MOAS, pp. 440\u2013445. ACTA Press (2007)\n\n30.\n\nTseitin, G.S.: On the complexity of derivation in propositional calculus. In: Siekmann, J.H., Wrightson, G. (eds.) Automation of Reasoning: 2: Classical Papers on Computational Logic, pp. 466\u2013483. Springer, Heidelberg (1983)CrossRef\n\n31.\n\nWei, W., Selman, B.: A new approach to model counting. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 324\u2013339. Springer, Heidelberg (2005). doi:10.\u200b1007\/\u200b11499107_\u200b24 CrossRef\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_10\n\n# Input Space Partitioning to Enable Massively Parallel Proof\n\nAshlie B. Hocking1 , M. Anthony Aiello1 , John C. Knight1 and Nikos Ar\u00e9chiga2\n\n(1)\n\nDependable Computing, Charlottesville, Virginia, USA\n\n(2)\n\nToyota InfoTechnology Center, Mountain View, Virginia, USA\n\nAshlie B. Hocking (Corresponding author)\n\nEmail: ben.hocking@dependablecomputing.com\n\nM. Anthony Aiello\n\nEmail: tony.aiello@dependablecomputing.com\n\nJohn C. Knight\n\nEmail: john.knight@dependablecomputing.com\n\nNikos Ar\u00e9chiga\n\nEmail: narechiga@us.toyota-itc.com\n\nAbstract\n\nReal-world applications often include large, empirically defined discrete-valued functions. When proving properties about these applications, the proof naturally breaks into one case per entry in the first function reached, and again into one case per entry in the next function, and continues splitting. This splitting yields a combinatorial explosion of proof cases that challenges traditional proof approaches. While each proof case represents a mathematical path from inputs to outputs through these functions, the full set of cases is not available up front, preventing a straightforward application of parallelism. Here we describe an approach that slices the input space, creating a partition based on pre-computed mathematical paths such that each slice has only a small number of proof cases. These slices are amenable to massively parallel proof. We evaluate this approach using an example model of an adaptive cruise control, where proofs are conducted in a highly parallel PVS environment.\n\n## 1 Introduction\n\nReal-world applications from many domains, such as embedded control systems in the automotive domain, depend upon large discrete-valued functions (DVFs) [3, 4]. Frequently, these systems operate on physical processes for which no sufficiently accurate analytic models are known. For example, the air-fuel ratio of an internal-combustion engine must be accurately and precisely controlled to maximize fuel efficiency and minimize pollutants [5, 7]. Since there are factors for which no sufficiently general and accurate analytic models exist, the values used are determined empirically and represented in the control system as DVFs.\n\nAttempting to prove theorems representing safety properties for applications including DVFs results in a large number of proof cases. When multiple DVFs are combined mathematically, the number of proof cases multiplies combinatorially. For realistic applications, merely running a theorem prover sequentially on the proof cases may take decades \u2014 even moderate-size examples require months.\n\nTwo approaches to solving this problem naturally arise: (1) replace the DVFs with suitable abstractions and (2) exploit the parallelism inherent in the proof cases to reduce wall-clock time. This paper focuses on exploiting parallelism.\n\nMathematical interactions amongst distinct DVFs prevent trivial enumeration of proof cases up-front, inhibiting straightforward application of parallelism. Our approach, shown in Fig. 1, enables parallelism by carefully partitioning the input space of the application, yielding proof slices with small and approximately equal numbers of proof cases. We then apply simple optimizations across all slices, significantly reducing the per-slice proof time. Finally, we use a custom tool to invoke the theorem prover in parallel and generate tailored proof reports.\n\nWe applied our approach to a Simulink model for an example adaptive cruise control system in which the DVFs are represented as lookup tables (LUTs). The approach, which relies on our Simulink2PVS tool [2], yields a 67,000% speedup as compared to sequential proof of the 74,170 proof cases.\n\nFig. 1.\n\nOverview of the parallelization process\n\n## 2 Input Space Partitioning and Parallel Proof\n\nProving proof cases in parallel is an obvious approach to dealing a large number of proof cases [1]. If N proof cases can be completed in parallel, then the total speedup is up to a factor of N. Moreover, if N equals the number of proof cases, then the total time required is the time required to prove the slowest proof cases.\n\nUnfortunately, the complete set of proof cases is not available up-front, especially when proof cases arise from the interactions amongst entries in multiple DVFs. An obvious solution is to partition the input space of the application, yielding proof slices that each contain a subset of the proof cases. A na\u00efve partitioning might yield proof slices with input intervals of the same size.\n\nSuch a partitioning, however, is unlikely to result in small and equal numbers of proof cases per proof slice. Mathematical interactions amongst entries in the discrete-valued functions may lead to large numbers of proof cases for some slices and small numbers of proof cases for other slices, dramatically reducing the efficacy of parallelization. The input space must be carefully partitioned so that the proof slices have a small and equal number of proof cases. Our approach to generating proof slices is shown in Fig. 2.\n\nFig. 2.\n\nProof slice generation\n\n 1. 1.\n\nA map of DVF domain intervals is created for each DVF in the application. For LUTs, these intervals correspond to breakpoints delineating the table data.\n\n 2. 2.\n\nThe DVF domain intervals are traced back through the application to inputs, to create input domain intervals that form the basis of the input space partitioning. This process requires careful consideration of interactions among inputs. For example, if two inputs are added before entering a DVF, each input domain's upper and lower bounds must be considered. For the smaller input domain, the input domain interval size is governed by the smallest DVF domain interval size. For a given pair of input domain intervals, the DVF domain intervals relevant are those between the sum of the lower bounds and the sum of the upper bounds.\n\n 3. 3.\n\nOften each input does not affect only one DVF. When multiple DVFs are affected by an input, the intersection of domain intervals is used. For example, if one input directly feeds into two DVFs where the first has breakpoints [0, 3, 9, 12] and the second has breakpoints [0, 4, 9, 12], then the input domain intervals are 0\u20133, 3\u20134, 4\u20139, and 9\u201312.\n\n 4. 4.\n\nInput domain intervals are analyzed to determine if they should be collapsed. For example, if there are three input domain intervals such that the first and last create 1 proof case and the middle input domain interval creates 2 proof cases (for a total of 4 proof cases), combining the first and second input domain intervals might still only yield 2 proof cases. This process reduces the total number of proof slices without changing the maximum number of proof cases per slice.\n\nFig. 3.\n\nHypothetical model of an adaptive cruise control system\n\nWe instantiated this process for the example Simulink model shown in Fig. 3. The result of the input-space partitioning is captured in a Matlab script that generates slices of the original Simulink model. Simulink2PVS is executed for each model slice, resulting in a set of PVS theories where each theory represents a single proof slice.\n\nTo support running PVS in a highly parallel environment, we created a new tool called ParaPVS that: (a) manages the parallel PVS processes based upon control input, (b) generates custom reports, and (c) can limit the proof to a random subset of the cases (input slices).\n\n## 3 Reducing Per-Slice Proof Time\n\nMechanical theorem provers like PVS [6] are often applied to complex proofs. In these applications, the time required for automatic decision procedures to complete the proof is important, but is not a primary goal of the analyst. Instead, the primary goal is completing the proof; much of the time required is identifying a sequence of steps that enable the decision procedures to complete the proof. Once the proof is completed, optimization of the proof steps is not beneficial.\n\nIn our parallel application of PVS to proof slices, however, the per-slice proof time is important. Proving N proof slices in parallel offers up to a factor N speedup. Reducing the per-slice proof time by a factor of M offers up to a factor speedup. In our experience, moreover, M can be a significant factor.\n\nWe explored two approaches to reduce per-slice proof time: (1) tailor the proof steps for each proof slice to reduce the time taken by automated decision procedures; and (2) increase the efficiency of the DVF representations.\n\nTo tailor the proof for each proof slice, we first used ParaPVS to complete proofs for a random sampling of proof slices. The initial proofs were completed automatically, e.g., by using PVS strategy (grind). We then analyzed results of a random sampling and manually developed more efficient proof strategies for the proof obligations that required the most time. While there is a time cost associated with this process ( 1 day), this cost is expected to be roughly constant. These proof strategies always terminate in calls to automatic decision procedures, ensuring that they are generally applicable across all proof slices.\n\nAdditionally, we identified an inefficiency in the DVF representation. For a generic DVF, the PVS specification describes the output of the DVF when the input is outside the breakpoints and also when the input is between the breakpoints. When the input space is partitioned, however, most of the resulting proof slices do not have inputs that lie outside the given breakpoints. To accommodate this, Simulink2PVS was modified to only specify the relevant breakpoint intervals given any lower and upper bounds present on the input data.\n\n## 4 Case Study\n\nWe assess the performance of our approach by application to the model shown in Fig. 3 [8]. This model has three DVFs represented as a 1-D, 2-D and 3-D LUT. The proof of the safety property for this model (that the projected relative distance is non-negative) requires that a total of 74,170 proof cases be completed.\n\nIdeally, the baseline for our assessment would be sequential proof of the safety property for this model. Unfortunately, PVS cannot complete this proof because the number of lines of text in the sequent grows exponentially as the composition of DVFs is expanded, quickly resulting in a sequent that cannot be manipulated.\n\nFig. 4.\n\nInput-space partitioning comparison\n\nTo provide a baseline, we first applied our input-space partitioning approach, generating a total of 26,880 proof slices. Our input-space partitioning approach is much more efficient than a uniform input-space partitioning approach that generates the same number of proof slices, as shown in Fig. 4. Our approach yields an average of 2.75 cases per slice and a total of 74,170 proof cases, whereas the uniform approach yields 16.04 and a total of over 430,000 proof cases, many of which are contained in more than one slice and are therefore redundant.\n\nWe then used ParaPVS to complete the proofs for all proof slices, using 44 PVS processes in parallel. All experiments were performed on a PowerEdge R730 Server with two 22-core 2.2 GHz Xeon hyper-threaded processors and 256 GB of main memory. The result was 98.4 days of CPU time, which we take as our baseline for further comparison. Table 1 presents our results; speedup in the table is the ratio of elapsed time to the baseline CPU time of 98.4 days, where CPU time is the sum of the amount of time spent by each process.\n\nUsing ParaPVS to complete 88 proof slices in parallel takes advantage of the test platform's hyper-threading, results in only a 1.13 speedup due to a diminishing return of increasing parallelism without additional computation resources. Applying the first per-slice optimization \u2014 proof-strategy improvement \u2014 yields a 9.78 speedup. Applying the second per-slice optimization \u2014 DVF-representation improvement \u2014 yields a 1.38 speedup. In total, the proof time is reduced from nearly 100 days to about 3.5 h, a 67,000% speedup.\n\nTable 1.\n\nTiming results | Baseline (44 Processes) | Hyper-threading (HT) (88 Processes) | HT + Imp strategies | HT + Imp strategies & representation\n\n---|---|---|---|---\n\nCPU time | 98.4 days | 173.6 days | 18.3 days | 13.2 days\n\nElapsed time | 53.7 h | 47.6 h | 4.87 h | 3.52 h\n\nAvg time per slice | 316.3 s | 558.2 s | 59.0 s | 42.7 s\n\nSpeedup | 4,400% | 4,960% | 48,500% | 67,000%\n\n## 5 Conclusion\n\nThis paper presents a novel approach to dealing with large numbers of proof cases: enabling parallelism through careful partitioning of the application input space, reducing the per-slice proof time, and leveraging a tool for parallel invocation of a theorem prover. Our results demonstrate a speedup of 67,000%.\n\nFor moderate-size examples, this approach works; we expect the approach to scale to handle proofs with up to proof cases. Further speedup can be achieved by leveraging additional parallelism. Some real-world examples we have seen, however, have proofs with on the order of or more proof cases. These proofs require additional techniques, such as replacement of the DVFs with abstractions that are simple enough to enable efficient proof, yet accurate enough to prove the property of interest. This approach is the subject of ongoing research.\n\nReferences\n\n1.\n\nBordeaux, L., Hamadi, Y., Samulowitz, H.: Experiments with massively parallel constraint solving. In: IJCAI, vol. 2009, pp. 443\u2013448 (2009)\n\n2.\n\nHocking, A.B., Aiello, M.A., Knight, J.C., Ar\u00e9chiga, N.: Proving critical properties of Simulink models. In: 2016 IEEE 17th International Symposium on High Assurance Systems Engineering (HASE), pp. 189\u2013196. IEEE (2016)\n\n3.\n\nHocking, A.B., Aiello, M.A., Knight, J.C., Shiraishi, S., Yamaura, M., Ar\u00e9chiga, N.: Proving properties of simulink models that include discrete valued functions. Technical report, SAE Technical Paper (2016)\n\n4.\n\nJeannin, J.B., Ghorbal, K., Kouskoulas, Y., Gardner, R., Schmidt, A., Zawadzki, E., Platzer, A.: Formal verification of ACAS X, an industrial airborne collision avoidance system. In: Proceedings of the 12th International Conference on Embedded Software, pp. 127\u2013136. IEEE Press (2015)\n\n5.\n\nJin, X., Deshmukh, J.V., Kapinski, J., Ueda, K., Butts, K.: Benchmarks for model transformations and conformance checking. In: 1st International Workshop on Applied Verification for Continuous and Hybrid Systems (ARCH) (2014)\n\n6.\n\nOwre, S., Rajan, S., Rushby, J.M., Shankar, N., Srivas, M.: PVS: combining specification, proof checking, and model checking. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 411\u2013414. Springer, Heidelberg (1996). doi:10.\u200b1007\/\u200b3-540-61474-5_\u200b91 CrossRef\n\n7.\n\nWu, C.W., Chen, R.H., Pu, J.Y., Lin, T.H.: The influence of air-fuel ratio on engine performance and pollutant emission of an si engine using ethanol-gasoline-blended fuels. Atmos. Environ. 38(40), 7093\u20137100 (2004)CrossRef\n\n8.\n\nYamaura, M., Ar\u00e9chiga, N., Shiraishi, S.: SimulinkVerificationBenchmark. https:\/\/\u200bgithub.\u200bcom\/\u200bToyota-ITC-SSD\/\u200bSimulinkVerifica\u200btionBenchmark\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_11\n\n# Compositional Model Checking of Interlocking Systems for Lines with Multiple Stations\n\nHugo Daniel Macedo1, 2 , Alessandro Fantechi1, 3 and Anne E. Haxthausen1\n\n(1)\n\nDTU Compute, Technical University of Denmark, Lyngby, Denmark\n\n(2)\n\nDepartment of Engineering, Aarhus University, Aarhus, Denmark\n\n(3)\n\nDINFO, University of Florence, Firenze, Italy\n\nHugo Daniel Macedo (Corresponding author)\n\nEmail: hdm@eng.au.dk\n\nAlessandro Fantechi\n\nEmail: alessandro.fantechi@unifi.it\n\nAnne E. Haxthausen\n\nEmail: aeha@dtu.dk\n\nAbstract\n\nIn the railway domain safety is guaranteed by an interlocking system which translates operational decisions into commands leading to field operations. Such a system is safety critical and demands thorough formal verification during its development process. Within this context, our work has focused on the extension of a compositional model checking approach to formally verify interlocking system models for lines with multiple stations. The idea of the approach is to decompose a model of the interlocking system by applying cuts at the network modelling level. The paper introduces an alternative cut (the linear cut) to a previously proposed cut (border cut). Powered with the linear cut, the model checking approach is then applied to the verification of an interlocking system controlling a real-world multiple station line.\n\nKeywords\n\nRailway interlockingCompositional verificationModel checking\n\nH.D. Macedo and A.E. Haxthausen\u2014The authors' research, conducted at DTU Compute, was funded by the RobustRailS project granted by Innovation Fund Denmark.\n\nA. Fantechi\u2014The author's research was funded by Villum Fonden.\n\n## 1 Introduction\n\nA railway is a mechanised means of mass movement where diverse vehicles take paths on a shared space\/network of tracks. Its main feature is guidance by mechanical contact of wheels on rails. Switch points are introduced to dynamically change the network topology allowing a vehicle to change tracks. Another distinctive feature is the poor braking response time given the physical properties of wheel on rail rolling friction. Such features impose hard restrictions on traffic, vehicle movements, and network configuration.\n\nTo regulate traffic, a railway signalling system [14] is deployed as an information processing\/transmission control loop. The system monitors the status of vehicles and track elements issuing network re-configuration and vehicle dispatch commands. The usually deployed monitoring scheme assumes that the network under control is divided into sections with train detection equipment and the existence of additional track side elements such as signals. The status (occupied or clear) of train detection sections, position of points, and configuration of track side elements (e.g. the setting of signals) is relayed to the control system. Issued decisions are then transmitted back to each element affecting its configuration (e.g.: issuing a change in point position) and vehicle movements (e.g.: sending dispatch commands to trains through signals).\n\nThe technology\/operation mode of signalling systems ranges from basic human communication, for instance telecommunications between stakeholders (human controllers, station masters, and vehicle operators), to advanced automation where computers are responsible for the whole control loop. Usually the different systems are used heterogeneously through a network. Several of the recent railway disasters were due to signalling system failures1 in networks lacking automated control.\n\nAutomated systems require railway engineers\/architects to define the appropriate operation requirements, for instance in the form of routes: each prescribing the path and the required network configuration for safe train traversal along that path. When the system issues a dispatch route command, the network must be reconfigured to comply with such requirements. In addition, the system must ensure the required configuration is maintained during the traversal. And above all, the command must not lead to a safety violation. For that purpose an interlocking system takes the responsibility of safely transform each dispatch decision into the control commands that must be executed before a proceed command to a train is issued.\n\nSuch responsibility demands for standards in the development of the software controlling interlocking systems. The standard CENELEC 50128 [1] labels such software with the highest safety integrity level (SIL4), and highly recommends the usage of formal methods and formal verification in its development process. However, full formal verification of interlocking systems demands heavy if not infeasible computational resources2, a phenomenon known as the state explosion problem. The pioneering research in model checking and in applying model checking to the domain of railways [3\u20135, 7, 9, 20] has developed techniques allowing the verification of models of the interlocking systems controlling larger and highly-complex networks. For example, abstraction techniques can be applied at the domain modelling level before the model checking is performed [9]. Other very efficient techniques applied for real world railways are bounded model checking [8] and k-induction [19]. The state explosion problem can also be tamed using techniques that allow a compositional approach to the model checking task [10]: the model checker must prove that assumptions imply the guarantees of each contract of the component. The authors report that this technique allowed the verification of a real world station.\n\nPursuing the same goal, in a previous work [11] we described a compositional approach to the verification of safety properties of models of interlocking systems controlling lines with multiple stations. The approach was developed in the context of the RobustRailS research project3 extending an automated method for the formal verification of the new Danish interlocking systems [17\u201319]. The idea in our previous work was based on the observation that decomposing a network at specific points which satisfy a given topological configuration (called border cut, see Fig. 1) generates sub-models corresponding to a complete partition of disjoint, connected components of the state space. It is therefore straightforward to combine the results of checking each sub-model to compute the result of checking the monolithic model. This is the case as the routes that can be set inside one sub-model are completely independent from those in the other sub-model.\n\nFig. 1.\n\nBorder cut dividing the network topology into two parts.\n\nWe have then realised that the border cut configuration does not occur in some real world networks, but instead a similar configuration (that we call linear cut, see Sect. 3.1), in which the routes of the two sub-models partially overlap, is frequent. Inspired by the already cited compositional approach [10], where a similar route overlap is taken into account, we have modified our compositional approach to consider linear cut configurations as the points at which to cut a network into sub-models. This requires a finer analysis of the interferences between sub-models, but again we show that checking each sub-model allows the result of checking the monolithic model to be computed, with significant verification time savings.\n\nThe exposition of our results is structured as follows: in Sect. 2 we recall some principles of railway interlocking systems and present the RobustRailS verification method and toolkit on the top of which we have built our compositional approach; in Sect. 3 we present our approach using a divide-and-conquer strategy: we introduce the linear cut and explain how our method first uses this to divide a network into sub-networks, then generates sub-models and finally conquer the model checking results for these. The soundness and completeness of the approach is proved in Sect. 4, and in Sect. 5 we report on the results given by the application of our compositional approach to a typical example and to a real-world line that nearly reached the capacity bounds of the adopted tools when proved as a whole. In both cases the results show that significant gains in verification effort can be achieved. Section 6 summarises the achieved results and discusses possible future extensions and improvements of the work presented here, especially in the direction of addressing interlocking systems that control large stations.\n\n## 2 The New Danish Route-Based Interlocking Systems\n\nIn this section we introduce briefly the new Danish interlocking systems and the domain terminology. The subsequent Sect. 2.1 explains different components of a specification of an interlocking system which is compatible with ERTMS\/ETCS Level 2 [2], and Sect. 2.2 explains how the safety properties are verified.\n\n### 2.1 Specification of Interlocking Systems\n\nThe specification of a given route-based interlocking system consists of two components: (N) a railway network, and (R) an interlocking table.\n\nRailway Networks. A railway network in ETCS Level 2 consists of a number of track and track-side elements of different types4: linear sections, points, and marker boards. Figure 2 shows an example layout of a railway network having six linear sections (b10,t10,t12,t14,t20,b14), two points (t11,t13), and eight marker boards (mb10, ..., mb21). These terms, and their functionality within the railway network, will be explained in more detail in the next paragraphs.\n\nFig. 2.\n\nAn example railway network layout.\n\nA linear section is a section with up to two neighbours: one in the up end, and one in the down end. For example, the linear section t12 in Fig. 2 has t13 and t11 as neighbours at its up end and down end, respectively. In Danish railway's terminology, up and down denote the directions in which the distance from a reference location is increasing and decreasing, respectively. The reference location is the same for both up and down, e.g., an end of a line. For simplicity, in the examples and figures in the rest of this article, the up (down) direction is assumed to be the left-to-right (right-to-left) direction.\n\nA point can have up to three neighbours: one at the stem, one at the plus end, and one at the minus end, e.g., point t11 in Fig. 2 has t10, t12, and t20 as neighbours at its stem, plus, and minus ends, respectively. The ends of a point are named so that the stem and plus ends form the straight (main) path, and the stem and minus ends form the branching (siding) path. A point can be switched between two positions: PLUS and MINUS. When a point is in the PLUS (MINUS) position, its stem end is connected to its plus (minus) end, thus traffic can run from its stem end to its plus (minus) end and vice versa. It is not possible for traffic to run from plus end to minus end and vice versa.\n\nLinear sections and points are collectively called (train detection) sections, as they are provided with train detection equipment used by the interlocking system to detect the presence of trains. Note that sections are bidirectional, i.e., trains are allowed to travel in both directions (but not at the same time).\n\nAlong each linear section, up to two marker boards (one for each direction) can be installed. A marker board can only be seen in one direction and is used as reference location (for the start and end of routes) for trains going in that direction. For example, in Fig. 2, marker board mb13 is installed along section t12 for travel direction up. Contrary to legacy systems, there are no physical signals in ETCS Level 2, but interlocking systems have a virtual signal associated with each marker board. Virtual signals play a similar role as physical signals in legacy systems: a virtual signal can be OPEN or CLOSED, respectively, allowing or disallowing traffic to pass the associated marker board. However, trains (more precisely train drivers) do not see the virtual signals, as opposed to physical signals. Instead, the aspect of virtual signals (OPEN or CLOSED) is communicated to the onboard computer in the train via a radio network. For simplicity, the terms virtual signals, signals, and marker boards are used interchangeably throughout this paper.\n\nInterlocking Tables. An interlocking system constantly monitors the status of track-side elements, and sets them to appropriate states in order to allow trains travelling safely through the railway network under control. The new Danish interlocking systems are route-based. A route is a path from a source signal to a destination signal in the given railway network. A route is called an elementary route if there are no signals that are located between its source signal and its destination signal, and that are intended for the same direction as the route.\n\nIn railway signalling terminology, setting a route denotes the process of allocating the resources \u2013 i.e., sections, points, and signals \u2013 for the route, and then locking it exclusively for only one train when the resources are allocated.\n\nAn interlocking table specifies the elementary routes in the given railway network and the conditions for setting these routes. The specification of a route and conditions for setting include the following information, that will be needed while verifying the expected properties:\n\n * \u2013 the source signal of ,\n\n * \u2013 the destination signal of ,\n\n * \u2013 the list of sections constituting 's path from to ,\n\n * \u2013 a list of the sections in 's overlap 5, i.e., the buffer space after that would be used in case trains overshoot the route's path,\n\n * \u2013 a map from points6 used by to their required positions,\n\n * \u2013 a set of protecting signals used for flank or front protection [14] for the route, and\n\n * \u2013 a set of conflicting routes which must not be set while is set.\n\nTable 1 shows an excerpt of an interlocking table for the network shown in Fig. 2. Each row of the table corresponds to a route specification. The column names indicate the information of the route specifications that these columns contain. As can be seen, one of the routes has id 1a, goes from mb10 to mb13 via three sections t10, t11 and t12 on its path, and has no overlap. It requires point t11 (on its path) to be in PLUS position, and point t13 (outside its path) to be in MINUS position (as a protecting point). The route has mb11, mb12 and mb20 as protecting signals, and it is in conflict with routes 1b, 2a, 2b, 3, 4, 5a, 5b, 6b, and 7.\n\nTable 1.\n\nExcerpt of the interlocking table for the network of Fig. 2. The overlap column is omitted as it is empty for all routes. (p = PLUS, m = MINUS)\n\nId | src | dst | path | points | signals | conflicts\n\n---|---|---|---|---|---|---\n\n1a | mb10 | mb13 | t10;t11;t12 | t11:p;t13:m | mb11;mb12;mb20 | 1b;2a;2b;3;4;5a;5b;6b;7\n\n.. | ... | ... | ... | ... | ... | ...\n\n7 | mb20 | mb11 | t11;t10 | t11:m | mb10;mb12 | 1a;1b;2a;2b;3;5b;6a\n\n### 2.2 The RobustRailS Verification Method and Toolkit\n\nThis section describes shortly the RobustRailS verification method and toolkit that we use as verification technology. For detailed information, see [6, 16\u201319].\n\nThe method for modelling and verifying railway interlocking systems is a combination of formal methods and a domain-specific language (DSL) to express network diagrams and interlocking tables. According to this, a toolkit consisting of the following components is provided.\n\n * An editor and static checker [6] for editing and checking that a DSL specification (describing an interlocking system) follows certain well-formedness rules.\n\n * The bounded model checker of RT-Tester [12, 15] which we use for performing k-induction proofs as explained in [19].\n\n * Generators transforming a DSL specification of an interlocking model into inputs to the model checker:\n\n * a behavioural model (a Kripke structure) of the interlocking system and its environment, defining the state space and possible state transitions, and\n\n * the required safety properties given as a state invariant (expressing that there are no hazards like train collisions). The invariant is a conjunction of high-level safety properties over the variables of the interlocking system model. An -property is satisfied by an interlocking specification I, written as , if it is valid in the model of the interlocking system . is valid in the model can be written as , where is either the subset of all linear sections or all point sections in N and is a section property related to .\n\nFor details of the models and properties, see [19].\n\nThe tools can be used to verify the design of an interlocking system in the following steps:\n\n 1. 1.\n\nA DSL specification of the configuration data (a network layout and its corresponding interlocking table) is constructed in the following order:\n\n 1. (a)\n\nfirst the network layout,\n\n 2. (b)\n\nand then the interlocking table (this is either done manually or generated automatically from the network layout).\n\n 2. 2.\n\nThe static checker verifies whether the configuration data is statically well-formed according to the static semantics [18] of the DSL.\n\n 3. 3.\n\nThe generators instantiate a generic behavioural model and generic safety properties with the well-formed configuration data to generate the model input of the model checker and the safety properties.\n\n 4. 4.\n\nThe generated model instance is then checked against the generated properties by the bounded model checker performing a k-induction proof.\n\nThe static checking in step (2) is intended to catch errors in the network layout and interlocking table, while the model checking in step (4) is intended to catch safety violations in the control algorithm of the instantiated model.\n\nThe tool-chain associated with the method has been implemented using the RT-tester framework [12, 15]. The bounded model checker in RT-tester uses the SONOLAR SMT solver [13] to compute counterexamples showing the violations of the base case or induction step. Using this SMT solver rather than a SAT solver allowed us to use very efficient bit-vector operations.\n\nAs proof technique in step 4, we used k-induction as this was the most promising (cf. the comparison with other techniques in [19]), however, our compositional method could also be used in combination with other proof techniques.\n\n## 3 Method\n\nWe now proceed to describe the details of how we use the locality features of railway networks to verify large interlocking systems in a compositional manner. The idea is to decompose the model into smaller models that are separately verified for safety properties, and to show that under given conditions such separate verifications are enough to guarantee that the whole network satisfies the safety properties as well. We show that a multi-station interlocking system satisfies such conditions if a suitable (and natural) divide strategy is applied. The strategy provides a completely automated method to verify this class of interlocking systems.\n\n### 3.1 Linear Cuts on Multiple Station Lines\n\nThe typical pattern of a railway is a line connecting multiple stations. Without loss of generality, we can consider a line, denoted , corresponding to a network diagram consisting of two stations denoted by and , interconnected by one or several linear sections. More complex multi-station layouts can be obtained by concatenation of such elementary lines.\n\nTo divide multiple station lines we search for an interface , which we define as a linear section7 with an up and down marker board subject to certain conditions described further below. A cut is then applied producing two sub-networks:\n\n * The network defined as the station and the interface . An entry marker board is added on the up ( ) side of this network.\n\n * The network defined as the station and the interface . An entry marker board is added on the down ( ) side of this network.\n\nWith the required configuration of marker boards on the interface and the addition of entry marker boards, the two sub-networks fulfil the required marker board configuration at borders of a railway network.\n\nFig. 3.\n\nThe multiple station line pattern where sections T2 and T3 connect two stations A and B.\n\nFig. 4.\n\nResulting network.\n\nFig. 5.\n\nResulting network.\n\nFor example in Fig. 3 we depict a highlight of a line network diagram in which T2 connects two stations and . In the example contains element P2 and its down neighbours and contains elements T3 and its up neighbours. Linear section T2 configures a candidate to a linear cut, which results in the two networks illustrated in Figs. 4 and 5, where the linear section (T2) is kept in both as it defines the interface .\n\nTo guarantee that the compositional approach (to be described in next subsection) is sound, the interface must satisfy the following linear cut conditions (LCCs):\n\n 1. 1.\n\nthere is an up marker board on the upper part of the interface section and a down marker board on the down part;\n\n 2. 2.\n\nthe two networks ( and ) resulting from the cut described above must only have in common;\n\n 3. 3.\n\nno flank\/front protection requirements for routes in the up (down) sub-network ( ) depends on elements outside ( ), except for routes in down (up) direction with destination marker board mounted in (i.e. routes that end at the entrance of the ( ) station).\n\n### 3.2 A Compositional Model Checking Approach\n\nIn the division process a network is inspected in search for regions that present candidate patterns to be cut, that is, linear sections of the form T2 of Fig. 3. The search is then recursively applied to the created sub-networks, until either no more suitable cut points can be found or the sub-networks produced are already sufficiently small.\n\nThe linear cut allows to automate the compositional verification of multi-station interlocking systems by dividing the network in sub-networks by means of four steps:\n\n 1. 1.\n\nSearch the network for suitable interfaces satisfying the LCCs. For each interface instantiate the pattern and divide recursively the network into sub-networks as described in Subsect. 3.1.\n\n 2. 2.\n\nFor each of the resulting sub-networks , complete the specification of a sub-interlocking system using the interlocking table generator mentioned in item 1 of Sect. 2.2. The resulting specifications are called the interlocking specifications.\n\n 3. 3.\n\nStatically check each of the resulting specifications and generate the models (called the models) and properties to be verified using the checker and generator mentioned in item 2 and item 3, respectively, of Sect. 2.2.\n\n 4. 4.\n\nVerify the models following item 4 of Sect. 2.2.\n\n## 4 Soundness and Completeness of the Approach\n\nTo prove that the decomposition approach is sound and complete one needs to show that the result of checking any of the high-level safety properties (as defined in Subsect. 2.2) for the and sub-models implies the result of checking the same property for the monolithic model, and vice versa. (The extension to more than one sub-model is then straightforward). First we prove soundness and then completeness.\n\n### 4.1 Soundness\n\nSoundness can be rephrased in terms of 's related invariant . If the invariant holds for every section in the interlocking specification and for every section in the interlocking specification we can conclude the whole interlocking specification satisfies , meaning its related invariant holds for every section in the interlocking specification.\n\nGiven that -properties are universal quantifications over the sets of linear\/point sections8, a natural strategy to produce such a proof is to decompose the property in terms of the disjoint sets of sections defining the and stations, and the interface . That is, the related property holds for every section in the network, if holds for every section of the network containing the station, for the interface section , and for every section of the network containing the station. In mathematical terms, if we denote by the set of sections of an interlocking specification , it corresponds to rewrite the formulation of the satisfiability of by the model of , i.e. , into:\n\n(1)\n\nThe aforementioned rewrite leads one to decompose the proof into three lemmas. The first two relate the local properties satisfied by and and similarly by and .\n\nLemma 1\n\nConsider a line interlocking specification with A and B stations satisfying the pattern, the and interlocking specifications resulting from the application of a linear cut, a high-level safety property and its related invariant . We relate the outcome of evaluating and through the following implication:\n\nProof\n\nBy contradiction. Let us assume that in the property holds for every section in and there is a section e in such that does not hold in the model. Then, as detailed in [19], there is a state s of , where is false, reachable from the initial state by a sequence of transitions (trace) that we denote as . The state s is characterised by an assignment of values to a vector of variables referring to the elements (sections, signals etc.) of the network. Due to the linear cut definition, such variables refer to elements that are in the or in the network. Any transition in changes such assignments: following we can find in a corresponding trace that makes the same changes to the variables in the state vector of , skipping those transitions in that do not change variables in . The trace therefore ends in a reachable state in which the assignments to variables in are the same of those of s, and hence does not hold, contradicting the hypothesis.\n\nLemma 2\n\nThe dual case of Lemma 1. Given by substitution of the interlocking specification by , by and A by B.\n\nThe two lemmas above allow us to transfer checking results on the sections of the two stations and to the check of the whole line; however, we still miss the contribution of the interface section, which is copied in both the and networks. The next lemma has this purpose.\n\nLemma 3\n\n(Interfacing lemma) Consider the interlocking specification, the interlocking specification and the interlocking specification resulting from applying a linear cut, a high-level safety property and its related invariant . For the interface we have:\n\nProof\n\nBy contradiction. Assume is true in both the and models, but false in the model. Furthermore assume s is the state of falsifying . Thus, there is a trace in leading from the model's initial state to the variable assignment in s. Similarly to what said for Lemma 1 it is then possible to form a trace in and a trace in from the initial states to two states and such that the state vector has an assignment falsifying in or . Thus arriving at a contradiction.\n\nGiven the proofs of Lemmas 1, 2, and 3, one is in the position to relate the result of the monolithic checking of the interlocking specification with the results of the compositional approach in which the and interlocking specifications are checked.\n\nTheorem 1\n\n(Soundness) Consider the interlocking specification, the and interlocking specifications resulting from the application of a linear cut, and a high-level safety property . Then\n\nwhich means that if is satisfied by and by , one can conclude that it is satisfied by .\n\nProof\n\nAssume is true, our goal is to prove , i.e. (cf. Formula (1)): which is equivalent to:\n\nApplying Lemma 1, Lemma 2, and Lemma 3, one obtains:\n\nwhich is equivalent to: .\n\n### 4.2 Completeness\n\nThe following theorem states that the method is complete.\n\nTheorem 2\n\n(Completeness) Consider the interlocking specification, the and interlocking specifications resulting from the application of a linear cut at an interface , and a high-level safety property . Assume that for each internal section b of which appears as a border section in one of the subnetworks \/ (i.e. b is an \/ neighbour to ), there exists a finite trace prefix in leading a train to b from some outer border of the \/ network without changing any of the variables that only exist in \/ . Then\n\nwhich means that if is dissatisfied by or by , one can conclude that it is dissatisfied by .\n\nProof\n\nAssume that is dissatisfied by \/ , and let t be the associated counter example (trace). t can now be lifted to a counter example in by first extending the states of t with the additional variables of mapped to their initial states, and then, if the t trace involves a train entering from the border b at the \/ side of , this extended trace should be preceded by a trace prefix from leading the train to b from some outer border of \/ without changing any of the variables that only exist in \/ .\n\n## 5 Experiments\n\nIn this section we present the results of applying our decomposition approach to an invented line ( ) with two stations and to a real world case study with eight stations. Both lines exhibit the pattern of a line with multiple stations which cannot be divided using the border cut defined in our previous work [11].\n\n### 5.1 Experimental Approach\n\nFor each of the case studies, we put the method described in Sect. 3.2 in practice by first obtaining sub-networks (in XML format) according to the divide strategy. Then for each sub-network, we use the RobustRailS verification tool [17\u201319] to generate a model instance and safety properties, and then to verify that the generated safety properties hold in the model.\n\nWe also use the RobustRailS verification tool to monolithically verify the railway network (without decomposing it) such that we can compare verification metrics for the compositional approach with verification metrics for the monolithic approach.\n\nWhile verifying each instance we measure (in seconds) the real time taken to obtain the verification result and what was the total memory (in MB) used by the verification tool. In addition we collect some statistics about the network and model instances as presented in Tables 2 and 3. Such statistics provide a basis for complexity comparison and include: the number of linear and point sections, the number of marker boards (signals), routes, and the potential state space dimension (in logarithmic scale).\n\nAll the experiments for both case studies have been performed on a machine with an Intel(R) Xeon(R) CPU E5-1650 @ 3.6 GHz, 125 GB RAM, and running Linux 4.4.0\u201347.x86_64 kernel.\n\n### 5.2 Two Stations Case Study\n\nLet us consider as an example the railway line of Fig. 6 denoted . In it we find two stations: the set of elements defines the station, whereas the set defines the station. The linear section T2 connects and .\n\nFig. 6.\n\n Network\n\nThe RobustRailS tool allows the automatic generation of interlocking tables from a given network layout, and for the network it generates 24 routes. A thorough inspection of the table shows that routes can be categorised into three blocks, partitioning the network into two disjoint networks and a common interface (linear section T2). The inspection of the route table reveals that it makes sense to divide the network into two networks, choosing the linear section T2 as an interface between a network containing the station and a network containing the station.\n\nAs planned, we have verified the model both compositionally and monolithically; Table 2 shows the verification metrics, first separately for the and networks. The metrics for the compositional analysis ( ) are obtained by summing the corresponding metrics for the networks, except for the state space and the memory usage, which are calculated as the respective maximum between the two sub-networks. The table also shows the verification metrics for the monolithic analysis of the network ( ).\n\nIn all cases the verification tool succeeded to verify the safety properties. As it can be observed the verification time and memory usage of the compositional analysis ( ) is, as expected, much better than for the monolithic analysis of ( ): The verification time is approximately three times faster and the memory usage (234 MB) is more than halved.\n\nMoreover, if the verification for the and networks were run in parallel, our compositional approach would achieve a running time of just 16 s. Even though memory consumption would increase in this case, the parallelisation would still use less memory resources (the sum of individual memory usages: 420 MB) than the monolithic case (556 MB).\n\nTable 2.\n\nVerification metrics for the case study. | Linears | Points | Signals | Routes | | Time | Memory\n\n---|---|---|---|---|---|---|---\n\n | 6 | 2 | 9 | 13 | 38 | 10 | 186\n\n | 7 | 2 | 9 | 13 | 41 | 16 | 234\n\n | 13 | 4 | 18 | 26 | 41 | 26 | 234\n\n | 10 | 4 | 14 | 24 | 68 | 68 | 556\n\n### 5.3 EDL: The Real World Case Study\n\nThe EDL is the first regional line in Denmark to be commissioned in the Danish Signalling Programme. The line spreads over 55 km from the station in Roskilde to N\u00e6stved's station, with 8 small to medium sized stations, and the statistics shown in Table 3 gives insight into its composition.\n\nWith the definition of the linear cut it is now directly possible to cut the EDL network into eight sub-networks, each corresponding to an EDL station. Six of the sub-networks (Gadstrup, Havdrup, Herf\u00f8lge, Tureby, Haslev, and Holme-Olstrup) are of fairly similar complexity, while two (L. Skensved and K\u00f8ge) are more complex. With such a division we decompose the verification of the interlocking system for EDL into the separate verification of the eight stations.\n\nAs in the case study, the verification tool succeeded to verify the safety properties for the eight sub-interlocking systems and the verification metrics show that for the compositional analysis (see the entry Compositional in Table 3) the verification time is approximately a third (approx. 1.5 h) of that for the monolithic analysis (approx. 4 h). Furthermore, the compositional analysis uses less than half of the memory resources (9243 MB) because we only need as much as the maximum value of memory used to verify each sub-interlocking. Although we are still far from the memory bounds of the used machine in this experiment, such memory reduction is important when checking real world interlocking systems where a single station with a complex network may quickly exhaust the amount of memory available. As already discussed, if run in parallel our compositional approach would achieve a much better running time. Even though memory consumption would increase, the parallelisation would only use roughly 50% (the sum of the individual memory usages: 11711 MB) of the memory resources than the monolithic case. The parallel verification time is dominated by the time to verify the K\u00f8ge station, which is the largest of the network: actually, the internal layouts of the stations do not present candidates for linear cuts, so they are not further decomposed in this approach.\n\nTable 3.\n\nVerification metrics for the EDL case study. | Linears | Points | Signals | Routes | | Time | Memory\n\n---|---|---|---|---|---|---|---\n\nGadstrup | 14 | 3 | 16 | 21 | 73 | 62 | 567\n\nHavdrup | 10 | 2 | 12 | 14 | 51 | 19 | 264\n\nL. Skensved | 15 | 3 | 16 | 21 | 75 | 72 | 616\n\nK\u00f8ge | 58 | 23 | 62 | 75 | 337 | 5170 | 9243\n\nHerf\u00f8lge | 6 | 2 | 10 | 14 | 39 | 13 | 210\n\nTureby | 6 | 2 | 10 | 14 | 39 | 11 | 203\n\nHaslev | 10 | 2 | 12 | 14 | 51 | 14 | 256\n\nHolme-Ol | 12 | 2 | 16 | 20 | 63 | 22 | 352\n\nCompositional | 131 | 39 | 154 | 193 | 337 | 5383 | 9243\n\nEDL | 110 | 39 | 126 | 179 | 651 | 14352 | 22476\n\n## 6 Conclusion\n\nWe have presented a compositional approach to the problem of model checking large railway interlocking systems. This approach, built on top of tools providing support for efficient verification of this kind of systems, is tailored to the characteristics of multi-station interlocking systems, that is, systems that control a line connecting several stations. The approach extends our previous work [11], by a new, realistic division process which can be applied in cases where the previous, simpler approach is not applicable. The approach has successfully been applied to a real world line with eight stations in which case it achieved significant improvements in verification time and memory usage compared to the previous non compositional verification process.\n\nIn order to compositionally address more general network layouts the linear cut concept put forward in this paper needs to be generalised. An immediate extension is to combine it with the border cut concept introduced in our previous work [11]: such interesting strategy should not demand any special efforts beyond the practicalities involved. But the generalisation of the concepts to the application to interlocking systems controlling large stations, which exhibit highly complex and densely connected networks, requires a novel cut concept, which is the subject of some of our new, ongoing work. In that case the main source of difficulty stems from the fact that a division of a large station into smaller areas implies that some routes have to go through the operated cuts, a situation that is not exhibited by the multiple station lines we have addressed till now. Actually, we have seen that the interface elements in the linear cut have the destination signals of routes coming from both sides of the interface: in the cut the added markerboard behaves as an abstraction of the removed subnetwork. We are currently studying a similar abstraction principle to support the more complex cut configuration required to address large station interlocking systems.\n\nAnother topic for future work could be to formalise the proofs done in Sect. 4 by using a proof assistant like Coq or Isabelle.\n\nAcknowledgement\n\nThe authors would like to express their gratitude to Jan Peleska and Linh Hong Vu with whom Anne Haxthausen developed the RobustRailS verification method and tools used in the presented work.\n\nReferences\n\n1.\n\nCENELEC European Committee for Electrotechnical Standardization. EN 50128:2011 - Railway applications - Communications, signalling and processing systems - Software for railway control and protection systems (2011)\n\n2.\n\nEuropean Railway Agency. ERTMS - System Requirements Specification - UNISIG SUBSET-026, April 2014. http:\/\/\u200bwww.\u200bera.\u200beuropa.\u200beu\/\u200bDocument-Register\/\u200bPages\/\u200bSet-2-System-Requirements-Specification.\u200baspx\n\n3.\n\nFerrari, A., Magnani, G., Grasso, D., Fantechi, A.: Model checking interlocking control tables. In: Schnieder, E., Tarnai, G. (eds.) FORMS\/FORMAT 2010 - Formal Methods for Automation and Safety in Railway and Automotive Systems, pp. 107\u2013115. Springer, Heidelberg (2010)\n\n4.\n\nHvid Hansen, H., Ketema, J., Luttik, B., Mousavi, M.R., Pol, J., Santos, O.M.: Automated verification of executable UML models. In: Aichernig, B.K., Boer, F.S., Bonsangue, M.M. (eds.) FMCO 2010. LNCS, vol. 6957, pp. 225\u2013250. Springer, Heidelberg (2011). doi:10.\u200b1007\/\u200b978-3-642-25271-6_\u200b12 CrossRef\n\n5.\n\nHaxthausen, A.E., Bliguet, M., Kj\u00e6r, A.A.: Modelling and verification of relay interlocking systems. In: Choppy, C., Sokolsky, O. (eds.) Monterey Workshop 2008. LNCS, vol. 6028, pp. 141\u2013153. Springer, Heidelberg (2010). doi:10.\u200b1007\/\u200b978-3-642-12566-9_\u200b8 CrossRef\n\n6.\n\nHaxthausen, A.E., \u00d8stergaard, P.H.: On the use of static checking in the verification of interlocking systems. In: Margaria, T., Steffen, B. (eds.) ISoLA 2016. LNCS, vol. 9953, pp. 266\u2013278. Springer, Cham (2016). doi:10.\u200b1007\/\u200b978-3-319-47169-3_\u200b19 CrossRef\n\n7.\n\nHaxthausen, A.E., Peleska, J., Kinder, S.: A formal approach for the construction and verification of railway control systems. Form. Asp. Comput. 23(2), 191\u2013219 (2011)CrossRefMATH\n\n8.\n\nHaxthausen, A.E., Peleska, J., Pinger, R.: Applied bounded model checking for interlocking system designs. In: Counsell, S., N\u00fa\u00f1ez, M. (eds.) SEFM 2013. LNCS, vol. 8368, pp. 205\u2013220. Springer, Cham (2014). doi:10.\u200b1007\/\u200b978-3-319-05032-4_\u200b16 CrossRef\n\n9.\n\nJames, P., Moller, F., Nguyen, H.N., Roggenbach, M., Schneider, S., Treharne, H.: Techniques for modelling and verifying railway interlockings. Int. J. Softw. Tools Technol. Transf. 16(6), 685\u2013711 (2014)CrossRef\n\n10.\n\nLimbr\u00e9e, C., Cappart, Q., Pecheur, C., Tonetta, S.: Verification of railway interlocking - compositional approach with OCRA. In: Lecomte, T., Pinger, R., Romanovsky, A. (eds.) RSSRail 2016. LNCS, vol. 9707, pp. 134\u2013149. Springer, Cham (2016). doi:10.\u200b1007\/\u200b978-3-319-33951-1_\u200b10\n\n11.\n\nMacedo, H.D., Fantechi, A., Haxthausen, A.E.: Compositional verification of multi-station interlocking systems. In: Margaria, T., Steffen, B. (eds.) ISoLA 2016. LNCS, vol. 9953, pp. 279\u2013293. Springer, Cham (2016). doi:10.\u200b1007\/\u200b978-3-319-47169-3_\u200b20 CrossRef\n\n12.\n\nPeleska, J.: Industrial-strength model-based testing - state of the art and current challenges. In: Petrenko, A.K., Schlingloff, H. (eds.) 8th Workshop on Model-Based Testing, Rome, Italy, vol. 111, Electronic Proceedings in Theoretical Computer Science, pp. 3\u201328. Open Publishing Association (2013)\n\n13.\n\nPeleska, J., Vorobev, E., Lapschies, F.: Automated test case generation with SMT-solving and abstract interpretation. In: Bobaru, M., Havelund, K., Holzmann, G.J., Joshi, R. (eds.) NFM 2011. LNCS, vol. 6617, pp. 298\u2013312. Springer, Heidelberg (2011). doi:10.\u200b1007\/\u200b978-3-642-20398-5_\u200b22 CrossRef\n\n14.\n\nTheeg, G., Vlasenko, S.V., Anders, E.: Railway Signalling & Interlocking: International Compendium. Eurailpress, Hamburg (2009)\n\n15.\n\nVerified Systems International GmbH. RT-Tester Model-Based Test Case and Test Data Generator - RTT-MBT - User Manual (2013). http:\/\/\u200bwww.\u200bverified.\u200bde\n\n16.\n\nVu, L.H., Haxthausen, A.E., Peleska, J.: A domain-specific language for railway interlocking systems. In: Schnieder, E., Tarnai, G. (eds.) FORMS\/FORMAT 2014\u201310th Symposium on Formal Methods for Automation and Safety in Railway and Automotive Systems, pp. 200\u2013209. Institute for Traffic Safety and Automation Engineering, Technische Universit\u00e4t Braunschweig (2014)\n\n17.\n\nVu, L.H., Haxthausen, A.E., Peleska, J.: Formal modeling and verification of interlocking systems featuring sequential release. In: Artho, C., \u00d6lveczky, P.C. (eds.) Formal Techniques for Safety-Critical Systems. Communications in Computer and Information Science, vol. 476, pp. 223\u2013238. Springer International Publishing, Cham (2015)\n\n18.\n\nVu, L.H.: Formal development and verification of railway control systems. In the context of ERTMS\/ETCS Level 2. Ph.D. thesis, Technical University of Denmark, DTU Compute (2015)\n\n19.\n\nLinh Hong, V., Haxthausen, A.E., Peleska, J.: Formal modelling and verification of interlocking systems featuring sequential release. Sci. Comput. Program. 133, 91\u2013115 (2017)CrossRef\n\n20.\n\nWinter, K.: Symbolic model checking for interlocking systems. In: Flammini, F. (ed.) Railway Safety, Reliability, and Security: Technologies and Systems Engineering. IGI Global (2012)\n\nFootnotes\n\n1\n\nFor instance the July 2016 rural Southern-Italy head-on train collision would have been prevented if automated train detection equipment had been in place.\n\n2\n\nA model of the interlocking for a fairly simple network may lead to the potential inspection of an astronomical number of states (e.g. in the order of [11]).\n\n3\n\nIn Denmark, in the years 2009\u20132021, new interlocking systems that are compatible with the standardised European Train Control System (ETCS) Level 2 [2] will be deployed in the entire country within the context of the Danish Signalling Programme. In the context of the RobustRailS project accompanying the signalling programme on a scientific level, the approach is applied to the new systems.\n\n4\n\nHere we only show types that are relevant for the work presented in this article.\n\n5\n\nAn overlap section is needed when, for the short distance of a marker board to the end of the section, there is the concrete danger that a braking train stops after the end of the section, e.g. in adverse atmospheric conditions.\n\n6\n\nThese points include points in the path and overlap, and points used for flank and front protection. Sometimes it is required to protect tracks occupied by a train from another train not succeeding to brake in due space. For details about flank and front protection, see [14].\n\n7\n\nThe extension of the interface to divide networks with parallel tracks is straightforward and defines the interface as a set of linear sections dividing a network into disjoint and valid connected sub-networks.\n\n8\n\nIn the following, for simplicity, we just quantify over the whole set of sections of a network, intending that we are referring either only to point or only to linear sections according to the nature of .\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_12\n\n# Modular Model-Checking of a Byzantine Fault-Tolerant Protocol\n\nBenjamin F. Jones1 and Lee Pike1\n\n(1)\n\nGalois, Inc., Portland, Oregon 97204, USA\n\nBenjamin F. Jones (Corresponding author)\n\nEmail: bjones@galois.com\n\nLee Pike\n\nEmail: leepike@galois.com\n\nAbstract\n\nWith proof techniques like IC3 and k-induction, model-checking scales further than ever before. Still, fault-tolerant distributed systems are particularly challenging to model-check given their large state spaces and non-determinism. The typical approach to controlling complexity is to construct ad-hoc abstractions of faults, message-passing, and behaviors. However, these abstractions come at the price of divorcing the model from its implementation and making refactoring difficult. In this work, we present a model for fault-tolerant distributed system verification that combines ideas from the literature including calendar automata, symbolic fault injection, and abstract transition systems, and then use it to model-check various implementations of the Hybrid Oral Messages algorithm that differ in the fault model, timing model, and local node behavior. We show that despite being implementation-level models, the verifications are scalable and modular, insofar as isolated changes to an implementation require isolated changes to the model and proofs. This work is carried out in the SAL model-checker.\n\n## 1 Introduction\n\nFault-tolerant distributed systems are famously complex, yet are the backbone of life-critical systems, such as commercial avionics. Consequently, this class of systems demands high-assurance of correct design and implementation. Formal verification can help provide that assurance.\n\nThe verification of this class of systems has usually been at the algorithmic level, eliding details about a concrete implementation. Historically, it has relied on formal models verified by interactive theorem-proving [1\u20134]. If formal verification is to be introduced into the workflow of system designers, though, we need more automated methods that scale for implementation-level models. (Mostly) automated proof techniques are required to reduce the need for specialized verification expertise. We also need programmatic verification of implementations. System designers create software and hardware implementations to test, simulate, and deploy. Discrepancies between implementations and algorithmic models can arise if the latter is abstracted too much from the former [5], particularly if those abstractions are ad-hoc and system specific. Furthermore, as implementations are modified to explore the design space, it is easy for the formal model and the implementation to become inconsistent, so the verification is no longer about the system deployed.\n\nThere are at least two classes of abstractions that separate protocol-level models of fault-tolerant distributed algorithms from their implementations. One is to intertwine the environmental model with the system description. For example, the behaviors of nodes are naturally specified as a transition system in which transitions are guarded by the node's fault state. But faults are part of the environment; an implementation does not typically use its own fault status to choose actions! Another class of abstractions is used to simplify models. For example, message passing might be abstracted with shared state, or a node's local behavior is elided and instead, the output is constrained by a specification of the behavior.\n\nIn this paper, we present a fault-tolerant distributed systems model, and use that model to verify several variant implementations of the Byzantine fault-tolerant Hybrid Oral Messages algorithm ( ) [3]. The model combines various ideas from the literature to build scalable and modular formal models suitable for infinite-state model-checking, and it reduces the need for ad-hoc abstractions and optimizations. In Sect. 2, we present the important aspects of the model, including calendar automata, originally developed by Dutertre and Sorea [6], symbolic fault-injection, and abstract transition systems for verification.\n\nWe use the model to verify implementation-level models of in which message passing is explicit, nodes are not forced to execute strictly synchronously, and voting is explicit. In short, the models corresponds closely with an implementation of the algorithm. In Sect. 3, we first describe , then an implementation of it that uses the Boyer-Moore Fast Majority Vote algorithm (Fast MJRT) [7]. We then describe a set of modular invariants, such that the invariants only concern specific aspects of the model (e.g., faults, local node behavior, or the passage of time). The verification is interesting in its own right, as it is the first fully parametric (on the number of nodes) model-checked implementation of the algorithm.\n\nIn Sect. 4, we first show that despite being implementation-level, the model is scalable. Developing invariants requires some user guidance, and isolated changes to an implementation should require isolated modifications to the model and proof. To demonstrate this, we modify the implementation along the dimensions of faults (by adding an omissive-asymetric fault type [8]), time (by making a time-triggered model), and local behavior (by changing the majority vote to a mid-value selection) and show that in each case, the modifications are small and modular.\n\nOur primary contributions are (1) a model-checking verification of an implementation, and (2) demonstrating that our modeling paradigm allows for modular verification. Additionally, the idea of symbolic fault injection (Sect. 2.2) is novel.\n\nFinally, in Sect. 5 we describe related work, and we make concluding remarks in Sect. 6.\n\nThe models and experiments reported herein can be found online.1\n\n## 2 Formal Model\n\nHere we describe our formal model specialized for fault-tolerant distributed systems. The model draws on three principal abstractions: calendar automata, symbolic fault injection, and abstract transition systems; we describe each below.\n\n### 2.1 Calendar Automata\n\nReal-time system verification in general-purpose model-checkers requires an explicit formalism of real-time progression. Trying to encode real-time clocks directly is difficult; in particular, one must avoid Zeno's paradox in which no progress is made because state transitions simply update real-valued variables by an infinite sequence of decreasing amounts whose sum is finite. To avoid this problem, Dutetre and Sorea developed calendar automata [6], which is itself inspired by event calendars used in discrete-event simulation. Rather than encoding \"how much time has passed since the last event\", it encodes \"how far into the future is the next scheduled event\", and a real-valued variable representing the current time is updated to the next event time.\n\nDefine a set of events . For now, we do not define events; intuitively, an event is a set of state variables (shortly, we will associate events with messages sent in a distributed system). When an event is enabled, the transitions over events are enabled; otherwise, the variables stutter (maintain the same value).\n\nAn event calendar is a set of ordered pairs called calendar events where is an event and is a timeout, the time at which the event is scheduled. We denote element of an event calendar by .\n\nLet cal be an event calendar and be calendar events. Define an ordering on calendar events such that iff , and are the minimum elements of cal.\n\nLet a transition system , be a set of states S, a set of initial states , and a transition relation . We implicitly assume a set of state variables such that each state is a total function that maps state variables to values. We sometimes prime a state to denote that it satisfies the transition relation: . We also sometimes use a variable assignment notation to describe what state variables are specifically updated: e.g., .\n\nWe distinguish two special state variables in a transition system: (1) denotes the current time in the state, and (2) cal is an event calendar.\n\nThe following laws must hold of a transition system implementing a calendar automaton:\n\n 1. 1.\n\nTime is initialized to be less than or equal to every calendar timeout: , , .\n\n 2. 2.\n\nIn all states, if the current time is strictly less than every calendar event, then the only enabled transition is a time progress update: , , if , then such that , .\n\n 3. 3.\n\nIn all states, if the current time equals a timeout, then the only transitions enabled are calendar event updates associated with the timeout: , such that implies such that , , for all such that (recalling that by convention, ), and .\n\nFrom the definitions, it follows that in every state, the timeouts are never in the past, and that time is monotonic:\n\nLemma 1\n\n(Future timeouts). , , .\n\nLemma 2\n\n(Monotonic time). , if , then .\n\nProofs of these two lemmas are straightforward and omitted.\n\nIn a distributed system, it is convenient to distinguish global actions and local actions. Global actions are principally interprocess communication, while local actions are those carried out by each process to update its local state and produce new messages to broadcast. While both global and local actions can both be modeled as events in a calendar automata, doing so is generally overkill and complicates the model. From the global perspective, individual processes can update their local state atomically.\n\nAgain, following Dutetre and Sorea, we associate calendar events with channels in a distributed system [6]. Specializing calendars to message passing does not lose generality since all external communication from an individual process can be abstracted as message passing. Furthermore, fault models can be abstracted to act over channels rather than processes [9]. The calendar introduces real-time constraints on when processes send and receive messages.\n\nAssume processes are indexed from a finite set . A channel from process i to j is an ordered pair (i, j). Fix a set of messages . Given a channel and a timeout, let send be a relation on messages sent on a channel at a given time:\n\nSo send(i, j, t, m) holds iff i sends to j message m at time t. Likewise, let\n\nbe a relation on messages received on a channel at a time, so that recv(i, j, t, m) holds iff the message m received by j from i at time t.\n\nIn the absence of faults, we require that messages received were previously sent and not previously received: if , then such that where , and such that and . (We address faults in Sect. 2.2.)\n\nThen an event calendar for sending and receiving messages on channels is the union of the send and recv relations.\n\nThe event of receiving a message initiates a process to update its local transition system and generate additional messages to send. When the process is updating its local transition system, the event calendar is paused. That is, updating an event also includes updating j's transition system.\n\n### 2.2 Symbolic Fault Injection: A Synchronous Kibitzer\n\nThe typical approach to modeling faults is to add new state variables to each process representing its fault state. Then a node chooses actions based on its fault state. As a simple example, we might define a node that sends a good message if it is non-faulty and a bad message otherwise. In pseudo-code using guarded commands, its definition might look like the following:\n\nBut this approach mixes the specification of a node's behavior with the fault model, an aspect of the environment. Generally, nodes do not contain state variables assigned to their faults, or use their fault-status to determine their behavior!2 The upshot is that combining faults and node state divorces the specification from its implementation.\n\nA second difficulty with model-checking fault-tolerant systems in general is that modeling faults requires adding state and non-determinism. The minimum number of additional states that must be introduced may depend non-obviously on other aspects of the fault model, specific protocol, and system size. Such constraints lead to \"meta-model\" reasoning, such as the following, in which Rushby describes the number of data values that a particular protocol model must include to model the full range of Byzantine faults (defined later in this section):\n\n> To achieve the full range of faulty behaviors, it seems that a faulty source should be able to send a different incorrect value to each relay, and this requires n different values. It might seem that we need some additional incorrect values so that faulty relays can exhibit their full range of behaviors. It would certainly be safe to introduce additional values for this purpose, but the performance of model checking is very sensitive to the size of the state space, so there is a countervailing argument against introducing additional values. A little thought will show that . Hence, we decide against further extension to the range of values [10].\n\nThe second problem is the most straightforward to solve. In infinite-state model-checking, we can use either the integers or the reals as the datatype for values. Fault-tolerant voting schemes, such as a majority vote or mid-value selection (see Sect. 3), require only equality, or a total order, respectively, to be defined for the data.\n\nThe solution to the first problem is more involved. Our solution is to introduce what we call a synchronous kibitzer that symbolically injects faults into the model. The kibitzer decomposes the state and transitions associated with the fault model from the system itself. For the sake of concreteness in describing the synchronous kibitzer, we introduce a particular fault model, the hybrid fault model of Thambidurai and Park [11]. This fault model distinguishes Byzantine, symmetric, and manifest faults. It applies to broadcast systems in which a process is expected to broadcast the same value to multiple receivers. A Byzantine (or arbitrary) fault is one in which a process that is intended to broadcast the same value to other processes may instead broadcast arbitrary values to different receivers (including no value or the correct value). A symmetric fault is one in which a process may broadcast the same, but incorrect, value to other processes. Finally, a manifest (or benign) fault is one in which a process's broadcast fault is detectable by the receivers; e.g., by performing a cyclic redundancy check (CRC) or because the value arrives outside of a predetermined window.\n\nDefine a set of fault types\n\nAs in the previous section, let be a finite set of process indices, and let the variable\n\nrange over possible mappings from processes to faults.\n\nThe hybrid fault model assumes a broadcast model of communication. A takes a sender, a set of receivers, a real-time, and a message to send each receiver, and returns a set of calendar events:\n\nWith this machinery, we can define the semantics of faults by constraining the relationship between a message broadcast and the values received by the recipients. For a nonfaulty process that broadcasts, every recipient receives the sent message, and for symmetric faults, there is no requirement that the messages sent are the ones received, only that every recipient receives the same value:\n\nByzantine faults are left completely unconstrained.\n\nThus, faults can be modeled solely in terms of their effects on sending and receiving messages. A node's specification does not have to depend on its fault status directly.\n\nIf the faults mapping is a constant, then faults are permanently but non-deterministically assigned to nodes. However, we can easily model transient faults in which nodes are faulty temporarily by making faults a state variable that is updated non-deterministically. Whether we model permanent or transient faults, a maximum fault assumption (MFA) describes the maximum number of faults permitted in the system. The faults mapping can be non-deterministically updated during execution while satisfying the MFA using a constraint such as , where the MFA is defined by the function .\n\n### 2.3 Abstract Transition Systems\n\nDue to the sheer size of implementation-level models, manually examining counterexamples is tedious. To scale up verification, we use abstract transition systems (also known as disjunctive invariants) [12, 13]. In this context, an abstract transition system, relative to a given transition system , is a set of state predicates over S and a transition system such that:\n\n 1. 1.\n\n is a set of \"abstract states\" which correspond one-to-one with the state predicates .\n\n 2. 2.\n\n .\n\n 3. 3.\n\n where are the abstract states to which may transition from .\n\nFor verification purposes, it is important to note that if and satisfy the requirements above, then is an inductive invariant of . We may use such an invariant freely as a powerful assumption in the proof of other invariants (see Sect. 3.3).\n\nThe use of abstract transition systems not only allows us to scale proofs farther, but also to improve traceability and debugging while developing a model. In models like the ones described in Sect. 4.2 where there are on the order of 100 state variables and counterexample traces could be 30 steps long, the designer can be easily lost trying to identify the essence. In such cases, the values of the abstract predicates can serve to focus the designer's attention on one particular mode of the system where the counter example is taking place. At the present we do not have a good method for synthesizing the predicates automatically for general systems; they must be supplied by the user.\n\n## 3 Modeling and Verification for Oral Messages\n\nThe Hybrid Oral Messages ( ) algorithm [3] is a variant of the classic Oral Messages ( ) algorithm [14], originally developed by Thambidurai and Park [11] to achieve distributed consensus in the presence of a hybrid fault model. However, had a bug, as originally formulated, which was corrected and the mended algorithm was formally verified by Lincoln and Rushby using interactive theorem-proving [3].\n\nFirst, we briefly describe the algorithm, sketch our instantiation of the model for the particular protocol in Sect. 2, then describe it's invariants.\n\n### 3.1 Algorithm\n\n is a recursive algorithm that proceeds in rounds of communication. Here we give a recursive specification for , parameterized by the number of rounds, m. Consider a finite set of nodes N. Distinguish one node as the general, g, and the remaining nodes as the lieutenants. We assume the identity of any general or lieutenant cannot be spoofed. Broadcast communication proceeds in rounds. Denote any message that is detectably faulty (e.g., fails a CRC) or is absent, by . Additionally, in the algorithm, nodes report on values they have previously received. In doing so, nodes must differentiate reporting from an itself. Let R denote that an error is being reported. Finally, let V be a special, designated value.\n\nThe algorithm is recursively defined for :\n\n * : g broadcasts a value to each lieutenant and the lieutenants return the value received (or ).\n\n * , :\n\n 1. 1.\n\ng broadcasts a value to each lieutenant, l.\n\n 2. 2.\n\nLet be the value received by from g. Then for each l, execute , assigning l to be the general and to be the lieutenants. l sends , or R if .\n\n 3. 3.\n\nFor each lieutenant , remove all values received in Step 2 from executing . Compute the majority value over the remaining values, or V if there is no majority. If the majority value is R, return E.\n\nIn particular, includes two rounds of broadcast communication: one in which the general broadcasts, and one in which the lieutenants exchange their values.\n\n is designed to ensure validity and agreement properties under suitable hypotheses on the number and type of faults in the system. Validity states that if the general is nonfaulty, then every lieutenant outputs the value sent by the general. Agreement states that each lieutenant outputs the same value. More formally, Let denote the outputs of lieutenants , respectively, and let v be the value the general broadcasts:\n\nWe described a hybrid fault model in Sect. 2.2. Under that fault model, validity and agreement hold if , where n is the total number of nodes, a is the number of Byzantine (or asymmetric) faults, s is the number of symmetric faults, and b is the number of benign faults. Additionally, the number of rounds m must be greater or equal to the number of Byzantine faults, a [3, 11].\n\n### 3.2 Model Sketch\n\nWe have implemented (as well as the variants described in Sect. 4.2) in the Symbolic Analysis Laboratory (SAL) [15]. SAL contains a suite of model-checkers. In our work, we use infinite-state (SMT-based) k-induction [6].\n\nWe follow Rushby [10] in \"unrolling\" the communication among lieutenants into two sets of logical nodes: relays and receivers. Relays encode the lieutenants' Step 2 of the algorithm, in which they rebroadcast the values received from the general after filtering manifestly bad messages, while the receivers encode the voting step. We refer to the general as the source. The unrolling shows that a generalization of the original algorithm holds: the number of relays and receivers need not be the same. We model communication through one-way, typed channels. The source broadcasts a message to each relay which, in turn, each broadcast their messages to all receivers.\n\nThe relays and receivers explicitly send and receive messages and store them in local buffers as needed. In addition, the receivers implement the Fast MJRY algorithm [7].\n\nOur SAL model defines seven transition systems in total: clock, source, relay (parametrized over an ID), receiver (parametrized over an ID), observer, abstractor, and abstract_monitor. The first four of these are composed asynchronously, in an intermediate system we label system, and share access to a global calendar consisting of event slots , one for each channel in the system. The clock transition system is responsible for updating a global variable t (called now in Sect. 2.1) representing time according to the rules for calendar automata.\n\nThe asynchronous composition of the system relaxes the original specification of the algorithm considerably. For example, in our implementation, a receiver may receive a message from one relay before another relay has received a message from the source. We only require that all relays and receivers have executed before voting. With a general asynchronous model, it is easy to refine it further; for example, we refine it to a time-triggered model in Sect. 4.2.\n\nThe observer is a synchronous observer [16] that encodes the validity and agreement properties as synchronously-composed transition systems. State variables denoting validity and agreement are set to be false if the receivers have completed their vote but the respective properties do not hold.\n\nFinally, the abstractor and abstract_monitor encode an abstract transition system for the system, as described in Sect. 2.3.\n\nFig. 1.\n\nInvariant classification and dependencies.\n\n### 3.3 Invariants\n\nTo make the proof scalable, we specify inductive invariants to be used by SAL's k-induction engine. There are 11 invariants, falling into five categories:\n\n 1. 1.\n\nCalendar automata: Lemmas relating to the calendar automata model. These include lemmas such as time being monotonic, channels missing messages if there is no calendar event, and only nodes associated with a calendar event may execute their local transition systems.\n\n 2. 2.\n\nAbstract transition sytem (ATS): Lemmas relating the ATS states to the implementation states.\n\n 3. 3.\n\nReceiver local behavior: Lemmas describing the modes of behavior of the receivers. The major modes of their behavior are receiving messages, then once it has filled its buffer, it votes, and after voting returns the result. An additional lemma notes that the messages currently received plus missing messages equals the total number of expected messages.\n\n 4. 4.\n\nFaults: Lemmas characterizing the effect of a fault in a single broadcast. Examples include lemmas stating that if a node receives a faulty message, some \"upstream\" node in the communication path was faulty. Another example is that the faults of messages latched by a node in its buffer match the faults ascribed to the sender in the calendar event.\n\n 5. 5.\n\nVoting: Lemmas proving that the Fast MJRTY algorithm implements a majority vote, if one exists. These lemmas are nearly verbatim transcriptions from the journal proofs for the algorithm [7].\n\nThe proof structure is shown in Fig. 1. The number of lemmas per category are shown in parentheses. Arrows denote dependencies. For example, the ATS lemmas depend on both the calendar automata and receiver state-machine lemmas. As can be seen, the proof structure is modular. The calendar lemmas are general and independent of any particular protocol or fault model. Similarly, lemmas about the internal behavior of a receiver is independent of the global protocol behavior. It is also independent of the effect of faults on the system\u2014the only \"knowledge\" of faults that receiver has is whether a fault is benign or not. Lemmas about the behavior of faults in the system are also independent of the particular protocol being modeled. Likewise, lemmas about the particular voting algorithm used depend only on the receiver's internal behavior. Only the ATS depends on both calendar-specific and local state-machine results, since it is an abstraction of the entire system implementation. Recall, however, that the ATS is a convenience for debugging and can be elided.\n\n## 4 Experimental Results\n\nHere we present two classes of experimental results. First, we demonstrate the scalability results of the verification, despite the low-level modeling. Then we describe modularity results, demonstrated by making modifications to the model and re-validating the model.\n\n### 4.1 Scalability\n\nWe present benchmarks in Fig. 2. The benchmarks were performed on a server with Intel Xeon E312xx (Sandy Bridge) CPUs. The table provides execution times in seconds, with a timeout limit of one hour, for verifying the model, given a selected number of relays and receivers. The voting logic is in the receivers, so they have substantially more state than the relays, and dominate the execution time. The execution times sums the execution times for verifying each of the eleven lemmas individually, as well as the final agreement and validity theorems. Each proof incurs the full startup, parsing, type-checking, and model-generation time of SAL. Observe the theorems hold even in the degenerate cases of one relay or one receiver.\n\nFig. 2.\n\nBenchmark of full proof computation time for implementation. Times are in seconds with a timeout ( ) limit of one hour. Dashes ('-') denote no benchmark was run.\n\nAs a point of comparison, Rushby presents an elegant high-level model of , also in SAL [10]. For small numbers of relays\/receivers, the verification of Rushby's model is much faster, likely due to making only one call to SAL. However, for six relays and two receivers, it takes 449 seconds and timeouts (at one hour) for seven relays and two receivers. Checking Rushby's model requires use of symbolic, BDD-based model-checking techniques which are well-known to scale poorly. On the other hand, our model requires the use of k-induction which scales well, but requires (inductive) invariants to be provided.\n\n### 4.2 Modular Verification\n\nTo demonstrate the modularity of the modelling and verification approach, in this section, we explore variants to the model and report the effort required to implement the modifications and repair the proofs. The results are summarized in Fig. 3 and sketched below. In the table, for each modification, we report how much of the model must be modified. We report on four aspects of the system: which transition systems are modified (as described in Sect. 3.2), how many definitions have to be added or modified, the number of invariants that have to be added or modified, and which invariant classes (as defined in Sect. 3.3) those lemmas belong to. We modify the implementation along the axes of faults, time, and local node behavior.\n\nFig. 3.\n\nRefactoring effort for protocol modifications, measured by which portions of the model have to be modified.\n\nOmissive Asymmetric Faults. Removing faults already described by the fault model is easy. Recall that in our model faults do not appear in the system specification and only operate on the calendar. Removing a fault from the system requires only setting the number of a particular kind of faults to zero in the maximum fault assumption.\n\nAdding new kinds of faults requires more work but is still modular. Consider adding omissive asymmetric faults, a restriction of Byzantine faults in which a broadcaster either sends the correct value or a benign fault [8], to the fault model. Doing so requires modifying none of transition systems, because of the synchronous kibitzer. We add a new uninterpreted function definition for omissive asymmetric faults, then modify the type of faults, and their effect on the calendar. Two invariants, both in the class of invariants cover faults, are extended to cover the cases where a sender is omissive asymmetric.\n\nTime-Triggered Messaging. A time-triggered distributed system is one in which nodes are independently clocked, but clock constraints allow the model to appear as if it is executing synchronously [17].\n\nChanging the model to be time-triggered principally requires making the source, relays, and receivers driven explicitly by the passage of time (we do not model clock drift or skew). As well, a \"receive window\" is defined at which messages from non-faulty nodes should be received. Messages received outside the window are marked as coming from manifest-faulty senders. The model requires three new definitions to encode nondeterministic message delay and two are small helper functions. The guards in the relays and receivers are modified to latch messages received outside the receive windows as being manifest faults. The ATS definition is modified to track the times in the calendar, not just the messages. Two new calendar invariants are introduced, stating that the calendar messages are either empty, or their time-stamps fall within the respective message windows. Then, three invariants classifying faults are relaxed to allow for the possibility of faulty nodes sending benign messages.\n\nMid-Value Selection. Our model leverages a majority vote in order to tolerate faults. Another choice for the fault masking algorithm used is mid-value selection. This choice is common in applications involving hardware, signal selection, or cases where information about congruence is useful. To implement mid-value selection in our model, we allow messages sent to take values in and the receiver transition system is modified in two ways. First, a second buffer is introduced which will hold the sorted contents of the main buffer once voting has commenced. Second, a mid-value select function is called on the sorted buffer and the result is stored as the receiver's vote. The only invariants needing modification were the ATS definition (to account for the values stored by the new buffer and the relation between it and the main buffer) and the voting invariant.\n\n### 4.3 Proof Effort Remarks\n\nThe lemmas described in Sect. 3.3 are constructed by-hand and represent multiple days of effort, but that effort includes both model and protocol construction and generalization as well as verification. The counterexamples returned by SAL are very useful for strengthening invariants, but tedious to analyze\u2014a model with five relays and two receivers contains 90 state variables, and there are known counterexamples to models that size [3]. Once we developed the synchronously-composed ATS observer, the verification effort was sped up considerably.\n\nThe invariants are surprisingly modular. One benefit of a model-checking based approach is that it is automated to rerun a proof of a theorem omitting lemmas to see if the proof still holds. This allowed us to explore reducing dependencies between invariants related to different aspects of the system.\n\nThe modifications to the implementation described in Sect. 4.2 took at most hours to develop. Moreover, most of the invariants do not concern the specific protocol modeled at all, and we hypothesize that for completely different fault-tolerance protocols, only the modeling aspects related to the protocol behavior and local node behavior would change, and the invariant structure would remain modular.\n\nMoreover, we are agnostic about how lemmas are discovered. As techniques like IC3 scale, they may be discovered automatically. k-induction in infinite-state model-checking blurs the lines between interactive and automated theorem proving. IC3 can even be strengthened using k-induciton [18].\n\n## 5 Related Work\n\nThe Oral Messages algorithm and its variants and its variants have a long history of formal verification. was verified in both the PVS and ACL2 interactive theorem-provers [2]. Also in ACL2, an implementation of a circuit design to implement is given [1]; the low-level model most closely relates to our level of detail. A refinement-based verification approach is used, and is specialized to a fixed number of nodes. Bokor et al. describe a message-passing model for synchronous distributed algorithms that is particularly amenable to partial-order reduction for explicit-state model-checking [19]. The model is efficient for up to five nodes, but results are not presented beyond that. Very recently, Jovanovi\u0107 and Dutertre use a \"flattened\" high-level model of as a benchmark for IC3 augmented with k-induction [18].\n\nMoreover, our work is heavily influenced by previous verifications of fault-tolerant and real-time systems in SAL [6, 10, 13].\n\n## 6 Conclusions\n\nThis work fits within a larger project, in collaboration with Honeywell Labs, to build an architectural domain-specific language (ADSL) for specifying and verifying distributed fault-tolerant systems. The ADSL should be able to synthesize both software and\/or hardware implementations as well as formal models for verification. Before building such an ADSL, we needed a scalable general formal model to which to compile, leading to the work presented in this paper. We hypothesize that the ADSL will make refactoring even easier, and we can generate invariants or invariant templates useful for verification. Indeed, we have developed a preliminary ADSL that generates C code as well as formal models in SRI's Sally [18], to be described in a future paper.3\n\nBeyond building an ADSL, another avenue of research is producing a formal proof that a software implementation satisfies the node specification in our formal model. While our model of node behavior is low-level, there are gaps. For example, our work is in SAL's language of guarded commands [15] and needs to be either refined or verified to be equivalent to a software implementation's semantics. Another aspect is that behavior related to networking, serialization, etc. is left abstract, implicit in the send and recv functions.\n\nAcknowledgments\n\nThis work is partially supported by NASA contract #NNL14AA08C. We are indebted to our collaborators Brendan Hall and Srivatsan Varadarajan at Honeywell Labs, and to Wilfredo Torres-Pomales at NASA Langley for their discussions and insights. Additionally, we acknowledge that this work is heavily inspired by a series of papers authored by John Rushby.\n\nReferences\n\n1.\n\nBevier, W.R., Young, W.D.: The proof of correctness of a fault-tolerant circuit design. Computational Logic Inc., Technical report 57 (1990). http:\/\/\u200bcomputationallog\u200bic.\u200bcom\/\u200breports\/\u200bindex.\u200bhtml\n\n2.\n\nYoung, W.D.: Comparing verification systems: interactive consistency in ACL2. IEEE Trans. Softw. Eng. 23(4), 214\u2013223 (1997)CrossRef\n\n3.\n\nLincoln, P., Rushby, J.: A formally verified algorithm for interactive consistency under a hybrid fault model. In: 23rd Fault Tolerant Computing Symposium, pp. 402\u2013411. IEEE Computer Society (1993)\n\n4.\n\nOwre, S., Rushby, J., Shankar, N., von Henke, F.: Formal verification for fault-tolerant architectures: prolegomena to the design of PVS. IEEE Trans. Software Eng. 21(2), 107\u2013125 (1995)CrossRef\n\n5.\n\nChandra, T.D., Griesemer, R., Redstone, J.: Paxos made live: an engineering perspective. In: ACM Symposium on Principles of Distributed Computing (PODC), pp. 398\u2013407. ACM (2007)\n\n6.\n\nDutertre, B., Sorea, M.: Modeling and verification of a fault-tolerant real-time startup protocol using calendar automata. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS\/FTRTFT -2004. LNCS, vol. 3253, pp. 199\u2013214. Springer, Heidelberg (2004). doi:10.\u200b1007\/\u200b978-3-540-30206-3_\u200b15 CrossRef\n\n7.\n\nBoyer, R.S., Moore, J.S.: MJRTY-a fast majority vote algorithm. In: Boyer, R.S. (ed.) Automated Reasoning. Automated Reasoning Series, vol. 1, pp. 105\u2013117. Springer, Dordrecht (1991)CrossRef\n\n8.\n\nAzadmanesh, M.H., Kieckhafer, R.M.: Exploiting omissive faults in synchronous approximate agreement. IEEE Trans. Comput. 49(10), 1031\u20131042 (2000)MathSciNetCrossRefMATH\n\n9.\n\nPike, L., Maddalon, J., Miner, P., Geser, A.: Abstractions for fault-tolerant distributed system verification. In: Slind, K., Bunker, A., Gopalakrishnan, G. (eds.) TPHOLs 2004. LNCS, vol. 3223, pp. 257\u2013270. Springer, Heidelberg (2004). doi:10.\u200b1007\/\u200b978-3-540-30142-4_\u200b19 CrossRef\n\n10.\n\nRushby, J.: SAL tutorial: analyzing the fault-tolerant algorithm OM(1). Computer Science Laboratory, SRI International, Menlo Park, CA, CSL Technical note. http:\/\/\u200bwww.\u200bcsl.\u200bsri.\u200bcom\/\u200busers\/\u200brushby\/\u200babstracts\/\u200bom1\n\n11.\n\nThambidurai, P., Park, Y.-K.: Interactive consistency with multiple failure modes. In: Symposium on Reliable Distributed Systems, pp. 93\u2013100. IEEE (1988)\n\n12.\n\nRushby, J.: Verification diagrams revisited: disjunctive invariants for easy verification. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 508\u2013520. Springer, Heidelberg (2000). doi:10.\u200b1007\/\u200b10722167_\u200b38 CrossRef\n\n13.\n\nDutertre, B., Sorea, M.: Timed systems in SAL. In: SRI International, Menlo Park, CA, SDL Technical report SRI-SDL-04-03, July 2004\n\n14.\n\nLamport, L., Shostak, R., Pease, M.: The Byzantine generals problem. ACM Trans. Program. Lang. Syst. 4(3), 382\u2013401 (1982)CrossRefMATH\n\n15.\n\nBensalem, S., Ganesh, V., Lakhnech, Y., Mu\u00f1oz, C., Owre, S., Rue\u00df, H., Rushby, J., Rusu, V., Sa\u00efdi, H., Shankar, N., Singerman, E., Tiwari, A.: An overview of SAL. In: NASA Langley Formal Methods Workshop, pp. 187\u2013196 (2000)\n\n16.\n\nRushby, J.: The versatile synchronous observer. In: Iida, S., Meseguer, J., Ogata, K. (eds.) Specification, Algebra, and Software. LNCS, vol. 8373, pp. 110\u2013128. Springer, Heidelberg (2014). doi:10.\u200b1007\/\u200b978-3-642-54624-2_\u200b6 CrossRef\n\n17.\n\nKopetz, H.: Real-Time Systems: Design Principles for Distributed Embedded Applications. Kluwer, Philadelphia (1997)MATH\n\n18.\n\nJavanovi\u0107, D., Dutertre, B.: Property-directed -induction. In: Formal Methods in Computer Aided Design (FMCAD) (2016)\n\n19.\n\nBokor, P., Serafini, M., Suri, N.: On efficient models for model checking message-passing distributed protocols. In: Hatcliff, J., Zucca, E. (eds.) FMOODS\/FORTE -2010. LNCS, vol. 6117, pp. 216\u2013223. Springer, Heidelberg (2010). doi:10.\u200b1007\/\u200b978-3-642-13464-7_\u200b17 CrossRef\n\nFootnotes\n\n1\n\nhttps:\/\/\u200bgithub.\u200bcom\/\u200bGaloisInc\/\u200bmmc-paper.\n\n2\n\nThere are exceptions; for example, benign faults may be detected by a node itself (e.g., in a built-in-test).\n\n3\n\nhttps:\/\/\u200bgithub.\u200bcom\/\u200bGaloisInc\/\u200batom-sally.\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_13\n\n# Improved Learning for Stochastic Timed Models by State-Merging Algorithms\n\nBraham Lotfi Mediouni1 , Ayoub Nouri1, Marius Bozga1 and Saddek Bensalem1\n\n(1)\n\nUniversit\u00e9 Grenoble Alpes, CNRS, VERIMAG, 38000 Grenoble, France\n\nBraham Lotfi Mediouni\n\nEmail: braham-lotfi.mediouni@univ-grenoble-alpes.fr\n\nAbstract\n\nThe construction of faithful system models for quantitative analysis, e.g., performance evaluation, is challenging due to the inherent systems' complexity and unknown operating conditions. To overcome such difficulties, we are interested in the automated construction of system models by learning from actual execution traces. We focus on the timing aspects of systems that are assumed to be of stochastic nature. In this context, we study a state-merging procedure for learning stochastic timed models and we propose several enhancements at the level of the learned model structure and the underlying algorithms. The results obtained on different examples show a significant improvement of timing accuracy of the learned models.\n\n## 1 Introduction\n\nA necessary condition for a successful system design is to rely on faithful models that reflect the actual system behavior. In spite of the long experience designers have on building system models, their construction remains a challenging task, especially with the increasing complexity of recent systems. For performance models, this is even harder because of the inherent complexity and the induced stochastic behavior that is usually combined with time constraints.\n\nMachine Learning (ML) is an active field of research where new algorithms are constantly developed and improved in order to address new challenges and new classes of problems (see [13] for a recent survey). Such an approach allows to automatically build a model out of system observations, i.e., given a learning sample S, a ML algorithm infers an automaton that, in the limit1, represents the language L of the actual system [11]. We believe that ML can be used to automatically build system models capturing performance aspects, especially the timing behavior and the stochastic evolution. Those system models may be useful for documenting legacy code, and for performing formal analyses in order to enhance the system performance, or to integrate new functionalities [11].\n\nDespite the wide development of ML techniques, only few works were interested in learning stochastic timed models [9, 10, 12, 14]. In this paper, we study the RTI+ algorithm [14] and we propose improvements that enhance its accuracy. This algorithm learns a sub-class of timed automata [1] augmented with probabilities, called Deterministic Real-Time Automata (DRTA). Given a timed learning sample S (traces of timestamped actions of the system), the algorithm starts by building a tree representation of S, called Augmented Prefix Tree Acceptor (APTA). Then, based on statistical tests, it performs state-merging and splitting operations until no more operations are possible. In this algorithm, clock constraints are captured as time intervals over transitions and are built in a coarse fashion. These time intervals are actually considered to be the largest possible, which makes the learning procedure converge faster. However, this introduces a lot of generalization in the built APTA, by allowing timing behaviors that are not part of the actual system language L. Furthermore, we identified that such behaviors cannot be refined during the learning process. The learned model is thus not accurate from a timing point of view.\n\nIn this work, we propose a more accurate learning procedure by investigating better compromises between the time generalization introduced in the APTA and its size (and consequently its learning time). We introduce three new APTA models representing different levels of time generalization; the first model is the exact representation of the learning sample, i.e., with no generalization, while the two others introduce some generalization which is less than the original RTI+. We implemented the new variants of the RTI+ algorithm and validated them on different examples. The obtained results show that the learned models are more accurate than the original implementation, albeit the learning time is generally higher.\n\nOutline. In Sect. 2, we discuss some related works on learning stochastic timed models. Section 3 introduces notations and key definitions used in the rest of the paper. We recall the RTI+ learning algorithm and study underlying time representation issues in Sect. 4. In Sect. 5, we present the three improvements we propose for RTI+ and discuss them. Section 6 presents experiments and results of the improved algorithms. Conclusions are drawn in Sect. 7.\n\n## 2 Related Works\n\nIn the literature, several algorithms have been proposed for automata learning [3, 3, 7, 14], mostly in the deterministic case. In the last decades, an increasing interest has been shown for learning probabilistic models, partly due to the success of verification techniques such as probabilistic and statistical model checking [5, 6]. Despite this development, only few works considered the problem of learning stochastic timed models [9, 10, 12, 14].\n\nMost of the algorithms proposed in this setting are based on the state-merging procedure made popular by the Alergia algorithm [3]. Moreover, many of them consider Continuous-Time Markov Chains (CTMCs) as the underlying model. For instance, in [12], an algorithm is proposed for model-checking black-box systems. More recently, the AAlergia algorithm [8], initially proposed for learning Discrete-Time Markov Chains and Markov Decision Processes, was extended to learn CTMCs [9]. This work is an extension of Alergia to learn models having timed in\/out actions.\n\nOther algorithms such as RTI+ [14] and BUTLA [7] focus on learning timed automata augmented with probability distributions on discrete transitions and uniform probabilities over timing constraints. Both follow a state-merging procedure but consider different statistical tests for checking states compatibility.\n\nIn [10], authors focus on learning more general stochastic timed models, namely Generalized Semi-Markov Processes, following the same state-merging procedure. This algorithm relies on new statistical clocks estimators, in addition to the state compatibility criterion used in Alergia.\n\n## 3 Background\n\nLet be a finite alphabet, the set of words over and the empty word. Let be a time domain and the set of time sequences over . In our work, we consider integer time values, i.e., . For a set of clocks , let denote the set of clock constraints over . Let be the intervals domain, where is an interval of the form such that , and represents the set of integer values between a and b. Let be an untimed word over and a time sequence over . We write (resp. ) whenever (resp. ) is a prefix of (resp. ). We also write (resp. ) for the concatenation of (resp. ) and (resp. ). (resp. ) is the size of (resp. ).\n\n### 3.1 Deterministic Real-Time Automata (DRTA)\n\nA Real-Time Automaton (RTA) is a timed automaton with a single clock that is systematically reset on every transition.\n\nDefinition 1\n\n(Real-Time Automaton (RTA)). An RTA is a tuple where: (1) is the alphabet, (2) L is a finite set of locations, (3) L is the initial location, (4) contains a single clock, (5) T is a set of edges with a systematic reset of the clock c, (6) inv : L associates invariants to locations.\n\nFor more convenience, transitions are denoted as , where and is a time interval including both transition guards and location invariants. For simplicity, we also omit the systematic reset.\n\nAn RTA is deterministic (DRTA) if, for each location l and a symbol , the timing constraints of any two transitions starting from l and labeled with are disjoint, i.e., and . A DRTA generates timed words over . Each timed word is a sequence of timed symbols =( )( )...( ), representing an untimed word together with a time sequence . A set of n timed words constitute a learning sample . We denote by the set of time values appearing in S.\n\nA Prefix Tree Acceptor (PTA) is a tree representation of the learning sample S where locations represent prefixes of untimed words in S. Timing information is captured in a PTA in form of intervals over transitions. This structure is called Augmented PTA (APTA). In the latter, each transition is annotated with a frequency that represents the number of words in S having as a prefix. An APTA can be seen as an acyclic DRTA annotated with frequencies. Let be this annotation function. Given a DRTA , a pair is an annotated DRTA, denoted .\n\n### 3.2 Stochastic Interpretation of a DRTA\n\nA DRTA starts at the initial location with probability 1. It moves from a location to another using transitions in T. At each location l, a transition is chosen among the set of available transitions . Selecting a transition consists of choosing a timed symbol . A probabilistic strategy that associates a probability function to each location l over the set of transitions is used to make this choice: , such that . For the chosen transition , the choice of the time value is done uniformly over the time interval I. Figure 1 shows an example where two transitions labeled A and B are possible from location 1. The strategy associates probability 0.6 to A and 0.4 to B. Then, uniform choices on the associated time intervals are performed.\n\nFig. 1.\n\nProbabilistic strategy with uniform choice\n\n## 4 The RTI+ Learning Procedure\n\nRTI+ [14] is a state-merging algorithm for learning DRTA models from a sample of timed words. The algorithm first builds a PTA then reduces it by merging locations having similar behaviors, according to a given compatibility criterion. Compared to other state-merging algorithms, RTI+ relies on a time-split operation to identify the different timed behaviors and to split them into disjoint ones. The algorithm is able to learn a stochastic DRTA, i.e., a where the strategy is obtained from the associated annotation function .\n\n### 4.1 Building the APTA\n\nThe timed learning sample is represented as an APTA where all the time intervals span over . Initially, the built APTA only contains a root node consisting of the empty word . RTI+ proceeds by adding a location in the tree for each prefix of untimed words in S. Then, a transition labeled with is created from location l to location if the prefix of is obtained by concatenating the prefix of l and symbol . Finally, transitions are augmented with the largest time constraint , where . The annotation function is built at the same time and represents transitions frequencies. In this work, we denote this construction as generalized-bound APTA.\n\nDefinition 2\n\n(Generalized-bound APTA). A generalized-bound APTA is a where:\n\n * , ,\n\n * T contains transitions of the form s.t. , and .\n\n### 4.2 The Learning Process\n\nThe learning process aims to identify the that represents the target language while reducing the size of the initial APTA. At each iteration, the algorithm first tries to identify the timing behavior of the system, by using time-split operations. The second step consists of merging compatible locations that show similar stochastic and timed behaviors. Locations that are not involved in merge or split operations are marked as belonging to the final model (promote operation). The algorithm proceeds by initially marking the root of the APTA as part of the final model and its successors as candidate locations. The latter will be considered for time-split, merge or promote operations.\n\nTime-Split Operation. For a given transition , splitting t at a specific time value consists of replacing t by two transitions and with disjoint time intervals [a; c] and , respectively. This operation alters the subtree of such that the corresponding timed words that used to trigger transition t with time values in [a; c] (resp. ) are reassigned to the subtree pointed by transition (resp. ).2\n\nMerge Operation. Given a marked location l (belongs to the final model) and a candidate location , this operation is performed by first redirecting the transitions targetting , to l and then by folding the subtree of on l (see footnote 2).\n\n### 4.3 Compatibility Evaluation\n\nThe compatibility criterion used in RTI+ is the Likelihood Ratio (LR) test. Intuitively, this criterion measures a distance between two hypotheses with respect to specific observations. In our case, the considered hypotheses are two models: H with m transitions and with transitions ( ), where H is the model after a merge operation (resp. before a split) and is the model before a merge (resp. after a split). The observations are the traces of S.\n\nWe define the likelihood function that estimates how S is likely to be generated by each model (H or ). It represents the product of the probability to generate each timed word in S 3. Note that the timed word in S corresponds to a unique path in the . The probability to generate is the product of the probabilities of each transition in :\n\nWhere corresponds to the probability to transit from the location to in H with the timed symbol . Given a learning sample S of size n, the likelihood function of H is . The likelihood ratio is then computed as follows\n\nLet Y be a random variable following a distribution with degrees of freedom, i.e., . Then, is asymptotically distributed. In order to evaluate the probability to obtain y or more extreme values, we compute the p-value . If , then we conclude that H and are significantly different, with confidence.\n\nThe compatibility criterion concludes that a time-split operation is accepted whenever it identifies a new timing behavior, that is, the model after split is significantly different from the model before split ( ). In constrast, a merge is rejected whenever the model after merge is significantly different from the model before merge since the merged locations are supposed to have similar stochastic and timed behaviors.\n\n### 4.4 Shortcomings\n\nThe RTI+ algorithm relies on the generalized-bound APTA as initial representation of the learning sample S. As pointed out before, this kind of APTA augments an untimed PTA with the largest possible time intervals, without considering the values that concretely appear in S. This introduces an initial generalization that leads the APTA to accept words that do not actually belong to S and might not belong to the target language L. In Example 1, we show that this initial generalization cannot be refined later in the learning process. More concretely, we observe that the time intervals that do not appear in S are not isolated and removed from the .\n\nExample 1\n\nLet us consider the following learning sample (A,5)(B,5); (A,4)(A,3); (A,3)(B,5); (B,1)(A,5); (B,3)(B,5); (B,5)(A,1) . The left-hand model in Fig. 2 presents the initial (H) of S on which we evaluate a time-split operation. The latter is expected to identify the empty interval [0; 2] on transition , since no timed word in S takes this transition with time values in [0; 2]. The right-hand figure represents the model assuming a split of transition t at time value 2 ( ). The LR test returns which leads to reject the time-split operation, and hence, the empty interval [0; 2] is not identified during the learning process.\n\nFig. 2.\n\nIdentifying empty intervals with time-split operation\n\nThe generalized-bound APTA introduces empty time intervals that cannot be removed during the learning process. To overcome this issue, we propose, in the next section, new representations of the learning sample S.\n\n## 5 Learning More Accurate Models\n\nA faithful representation of the learning sample consists of building an APTA that accepts only words in S by taking into account the time values. This can be done at different granularities, which results on different tradeoffs between the introduced initial generalization and the APTA size. We propose three different APTA models denoted unfolded, constructive-bound and tightened-bound APTAs.\n\n### 5.1 Unfolded APTA\n\nThis APTA model fits perfectly the traces in S, that is, accepts exactly the timed words in S. Hence, it does not introduce any initial generalization. To build such a model, we need to consider both symbols and time values. The APTA initially contains the empty word. Locations are added for every timed prefix and corresponding transitions are created such that each transition only accepts a single time value, i.e., time intervals are equalities of the form .\n\nDefinition 3\n\n(Unfolded APTA). An unfolded APTA is a where:\n\n * ,\n\n * T contains transitions of the form such that: (1) , (2) , and .\n\n### 5.2 Constructive-Bound APTA\n\nA more compact representation of S compared to the unfolded APTA can be obtained by reducing the size of the initial APTA. At each location, a reduction of the number of transitions is performed by grouping all the contiguous time values for the same symbol into a single transition where the time interval I is the union of the different time intervals.\n\nDefinition 4\n\n(Constructive-bound APTA). A constructive-bound APTA is a where:\n\n * ,\n\n * T contains transitions of the form such that: (1) , (2) and , and .\n\nIn Definition 4, each location corresponds to a subset of timed words that have a common untimed prefix where each symbol (of the prefix) apprears with contiguous time values. A location is labeled by the given untimed prefix and the sequence of intervals corresponding to each symbol of . is the interval grouping the contiguous time values for the symbol of . All time values of these intervals are present in at least one timed word in S. A transition is added between locations l and such that: (1) the concatenation of the untimed prefix relative to l and symbol produces the untimed prefix relative to , and (2) adding I to the interval sequence of l gives the interval sequence of .\n\n### 5.3 Tightened-Bound APTA\n\nThe minimal size of APTA is obtained by allowing the minimal number of transitions from each location. This minimal number is obtained by assigning at most one transition for each symbol of . The initial generalization is reduced (compared to the generalized-bound APTA) by identifying the minimum (resp. the maximum ) time value (resp. ) among all the time values for each location l and symbol . Then, a single transition is created from l with symbol and a time interval . We call this APTA model a tightened-bound APTA. It has the same structure as the generalized-bound APTA but with tighter bounds. The time interval of each transition is computed locally depending on the corresponding timed words in S.\n\nDefinition 5\n\n(Tightened-bound APTA). A tightened-bound APTA is a where:\n\n * , ,\n\n * T contains transitions of the form such that: (1) , (2) , (3) , and , where .\n\n### 5.4 Evaluation\n\nIn this section, we discuss the proposed APTA models with respect to their ability to faithfully represent S and to their size. We consider the following sample (A,5)(B,5); (A,4)(A,3); (A,3)(B,5); (B,3)(A,5); (B,3)(B,5); (B,1)(A,1) . Figure 3 depicts the three types of APTAs representing S.\n\nFig. 3.\n\nThe three APTA models for the sample S\n\nInitial Generalization. The unfolded APTA does not introduce any initial generalization (Fig. 3a). The constructive-bound APTA is a more compact representation of S compared to the unfolded APTA with less generalization than the generalized-bound APTA. Some generalization is introduced due to the possible combination of grouped time values. In other words, the time values of the time intervals appear in S, but the language generated by the APTA overapproximates S since it accepts more time sequences. For instance, in Fig. 3b, the timed word (A,3)(A,3) is accepted although not in S. This is due to the combination of time values coming from the timed words (A,4)(A,3) and (A,3)(B,5).\n\nFig. 4.\n\nGeneralization introduced by the different APTAs\n\nThe tightened-bound APTA introduces two kinds of generalization. The first is due to the combination of grouped time values, as for the constructive-bound APTA. The second one is caused by the presence of empty intervals. An example is given in Fig. 3c where transitting from the root is possible using the timed symbol (B,2) which is not in S. This latter generalization is similar to the one we pointed out for the generalized-bound APTA albeit with more restrictive time intervals, since the empty intervals and are initially removed. The relationship between these models and the generalization they introduce is summarized inFig. 4.\n\nAPTA Size. In terms of the size of initial representation, the unfolded APTA is the largest. The APTA size depends on the size of and . The worst case is encountered when all the traces in S are of the same length N and when S contains all the combinations of symbols and time values. The resulting complete tree, in this case, represents the upper bound on the exponential number of locations and can be expressed as\n\nThis maximum number of locations is reduced in the constructive-bound APTA by grouping contiguous time values. However, this improvement is meaningless in the case where all the time values are disjoint. For a given interval , the maximum number of disjoint intervals is encountered when all the time values are disjoint and is equal to . The worst case number of locations of a complete tree of depth is\n\nThe number of locations, in this case, is highly dependent on the size of and less on the size of . This latter can be removed by allowing only one interval for each symbol at each location. This is the case of the generalized-bound APTA and the tightened-bound APTA which return the minimum number of locations.\n\n## 6 Experiments\n\nIn this section, we evaluate the learned model according to its ability to accept the words belonging to L and to reject the others. This gives insight into how accurate the learned model is. A C++ implementation of the proposed algorithms and the considered examples can be found in http:\/\/\u200bwww-verimag.\u200bimag.\u200bfr\/\u200b~nouri\/\u200bdrta-learning. The same page also contains additional materials such as algorithms and formal definitions of the elementary operations, in addition to a discussion about the proposed models' accuracy.\n\n### 6.1 Evaluation Procedure\n\nThe accuracy of the learned model can be quantified using two metrics: the precision and the recall. The precision is calculated as the proportion of words that are correctly recognized (true positives) in the learned model over all the words recognized by , while the recall represents the proportion of words that are correctly recognized in over all the words recognized by the initial model H. The precision and the recall can be combined in a single metric called F1 score. A high F1 score corresponds to a high precision and recall, and conversely.\n\nBased on these metrics, we distinguish four degrees of generalization for the learned models (see Fig. 5):\n\n 1. 1.\n\nThe maximum F1 score is obtained when the exact target language L(H) is learned.\n\n 2. 2.\n\nA precision of 1 and a recall strictly lower than 1 characterize an under-approximation, i.e., the learned model recognizes a subset of words of L(H).\n\n 3. 3.\n\nA recall of 1 and a precision strictly lower than 1 characterize an over-approximation, i.e., the learned model accepts all the words of L(H) in addition to extra words not in L(H).\n\n 4. 4.\n\nA precision and a recall strictly lower than 1 characterize a cross-approximation, i.e., contains only a subset of words in L(H) plus additional words not in L(H).\n\nFig. 5.\n\nDegrees of generalization of the learned language with respect to the target language L(H)\n\nOur experimental setup shown in Fig. 6, consists of three modules responsible for trace generation, model learning and model evaluation. Since we are trying to evaluate how accurate the learning algorithm is, the initial model H, designed as a , is only known by the trace generator and the model evaluator, while the model learner has to guess it. The trace generator produces a timed learning sample S and a test sample. The latter contains timed traces that do not appear in S. This sample is used to evaluate the learned model with respect to new traces that were not used during the learning phase.\n\nFig. 6.\n\nExperimental setup to validate the improved learning procedure\n\n### 6.2 Benchmarks\n\nWe run our experimental setup on three examples, namely, Periodic A, Periodic A-B and CSMA\/CD communication medium model.\n\nPeriodic A is a synthetic periodic task A that executes for 1 to 3 time units in a period of 5 time units. The goal of this benchmark is to check if the algorithm is able to learn the periodicity and the duration of a single task. Two less constrained variants of this model are also considered. In both of them, we remove the periodicity of the task by setting a predefined waiting time of 5 time units after the task A finishes. In the first variant, called aperiodic contiguous-time (ap_cont A), the execution time of the task A can take contiguous time values in [1; 3]. In the second one, called aperiodic disjoint (ap_dis A), the execution time takes the disjoint time values 0, 2 and 4. Our goal is to check if the algorithm is able to detect the unused time values 1 and 3.\n\nPeriodic A-B consists of two sequential tasks A and B, taking execution time values, respectively, in intervals [1;3] and [1;2] with a periodicity of 5 time units. In this example, the learning algorithm is faced with dependencies between clock constraints for the task A, the task B and their periodicities, which is a more complex setting.\n\nFig. 7.\n\nCSMA\/CD communication medium model for a 2-station network\n\nCSMA\/CD communication Medium Model is a media access control protocol for single-channel networks that solves data collision problems. We focus on the CSMA\/CD communication medium model for a 2-station network presented in [5]. Figure 7 represents the underlying CSMA\/CD communication medium model where represents the propagation time. We assume that is the maximum time elapsing between two consecutive events.\n\n### 6.3 Results\n\nExperiments have been done on the described examples using a learning sample of size 200 and a test sample of size 1000.\n\nThe Synthetic Examples. Table 1 summerizes the results for periodic A (and variants) and periodic A-B. Since all the learned models have a 100% recall, only the precision is discussed in the sequel. The obtained results show that the original RTI+ learns an over-approximating model with a poor precision for all the considered examples. In contrast, as shown by the F1 score, the exact model is learned using the unfolded APTA for periodic A and its variants. Both the constructive and the tightened-bound APTAs do not learn the exact periodic A model (although more accurate than RTI+). They actually fail to identify the periodicity of task A. For ap_cont A, the constructive and the tightened-bound APTAs learn the exact model. However, for ap_dis A, the constructive-bound approach learns the exact model, while the tightened-bound one returns a model with a low precision since it does not detect the unused time values 1 and 3.\n\nFor the periodic A-B example, none of the variants was able to learn an accurate model: the obtained precision is at most 2.27% (using the constructive-bound APTA). They all fail to capture dependencies over clock constraints. Nevertheless, the precision is still better than the original RTI+ (0.18%).\n\nTable 1.\n\nAccuracy results for the synthetic benchmarks with the four APTAs\n\nBenchmark | Periodic A | Ap_dis A | Ap_cont A | Periodic AB\n\n---|---|---|---|---\n\nGeneralized-bound | Precision | 11% | 0.8% | 0.6% | 0.18%\n\nRecall | 100% | 100% | 100% | 100%\n\nF1 score | 0.1982 | 0.0159 | 0.0119 | 0.0036\n\nUnfolded | Precision | 100% | 100% | 100% | 1.97%\n\nRecall | 100% | 100% | 100% | 100%\n\nF1 score | 1.0000 | 1.0000 | 1.0000 | 0.0386\n\nConstructive-bound | Precision | 16.4% | 100% | 100% | 2.27%\n\nRecall | 100% | 100% | 100% | 100%\n\nF1 score | 0.2818 | 1.0000 | 1.0000 | 0.0444\n\nTightened-bound | Precision | 16.9% | 3.01% | 100% | 2.18%\n\nRecall | 100% | 100% | 100% | 100%\n\nF1 score | 0.2891 | 0.0584 | 1.0000 | 0.0427\n\nFigure 8 shows the impact of bigger time periods in the periodic A example on the quality of the learned model (Fig. 8a) and the learning time (Fig. 8b). We observe that increasing the period makes it more difficult to learn accurate models; Increasing the period decreases the precision as shown in Fig. 8a and increases the learning time as shown in Fig. 8b. For instance, the original RTI+ with generalized-bound APTA is quite fast but its precision tends to zero. Using constructive and tightened-bound APTAs improves the precision with a similar learning time. Finally, relying on the unfolded APTA produces very precise models but induces an important learning time when the period exceeds 15 time units.\n\nFig. 8.\n\nImpact of varying the task A period on the precision\/the learning time\n\nThe CSMA\/CD Example. Table 2 summerizes the experiments done on CSMA\/CD. On the one hand, one can notice that RTI+, like in the previous cases, learns an over-approximating model with a poor precision (6.20%) but in a short time ( 6 s). Moreover, the generalized-bound APTA, initially having 2373 locations, is reduced to a final model with only 4 locations which represents a high reduction. On the other hand, the proposed APTAs produce significantly different models that cross-approximate the original CSMA\/CD. For instance, the tightened-bound APTA learns a very precise model (93.70%). However, the model is obtained in more than 8 hours and has 370 locations. Using the constructive-bound APTA gives a model with less precision (85.80%) in a lower execution time ( 3 h). Finally, the unfolded APTA gives a model with a 49.40% precision and a 96.70% recall, which corresponds to the best F1 score (0.6539). Furthermore, compared to constructive and tightened-bound APTAs, the learning time for the unfolded APTA is lower ( 9 min). Hence, we conclude that, for this example, the unfolded APTA provides a good tradeoff between accuracy and learning time.\n\nTable 2.\n\nExperimental results for CSMA\/CD using the four APTA models\n\nAPTA type | Precision | Recall | F1 score | Time | APTA size | DRTA size | Reduction\n\n---|---|---|---|---|---|---|---\n\nGeneralized | 6.20% | 100.00% | 0.1168 | 6 s | 2373 | 4 | 99.83%\n\nUnfolded | 49.40% | 96.70% | 0.6539 | 9 min | 3586 | 19 | 99.47%\n\nConstructive | 85.80% | 52.00% | 0.6475 | 3 h | 2652 | 207 | 92.19%\n\nTightened | 93.70% | 49.90% | 0.6512 | 8 h | 2373 | 370 | 84.41%\n\n## 7 Conclusion\n\nIn this work, we proposed different variants of the RTI+ algorithm for learning models with both stochastic and timed behaviors. We formally defined three APTA models with different levels of generalization and representation sizes. We validated our proposal by performing different experiments that showed that using the new APTA variants provides more accurate models regarding the time behaviors. However, we observed that a higher learning time is generally required, depending on the desired accuracy. In the future, we are planning to improve our algorithms to better handle models with dependencies over clock constraints such as in the periodic A-B example. We are investigating a new compatibility criterion that takes into account such dependencies and that is able to isolate empty time intervals.\n\nReferences\n\n1.\n\nAlur, R., Dill, D.L.: A theory of timed automata. Theoret. Comput. Sci. 126(2), 183\u2013235 (1994)MathSciNetCrossRef90010-8)MATH\n\n2.\n\nAngluin, D.: Learning regular sets from queries and counterexamples. Inf. Comput. 75(2), 87\u2013106 (1987)MathSciNetCrossRef90052-6)MATH\n\n3.\n\nCarrasco, R.C., Oncina, J.: Learning stochastic regular grammars by means of a state merging method. In: Carrasco, R.C., Oncina, J. (eds.) ICGI 1994. LNCS, vol. 862, pp. 139\u2013152. Springer, Heidelberg (1994). doi:10.\u200b1007\/\u200b3-540-58473-0_\u200b144 CrossRef\n\n4.\n\nDe la Higuera, C.: Grammatical Inference: Learning Automata and Grammars. Cambridge University Press, Cambridge (2010)CrossRefMATH\n\n5.\n\nKwiatkowska, M., Norman, G., Sproston, J., Wang, F.: Symbolic model checking for probabilistic timed automata. Inf. Comput. 205(7), 1027\u20131077 (2007)MathSciNetCrossRefMATH\n\n6.\n\nLegay, A., Delahaye, B., Bensalem, S.: Statistical model checking: an overview. In: Barringer, H., Falcone, Y., Finkbeiner, B., Havelund, K., Lee, I., Pace, G., Ro\u015fu, G., Sokolsky, O., Tillmann, N. (eds.) RV 2010. LNCS, vol. 6418, pp. 122\u2013135. Springer, Heidelberg (2010). doi:10.\u200b1007\/\u200b978-3-642-16612-9_\u200b11 CrossRef\n\n7.\n\nMaier, A., Vodencarevic, A., Niggemann, O., Just, R., Jaeger, M.: Anomaly detection in production plants using timed automata. In: 8th International Conference on Informatics in Control, Automation and Robotics. pp. 363\u2013369 (2011)\n\n8.\n\nMao, H., Chen, Y., Jaeger, M., Nielsen, T.D., Larsen, K.G., Nielsen, B.: Learning probabilistic automata for model checking. In: 2011 Eighth International Conference on Quantitative Evaluation of Systems (QEST), pp. 111\u2013120. IEEE (2011)\n\n9.\n\nMao, H., Chen, Y., Jaeger, M., Nielsen, T.D., Larsen, K.G., Nielsen, B.: Learning deterministic probabilistic automata from a model checking perspective. Mach. Learn. 105(2), 255\u2013299 (2016)MathSciNetCrossRef\n\n10.\n\nde Matos Pedro, A., Crocker, P.A., de Sousa, S.M.: Learning stochastic timed automata from sample executions. In: Margaria, T., Steffen, B. (eds.) ISoLA 2012. LNCS, vol. 7609, pp. 508\u2013523. Springer, Heidelberg (2012). doi:10.\u200b1007\/\u200b978-3-642-34026-0_\u200b38 CrossRef\n\n11.\n\nNouri, A., Bozga, M., Molnos, A., Legay, A., Bensalem, S.: ASTROLABE: a rigorous approach for system-level performance modeling and analysis. ACM Trans. Embed. Comput. Syst. 15(2), 31:1\u201331:26 (2016)CrossRef\n\n12.\n\nSen, K., Viswanathan, M., Agha, G.: Learning continuous time markov chains from sample executions. In: Proceedings of the First International Conference on The Quantitative Evaluation of Systems, pp. 146\u2013155. QEST 2004, IEEE Computer Society, Washington, DC (2004)\n\n13.\n\nVerwer, S.E., Eyraud, R., De La Higuera, C.: PAutomaC: a probabilistic automata and hidden markov models learning competition. Mach. Learn. 96(1\u20132), 129\u2013154 (2014)MathSciNetCrossRefMATH\n\n14.\n\nVerwer, S.E.: Efficient identification of timed automata: theory and practice. Ph.D. thesis, TU Delft, Delft University of Technology (2010)\n\nFootnotes\n\n1\n\nBy considering a sufficient number of observations [4].\n\n2\n\nFor further details, see: http:\/\/\u200bwww-verimag.\u200bimag.\u200bfr\/\u200b~nouri\/\u200bdrta-learning\/\u200bAppendice.\u200bpdf.\n\n3\n\nSince the timed words in S are generated independently.\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_14\n\n# Verifying Safety and Persistence Properties of Hybrid Systems Using Flowpipes and Continuous Invariants\n\nAndrew Sogokon1 , Paul B. Jackson2 and Taylor T. Johnson1\n\n(1)\n\nInstitute for Software Integrated Systems, Vanderbilt University, Nashville, Tennessee, USA\n\n(2)\n\nLaboratory for Foundations of Computer Science, University of Edinburgh, Edinburgh, Scotland, UK\n\nAndrew Sogokon (Corresponding author)\n\nEmail: andrew.sogokon@vanderbilt.edu\n\nPaul B. Jackson\n\nEmail: Paul.Jackson@ed.ac.uk\n\nTaylor T. Johnson\n\nEmail: taylor.johnson@vanderbilt.edu\n\nAbstract\n\nWe propose a method for verifying persistence of nonlinear hybrid systems. Given some system and an initial set of states, the method can guarantee that system trajectories always eventually evolve into some specified target subset of the states of one of the discrete modes of the system, and always remain within this target region. The method also computes a time-bound within which the target region is always reached. The approach combines flow-pipe computation with deductive reasoning about invariants and is more general than each technique alone. We illustrate the method with a case study concerning showing that potentially destructive stick-slip oscillations of an oil-well drill eventually die away for a certain choice of drill control parameters. The case study demonstrates how just using flow-pipes or just reasoning about invariants alone can be insufficient. The case study also nicely shows the richness of systems that the method can handle: the case study features a mode with non-polynomial (nonlinear) ODEs and we manage to prove the persistence property with the aid of an automatic prover specifically designed for handling transcendental functions.\n\nThis material is based upon work supported by the UK Engineering and Physical Sciences Research Council under grants EPSRC EP\/I010335\/1 and EP\/J001058\/1, the National Science Foundation (NSF) under grant numbers CNS 1464311 and CCF 1527398, the Air Force Research Laboratory (AFRL) through contract number FA8750-15-1-0105, and the Air Force Office of Scientific Research (AFOSR) under contract number FA9550-15-1-0258.\n\n## 1 Introduction\n\nHybrid systems combine discrete and continuous behaviour and provide a very general framework for modelling and analyzing the behaviour of systems such as those implemented in modern embedded control software. Although a number of tools and methods have been developed for verifying properties of hybrid systems, most are geared towards proving bounded-time safety properties, often employing set reachability computations based on constructing over-approximating enclosures of the reachable states of ordinary differential equations (e.g. [7, 13, 14, 21]). Methods capable of proving unbounded-time safety properties often rely (explicitly or otherwise) on constructing continuous invariants (e.g. [25, 42], and referred to in short as invariants). Such invariants may be thought of as a generalization of positively invariant sets (see e.g. [5]) and which are analogous to inductive invariants used in computer science to reason about the correctness of discrete programs using Hoare logic.\n\nWe argue in this paper that a combined approach employing bounded time reachability analysis and reasoning about invariants can be effective in proving persistence and safety properties in non-polynomial (nonlinear) hybrid systems. We illustrate the combined approach using a detailed case study with non-polynomial ODEs for which neither approach individually was sufficient to establish the desired safety and persistence properties.\n\nMethods for bounded time safety verification cannot in general be applied to prove safety for all time and their accuracy tends to degrade for large time bounds, especially for nonlinear systems. Verification using invariants, while a powerful technique that can prove strong properties about nonlinear systems, relies on the ability to find invariants that are sufficient for proving the unbounded time safety property. In practice, many invariants for the system can be found which fall short of this requirement, often for the simple reason that they do not include all the initial states of the system. We show how a combined approach employing both verification methods can, in some cases, address these limitations.\n\nContributions\n\nIn this paper we (I) show that bounded time safety verification based on flowpipe construction can be naturally combined with invariants to verify persistence and unbounded time safety properties, addressing some of the limitations of each verification method when considered in isolation. (II) To illustrate the approach, we consider a simplified torsional model of a conventional oil well drill string that has been the subject of numerous studies by Navarro-L\u00f3pez et al. [34]. (III) We discuss some of the challenges that currently stand in the way of fully automatic verification using this approach. Additionally, we provide a readable overview of the methods employed in the verification process and the obstacles that present themselves when these methods are applied in practice.\n\n## 2 Safety and Persistence for Hybrid Automata\n\n### 2.1 Preliminaries\n\nA number of formalisms exist for specifying hybrid systems. The most popular framework at present is that of hybrid automata [3, 19], which are essentially discrete transition systems in which each discrete state represents an operating mode inside which the system evolves continuously according to an ODE under some evolution constraint. Additionally, transition guards and reset maps are used to specify the discrete transition behaviour (i.e. switching) between the operating modes. A sketch of the syntax and semantics of hybrid automata is as follows.\n\nDefinition 1\n\n(Hybrid automation [26]). Formally, a hybrid automaton is given by where\n\n * is a finite set of discrete states (modes),\n\n * is a finite set of continuous variables,\n\n * gives the vector field defining continuous evolution inside each mode,\n\n * is the set of initial states,\n\n * gives the mode invariants constraining evolution for every discrete state,\n\n * is the transition relation,\n\n * gives the guard conditions for enabling transitions,\n\n * gives the reset map.\n\nA hybrid state of the automaton is of the form . A hybrid time trajectory is a sequence (which may be finite or infinite) of intervals , for which for all and for all i. If the sequence is finite, then either or . Intuitively, one may think of as the times at which discrete transitions occur. An execution (or a run or trajectory) of a hybrid automaton defined to be , where is a hybrid time trajectory, (where is defined to be the set if is finite and otherwise) and is a collection of diffeomorphisms such that , for all and . For all it is also required that transitions respect the guards and reset maps, i.e. , and .\n\nWe consider MTL1 formulas satisfied by trajectories. The satisfaction relation is of form , read as \"trajectory at position p satisfies temporal logic formula \", where positions on a trajectory are identified by pairs of form (i, t) where and time . We use the MTL modality which states that formula always holds in time interval I in the future. Formally, this can be defined as , where . Similarly we can define the modality which states that formula eventually holds at some time in the time interval I in the future. An MTL formula is valid for a given hybrid automaton if it is satisfied by all trajectories of that automaton starting at position (0, 0). For clarity when writing MTL formulas, we assume trajectories are not restricted to start in states and instead introduce predicates into the formulas when we want restrictions.\n\nAlternative formalisms for hybrid systems, such as hybrid programs [41], enjoy the property of having a compositional semantics and can be used to verify properties of systems by verifying properties of their parts in a theorem prover [15, 44]. Other formal modelling frameworks for hybrid systems, such as Hybrid CSP [24], have also found application in theorem provers [60, 62].\n\n### 2.2 Bounded Time Safety and Eventuality\n\nThe bounded-time safety verification problem (with some finite time bound ) is concerned with establishing that given an initial set of states and a set of safe states , the state of the system may not leave within time t along any valid trajectory of the system. In the absence of closed-form solutions to the ODEs, this property may be established by verified integration, i.e. by computing successive over-approximating enclosures (known as flowpipes) of the reachable states in discrete time steps. Bounded-time reachability analysis can be extended to full hybrid systems by also computing\/over-approximating the discrete reachable states (up to some finite bound on the number of discrete transitions).\n\nA number of bounded-time verification tools for hybrid systems have been developed based on verified integration using interval enclosures. For instance, iSAT-ODE, a verification tool for hybrid systems developed by Eggers et al. [13] relies on the verified integration tool VNODE-LP by Nedialkov [37] for computing the enclosures. Other examples include dReach, a reachability analysis tool for hybrid systems developed by Kong et al. [21], which uses the CAPD library [1]. Over-approximating enclosures can in practice be very precise for small time horizons, but tend to become conservative when the time bound is large (due to the so-called wrapping effect, which is a problem caused by the successive build-up of over-approximation errors that arises in interval-based methods; see e.g. [38]). An alternative verified integration method using Taylor models was introduced by Makino and Berz (see [4, 38]) and can address some of these drawbacks, often providing tighter enclosures of the reachable set. Implementations of the method have been reported in COSY INFINITY, a scientific computing tool by Makino and Berz [29]; VSPODE, a tool for computing validated solutions to parametric ODEs by Lin and Stadtherr [23]; and in Flow , a bounded-time verification for hybrid systems developed by Chen et al. [7].\n\nBecause flowpipes provide an over-approximation of the reachable states at a given time, verified integration using flowpipes can also be used to reason about liveness properties such as eventuality, i.e. when a system is guaranteed to eventually enter some target set having started off at some point in an initial set. The bounded-time safety and eventuality properties may be more concisely expressed by using MTL notation, i.e. by writing , and , where describes the initial set of states, is the set of safe states and is the target region which is to be eventually attained.\n\nRemark 2\n\nThe bounded time eventuality properties we consider in this paper are more restrictive than the general (unbounded time) case. For instance, consider a continuous 2-dimensional system governed by and confined to evolve in the region where . If one starts this system inside a state where , it will eventually evolve into a state where by following the solution, however one may not put a finite bound on the time for this to happen. Thus, while is true for this system the bounded time eventuality property will not hold for any finite .\n\n### 2.3 Unbounded Time Safety\n\nA safety property for unbounded time may be more concisely expressed using an MTL formula:\n\nA proof of such a safety assertion is most commonly achieved by finding an appropriate invariant, , which contains no unsafe states (i.e. ) and such that the state of the system may not escape from I into an unsafe state along any valid trajectory of the system. Invariance is a special kind of safety assertion and may be written as . A number of techniques have been developed for proving invariance properties for continuous systems without the need to compute solutions to the ODEs [17, 25, 41, 49, 53, 58].\n\n### 2.4 Combining Unbounded Time Safety with Eventuality to Prove Persistence\n\nIn linear temporal logic, a persistence property states that a formula is 'eventually always' true. For instance, using persistence one may express the property that a system starting in any initial state always eventually reaches some target set and then always stays within this set. Using MTL notation, we can write this as:\n\nPersistence properties generalize the concept of stability. With stability one is concerned with showing that the state of a system always converges to some particular equilibrium point. With persistence, one only requires that the system state eventually becomes always trapped within some set of states.\n\nIn this paper we are concerned with a slightly stronger form of persistence, where one ensures that the target set is always reached within some specified time t:\n\nWe observe that a way of proving this is to find a set such that:\n\n 1. 1.\n\n holds, and\n\n 2. 2.\n\nI is an invariant for the system.\n\nThis fact can be stated more formally as a rule of inference:\n\nPrevious Sects. 2.2 and 2.3 respectively surveyed how the eventuality premise and invariant premise can be established by a variety of automated techniques. In Sect. 5 we explore automation challenges further and remark on ongoing work addressing how to automatically generate suitable invariants I.\n\n### 2.5 Using Persistence to Prove Safety\n\nFinding appropriate invariants to prove unbounded time safety as explained above in Sect. 2.3 can in practice be very difficult. It might be the case that invariants for the system can be found, but also ensuring that is infeasible. Nevertheless it might be the case that one of these invariants I is always eventually reached by trajectories starting in and all those trajectories are contained within . In such cases, is indeed a safety property of the system when starting from any point in . More precisely, if one can find an invariant I as explained above in Sect. 2.4 to show the persistence property: , and further one can show for the same time bound t that: , then one has: . As a result, one may potentially utilize invariants that were by themselves insufficient for proving the safety property.\n\nRemark 3\n\nThe problem of showing that a state satisfying is reached in finite time t, while ensuring that the formula also holds (i.e. states satisfying are avoided up to time t) is sometimes called a reach-avoid problem [61].\n\nEven if one's goal is to establish bounded-time rather than unbounded-time safety properties, this inference scheme could still be of use, as it could significantly reduce the time bound t needed for bounded time reachability analysis. In practice, successive over-approximation of the reachable states using flowpipes tends to become conservative for large values of t. In highly non-linear systems one can realistically expect to compute flowpipes only for very modest time bounds (e.g. in chaotic systems flowpipes are guaranteed to 'blow up', but invariants may still sometimes be found). Instead, it may in some cases be possible to prove the safety property by computing flowpipes up to some small time bound, after which the system can be shown to be inside an invariant that implies the safety property for all times thereafter.\n\n## 3 An Example Persistence Verification Problem\n\nStick-slip oscillations are commonly encountered in mechanical engineering in the context of modelling the effects of dynamic friction. Informally, the phenomenon manifests itself in the system becoming \"stuck\" and \"unstuck\" repeatedly, which results in unsteady \"jerky\" motions. In engineering practice, stick-slip oscillations can often degrade performance and cause failures when operating expensive machinery [36]. Although the problem of demonstrating absence of stick-slip oscillations in a system is primarily motivated by safety considerations, it would be misleading to call this a safety verification problem. Instead, the problem may broadly be described as that of demonstrating that the system (in finite time) enters a state in which no stick-slip motion is possible and remains there indefinitely. Using MTL one may write:\n\nwhere describes the states in which harmful oscillations cannot occur. The formula may informally be read as saying that \"from any initial configuration, the system will eventually evolve within time t into a state region where it is always steady\".\n\nAs an example of a system in which eventual absence of stick-slip oscillations is important, we consider a well-studied [34] model of a simplified conventional oil well drill string. The system can be characterized in terms of the following variables: , the angular displacement of the top rotary system; , the angular displacement of the drilling bit; , the angular velocity of the top rotary system; and , the angular velocity of the drilling bit. The continuous state of the system can be described in terms of these variables, i.e. . The system has two control parameters: giving the weight applied on the drilling bit, and giving the surface motor torque. The dynamics is governed a non-linear system of ODEs , given by:\n\n(1)\n\n(2)\n\n(3)\n\nThe term denotes the friction modelling the bit-rock contact and is responsible for the non-polynomial non-linearity. It is given by\n\nwhere if and if . Constants used in the model [34] are as follows: , , , , , , , , , . Even though at first glance the system looks like a plain continuous system with a single set of differential equations, it is effectively a hybrid system with at least 3 modes, where the drilling bit is: \"rotating forward\" ( ), \"stopped\" ( ), and \"rotating backward\" ( ). A sub-mode of the stopped mode models when the drill bit is stuck. In this sub-mode, the torque components on the drill bit due to , and are insufficient to overcome the static friction , and is further constrained so as to ensure .\n\nOnce the drill is in operation, so-called stick-slip oscillations can cause damage when the bit repeatedly becomes stuck and unstuck due to friction in the bottom hole assembly. In the model this behaviour would correspond to the system entering a state where repeatedly. The objective is to verify the eventual absence of stick-slip oscillations in the system initialised at the origin (i.e. at rest) for some given choice of the control parameters and u. Previous work by Navarro-L\u00f3pez and Carter [34] explored modelling the simplified model of the drill as a hybrid automaton and simulated the resulting models in Stateflow and Modelica.\n\nFig. 1.\n\nSimulations can exhibit stabilization with positive bit angular velocity and stick-slip bit motion.\n\nSimulations, such as those obtained in [34], using different models and control parameters for the drill can suggest stick-slip oscillations or their absence (illustrated in Fig. 1) in a particular model, however the task of verifying their eventual absence cannot be adequately addressed with simulation alone. In practice however, simulation is incredibly useful in providing some degree of confidence in the overall result, which is very important to know before attempting verification.\n\nA simulation of the system with a concrete choice for the control parameters and , shown as a trajectory in the 3-dimensional state space in Fig. 3a, suggests that the system does not exhibit stick-slip oscillations, because the trajectory is observed to start at the origin, escape the surface ( )2 and stabilize around a point where the angular velocity of the drilling bit is positive ( ).\n\n## 4 Verifying Persistence\n\nThe property of interest, i.e. the eventual absence of stick-slip oscillation that we observe in the simulation, may be phrased as the following formula in metric temporal logic: which informally asserts that the system initialised at the origin will eventually (diamond modality) enter a state where it is always (box modality) the case that . In the following sections we describe a method for proving this assertion. Following our approach, we break the problem down into the following two sub-problems:\n\n 1. 1.\n\nFinding an appropriate invariant I in which the property holds. For this we employ continuous\/positive invariants, discussed in the next section.\n\n 2. 2.\n\nProving that the system reaches a state in the set I in finite time when initialised at the origin, i.e. .3\n\n### 4.1 Continuous Invariant\n\nFinding continuous invariants that are sufficient to guarantee a given property is in practice remarkably difficult. Methods for automatic continuous invariant generation have been reported by numerous authors [16, 18, 25, 30, 49, 52\u201354, 59, 63], but in practice often result in \"coarse\" invariants that cannot be used to prove the property of interest, or require an unreasonable amount of time due to their reliance on expensive real quantifier elimination algorithms.\n\nStability analysis (involving a linearisation; see [56] for details) can be used to suggest a polynomial function , given by\n\nfor which we can reasonably conjecture that defines a positively invariant set under the flow of our non-linear system. Geometrically, this represents an ellipsoid that lies above the surface defined by in the state space (see Fig. 3b). In order to prove the invariance property, it is sufficient to show that the following holds:4\n\n(4)\n\nUnfortunately, in the presence of non-polynomial terms5 a first order sentence will in general not belong to a decidable theory [51], although there has recently been progress in broadening the scope of the popular CAD algorithm [9] for real quantifier elimination to work with restricted classes of non-polynomial problems [57].\n\nIn practice, this conjecture is easily proved in under 5 s using MetiTarski, an automatic theorem prover, developed by L.C. Paulson and co-workers at the University of Cambridge, designed specifically for proving universally quantified first order conjectures featuring transcendental functions (such as , etc). The interested reader may find more details about the MetiTarski system in [2, 40].\n\nRemark 4\n\nAlthough Wolfram's Mathematica 10 computer algebra system also provides some functionality for proving first-order conjectures featuring non-polynomial expressions using its Reduce[] function, we were unable (on our system6) to prove conjecture (4) this way after over an hour of computation, after which the Mathematica kernel crashed.\n\nThe automatic proof of conjecture (4) obtained using MetiTarski (provided we trust the system) establishes that defines a positively invariant set, and thus we are guaranteed that solutions initialised inside this set remain there at all future times. In order to be certain that no outgoing discrete transitions of the hybrid system are possible when the system is evolving inside , we further require a proof of the following conjecture featuring only polynomial terms:\n\n(5)\n\nAn automatic proof of this conjecture may be obtained using an implementation of a decision procedure for first-order real arithmetic.\n\n### 4.2 Verified Integration\n\nIn order to show that the system does indeed enter the positively invariant ellipsoid in finite time, it is not sufficient to observe this in a simulation (as in Fig. 3b), which is why we use a tool employing verified integration based on Taylor models. Flow (implemented by Chen et al. [7]) is a bounded-time safety verification tool for hybrid systems that computes Taylor models to analyze continuous reachability. The tool works by computing successive over-approximations (flowpipes) of the reachable set of the system, which are internally represented using Taylor models (but which may in turn be over-approximated by a bounding hyper-box and easily rendered).\n\nFig. 2.\n\nVerified integration using Flow .\n\nFigure 2a shows the bounding boxes of solution enclosures computed from the point initial condition at the origin using Flow with adaptive time steps and Taylor models of order 13, a time bound of 12.7 and the same control parameters used in the simulation (i.e. , ). We observe that once solutions escape to the region where , they maintain a positive component for the duration of the time bound.\n\nThe last flowpipe computed by Flow for this problem can be bounded inside the hyper-rectangle characterized by the formula\n\nOnce more, using a decision procedure for real arithmetic, we can check that the following sentence is true:\n\nIf we are able to establish the following facts:\n\n 1. 1.\n\n (I is a continuous invariant),\n\n 2. 2.\n\n (inside I, there are no harmful oscillations), and\n\n 3. 3.\n\n (the system enters the region I in finite time),\n\nthen we can conclude that is also true and the system does not exhibit harmful stick-slip oscillations when started inside . By taking to be the origin , I to be the positively invariant sub-level set and to be , we are able to conclude the temporal property:\n\nVerified integration using Taylor models also allows us to consider sets of possible initial conditions, rather than initial points (illustrated in Fig. 2b). This is useful when there is uncertainty about the system's initial configuration; however, in practice this comes with a significant performance overhead for verified integration.\n\nFig. 3.\n\nSimulation of the hybrid system initialised at the origin with N and Nm. The trajectory is contained by the flowpipes shown in Fig. 2a and is observed to enter the positively invariant ellipsoid , illustrating the persistence property of eventual absence of stick-slip oscillations.\n\n## 5 Outlook and Challenges to Automation\n\nCorrectness of reachability analysis tools based on verified integration is a soundness critical to the overall verification approach, which makes for a strong case in favour of using formally verified implementations. At present few are available, e.g. see recent work by Immler [20] which presented a formally verified continuous reachability algorithm based on adaptive Runge-Kutta methods. Verified implementations of Taylor model-based reachability analysis algorithms for continuous and hybrid systems would clearly be very valuable. One alternative to over-approximating reachable sets of continuous systems using flowpipes is based on simulating the system using a finite set of sampling trajectories and employs sensitivity analysis to address the coverage problem. This technique was explored by Donz\u00e9 and Maler in [10]. A similar approach employing matrix measures has more recently been studied by Maidens and Arcak [27, 28].\n\nAs an alternative to using verified integration, a number of deductive methods are available for proving eventuality properties in continuous and hybrid systems (e.g. [42, 55]). These approaches can be much more powerful since they allow one to work with more general classes of initial and target regions that are necessarily out of scope for methods based on verified integration (e.g. they can work with initial sets that are unbounded, disconnected, etc.) Making effective use of the deductive verification tools currently in existence typically requires significant input and expertise on part of the user (finding the right invariants being one of the major stumbling blocks in practice), in stark contrast to the near-complete level of automation offered by tools based on verified integration. Methods for automatic continuous invariant generation are crucial to the mechanization of the overall verification approach. Progress on this problem would be hugely enabling for non-experts and specialists alike, as it would relieve them from the task of manually constructing appropriate invariants, which often requires intuition and expertise. Work in this area is ongoing (see e.g. [25, 43, 54]). Indeed, progress on this problem is also crucial to providing a greater level of automation in deductive verification tools.\n\n## 6 Related Work\n\nCombining elements of qualitative and quantitative reasoning7 to study the behaviour of dynamical systems has previously been explored in the case of planar systems by Nishida et al. [39]. The idea of combining bounded-time reachability analysis with qualitative analysis in the form of discrete abstraction was investigated by Clarke et al. in [8]. Similar ideas are employed by Carter [6] and Navarro-L\u00f3pez in [35], where the concept of deadness is introduced and used as a way of disproving liveness properties. Intuitively, deadness is a formalization of an idea that inside certain regions the system cannot be live, i.e. some desired property may never become true as the system evolves inside a \"deadness region\". These ideas were used in a case study [6, Chap. 5] also featuring the drill system studied in [34], but with a different set of control parameters and in which the verification objective was to prove the existence of a single trajectory for which the drill eventually gets \"stuck\", which is sufficient to disprove the liveness (oscillation) property.\n\nRegion stability is similar to our notion of persistence [45], which requires all trajectories to eventually reach some region of the state space. Sound and complete proof rules for establishing region stability have been explored and automated [47], as have more efficient encodings of the proof rule that scale better in dimensionality [31]. However, all algorithms we are aware of for checking region stability require linear or simpler (timed or rectangular) ODEs [11, 31, 45\u201348]. Strong attractors are basins of attraction where every state in the state space eventually reaches a region of the state space [45]. Some algorithms do not check region stability, but actually check stronger properties such as strong attraction, that imply region stability [45]. In contrast to these works, our method checks the weaker notion of persistence for nonlinear ODEs.\n\nShe and Ratschan studied methods of proving set eventuality in continuous systems under constraints using Lyapunov-like functions [50]. Duggirala and Mitra also employed Lyapunov-like function concepts to prove inevitability properties in hybrid systems [12]. M\u00f6hlmann et al. developed Stabhyil [33], which can be applied to nonlinear hybrid systems and checks classical notions of Lyapunov stability, which is a strictly stronger property than persistence. In [32] M\u00f6hlmann et al. extended their work and applied similar ideas, using information about (necessarily invariant) sub-level sets of Lyapunov functions to terminate reachability analysis used for safety verification. Prabhakar and Soto have explored abstractions that enable proving stability properties without having to search for Lyapunov functions, albeit these are not currently applicable to nonlinear systems [48]. In summary, in contrast to other works listed above, our approach enables proving persistence properties in conjunction with safety properties for nonlinear, non-polynomial hybrid systems and does not put restrictions on the form or the type of the invariant used in conjunction with bounded time reachability analysis.\n\n## 7 Conclusion\n\nThis paper explored a combined technique for safety and persistence verification employing continuous invariants and reachable set computation based on constructing flowpipes. The approach was illustrated on a model of a simplified oil well drill string system studied by Navarro-L\u00f3pez et al., where the verification objective is to prove absence of damaging stick-slip oscillations. The system was useful in highlighting many of the existing practical challenges to applying and automating the proposed verification method. Many competing approaches already exist for verifying safety in hybrid systems, but these rarely combine different methods for reachability analysis and deductive verification, which our approach combines. We demonstrate that a combination of different approaches can be more practically useful than each constituent approach taken in isolation.\n\nAcknowledgements\n\nThe authors wish to thank to the anonymous reviewers for their careful reading and valuable suggestions for improving this paper.\n\nReferences\n\n1.\n\nCAPD library. http:\/\/\u200bcapd.\u200bii.\u200buj.\u200bedu.\u200bpl\/\u200b\n\n2.\n\nAkbarpour, B., Paulson, L.C.: MetiTarski: an automatic theorem prover for real-valued special functions. J. Autom. Reason. 44(3), 175\u2013205 (2010)MathSciNetCrossRefMATH\n\n3.\n\nAlur, R., Courcoubetis, C., Henzinger, T.A., Ho, P.-H.: Hybrid automata: an algorithmic approach to the specification and verification of hybrid systems. In: Grossman, R.L., Nerode, A., Ravn, A.P., Rischel, H. (eds.) HS 1991\u20131992. LNCS, vol. 736, pp. 209\u2013229. Springer, Heidelberg (1993). doi:10.\u200b1007\/\u200b3-540-57318-6_\u200b30 CrossRef\n\n4.\n\nBerz, M., Makino, K.: Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models. Reliab. Comput. 4(4), 361\u2013369 (1998)MathSciNetCrossRefMATH\n\n5.\n\nBlanchini, F.: Set invariance in control. Automatica 35(11), 1747\u20131767 (1999)MathSciNetCrossRef00113-2)MATH\n\n6.\n\nCarter, R.A.: Verification of liveness properties on hybrid dynamical systems. Ph.D. thesis, University of Manchester, School of Computer Science (2013)\n\n7.\n\nChen, X., \u00c1brah\u00e1m, E., Sankaranarayanan, S.: Flow*: an analyzer for non-linear hybrid systems. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 258\u2013263. Springer, Heidelberg (2013). doi:10.\u200b1007\/\u200b978-3-642-39799-8_\u200b18 CrossRef\n\n8.\n\nClarke, E.M., Fehnker, A., Han, Z., Krogh, B.H., Ouaknine, J., Stursberg, O., Theobald, M.: Abstraction and counterexample-guided refinement in model checking of hybrid systems. Int. J. Found. Comput. Sci. 14(4), 583\u2013604 (2003)MathSciNetCrossRefMATH\n\n9.\n\nCollins, G.E.: Quantifier elimination for real closed fields by cylindrical algebraic decompostion. In: Brakhage, H. (ed.) GI-Fachtagung 1975. LNCS, vol. 33, pp. 134\u2013183. Springer, Heidelberg (1975). doi:10.\u200b1007\/\u200b3-540-07407-4_\u200b17 CrossRef\n\n10.\n\nDonz\u00e9, A., Maler, O.: Systematic simulation using sensitivity analysis. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 174\u2013189. Springer, Heidelberg (2007). doi:10.\u200b1007\/\u200b978-3-540-71493-4_\u200b16 CrossRef\n\n11.\n\nDuggirala, P.S., Mitra, S.: Abstraction refinement for stability. In: Proceedings of 2011 IEEE\/ACM International Conference on Cyber-Physical Systems, ICCPS, pp. 22\u201331, April 2011\n\n12.\n\nDuggirala, P.S., Mitra, S.: Lyapunov abstractions for inevitability of hybrid systems. In: HSCC, pp. 115\u2013124. ACM, New York (2012)\n\n13.\n\nEggers, A., Ramdani, N., Nedialkov, N.S., Fr\u00e4nzle, M.: Improving the SAT modulo ODE approach to hybrid systems analysis by combining different enclosure methods. Softw. Syst. Model. 14(1), 121\u2013148 (2015)CrossRefMATH\n\n14.\n\nFrehse, G., Guernic, C., Donz\u00e9, A., Cotton, S., Ray, R., Lebeltel, O., Ripado, R., Girard, A., Dang, T., Maler, O.: SpaceEx: scalable verification of hybrid systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 379\u2013395. Springer, Heidelberg (2011). doi:10.\u200b1007\/\u200b978-3-642-22110-1_\u200b30 CrossRef\n\n15.\n\nFulton, N., Mitsch, S., Quesel, J.-D., V\u00f6lp, M., Platzer, A.: KeYmaera X: an axiomatic tactical theorem prover for hybrid systems. In: Felty, A.P., Middeldorp, A. (eds.) CADE 2015. LNCS (LNAI), vol. 9195, pp. 527\u2013538. Springer, Cham (2015). doi:10.\u200b1007\/\u200b978-3-319-21401-6_\u200b36 CrossRef\n\n16.\n\nGhorbal, K., Platzer, A.: Characterizing algebraic invariants by differential radical invariants. In: \u00c1brah\u00e1m, E., Havelund, K. (eds.) TACAS 2014. LNCS, vol. 8413, pp. 279\u2013294. Springer, Heidelberg (2014). doi:10.\u200b1007\/\u200b978-3-642-54862-8_\u200b19 CrossRef\n\n17.\n\nGhorbal, K., Sogokon, A., Platzer, A.: A hierarchy of proof rules for checking differential invariance of algebraic sets. In: D'Souza, D., Lal, A., Larsen, K.G. (eds.) VMCAI 2015. LNCS, vol. 8931, pp. 431\u2013448. Springer, Heidelberg (2015). doi:10.\u200b1007\/\u200b978-3-662-46081-8_\u200b24\n\n18.\n\nGulwani, S., Tiwari, A.: Constraint-based approach for analysis of hybrid systems. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 190\u2013203. Springer, Heidelberg (2008). doi:10.\u200b1007\/\u200b978-3-540-70545-1_\u200b18 CrossRef\n\n19.\n\nHenzinger, T.A.: The Theory of Hybrid Automata, pp. 278\u2013292. IEEE Computer Society Press, Washington, DC (1996)\n\n20.\n\nImmler, F.: Verified reachability analysis of continuous systems. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 37\u201351. Springer, Heidelberg (2015). doi:10.\u200b1007\/\u200b978-3-662-46681-0_\u200b3\n\n21.\n\nKong, S., Gao, S., Chen, W., Clarke, E.: dReach: -reachability analysis for hybrid systems. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 200\u2013205. Springer, Heidelberg (2015). doi:10.\u200b1007\/\u200b978-3-662-46681-0_\u200b15\n\n22.\n\nKoymans, R.: Specifying real-time properties with metric temporal logic. Real-Time Syst. 2(4), 255\u2013299 (1990)CrossRef\n\n23.\n\nLin, Y., Stadtherr, M.A.: Validated solutions of initial value problems for parametric ODEs. Appl. Numer. Math. 57(10), 1145\u20131162 (2007)MathSciNetCrossRefMATH\n\n24.\n\nLiu, J., Lv, J., Quan, Z., Zhan, N., Zhao, H., Zhou, C., Zou, L.: A calculus for hybrid CSP. In: Ueda, K. (ed.) APLAS 2010. LNCS, vol. 6461, pp. 1\u201315. Springer, Heidelberg (2010). doi:10.\u200b1007\/\u200b978-3-642-17164-2_\u200b1 CrossRef\n\n25.\n\nLiu, J., Zhan, N., Zhao, H.: Computing semi-algebraic invariants for polynomial dynamical systems. In: EMSOFT, pp. 97\u2013106. ACM (2011)\n\n26.\n\nLygeros, J., Johansson, K.H., Simi\u0107, S.N., Zhang, J., Sastry, S.S.: Dynamical properties of hybrid automata. IEEE Trans. Autom. Control 48(1), 2\u201317 (2003)MathSciNetCrossRef\n\n27.\n\nMaidens, J.N., Arcak, M.: Reachability analysis of nonlinear systems using matrix measures. IEEE Trans. Autom. Control 60(1), 265\u2013270 (2015)MathSciNetCrossRef\n\n28.\n\nMaidens, J.N., Arcak, M.: Trajectory-based reachability analysis of switched nonlinear systems using matrix measures. In: CDC, pp. 6358\u20136364, December 2014\n\n29.\n\nMakino, K., Berz, M.: Cosy infinity version 9. Nucl. Instrum. Methods Phys. Res., Sect. A 558(1), 346\u2013350 (2006)CrossRef\n\n30.\n\nMatringe, N., Moura, A.V., Rebiha, R.: Generating invariants for non-linear hybrid systems by linear algebraic methods. In: Cousot, R., Martel, M. (eds.) SAS 2010. LNCS, vol. 6337, pp. 373\u2013389. Springer, Heidelberg (2010). doi:10.\u200b1007\/\u200b978-3-642-15769-1_\u200b23 CrossRef\n\n31.\n\nMitrohin, C., Podelski, A.: Composing stability proofs for hybrid systems. In: Fahrenberg, U., Tripakis, S. (eds.) FORMATS 2011. LNCS, vol. 6919, pp. 286\u2013300. Springer, Heidelberg (2011). doi:10.\u200b1007\/\u200b978-3-642-24310-3_\u200b20 CrossRef\n\n32.\n\nM\u00f6hlmann, E., Hagemann, W., Theel, O.: Hybrid tools for hybrid systems \u2013 proving stability and safety at once. In: Sankaranarayanan, S., Vicario, E. (eds.) FORMATS 2015. LNCS, vol. 9268, pp. 222\u2013239. Springer, Cham (2015). doi:10.\u200b1007\/\u200b978-3-319-22975-1_\u200b15 CrossRef\n\n33.\n\nM\u00f6hlmann, E., Theel, O.: Stabhyli: a tool for automatic stability verification of non-linear hybrid systems. In: HSCC, pp. 107\u2013112. ACM (2013)\n\n34.\n\nNavarro-L\u00f3pez, E.M., Carter, R.: Hybrid automata: an insight into the discrete abstraction of discontinuous systems. Int. J. Syst. Sci. 42(11), 1883\u20131898 (2011)MathSciNetCrossRefMATH\n\n35.\n\nNavarro-L\u00f3pez, E.M., Carter, R.: Deadness and how to disprove liveness in hybrid dynamical systems. Theor. Comput. Sci. 642(C), 1\u201323 (2016)MathSciNetCrossRefMATH\n\n36.\n\nNavarro-L\u00f3pez, E.M., Su\u00e1rez, R.: Practical approach to modelling and controlling stick-slip oscillations in oilwell drillstrings. In: Proceedings of the 2004 IEEE International Conference on Control Applications, vol. 2, pp. 1454\u20131460. IEEE (2004)\n\n37.\n\nNedialkov, N.S.: Interval tools for ODEs and DAEs. In: SCAN (2006)\n\n38.\n\nNeher, M., Jackson, K.R., Nedialkov, N.S.: On Taylor model based integration of ODEs. SIAM J. Numer. Anal. 45(1), 236\u2013262 (2007)MathSciNetCrossRefMATH\n\n39.\n\nNishida, T., Mizutani, K., Kubota, A., Doshita, S.: Automated phase portrait analysis by integrating qualitative and quantitative analysis. In: Proceedings of the 9th National Conference on Artificial Intelligence, pp. 811\u2013816 (1991)\n\n40.\n\nPaulson, L.C.: MetiTarski: past and future. In: Beringer, L., Felty, A. (eds.) ITP 2012. LNCS, vol. 7406, pp. 1\u201310. Springer, Heidelberg (2012). doi:10.\u200b1007\/\u200b978-3-642-32347-8_\u200b1 CrossRef\n\n41.\n\nPlatzer, A.: Differential dynamic logic for hybrid systems. J. Autom. Reason. 41(2), 143\u2013189 (2008)MathSciNetCrossRefMATH\n\n42.\n\nPlatzer, A.: Differential-algebraic dynamic logic for differential-algebraic programs. J. Log. Comput. 20(1), 309\u2013352 (2010)MathSciNetCrossRefMATH\n\n43.\n\nPlatzer, A., Clarke, E.M.: Computing differential invariants of hybrid systems as fixedpoints. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 176\u2013189. Springer, Heidelberg (2008). doi:10.\u200b1007\/\u200b978-3-540-70545-1_\u200b17 CrossRef\n\n44.\n\nPlatzer, A., Quesel, J.-D.: KeYmaera: a hybrid theorem prover for hybrid systems (system description). In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 171\u2013178. Springer, Heidelberg (2008). doi:10.\u200b1007\/\u200b978-3-540-71070-7_\u200b15 CrossRef\n\n45.\n\nPodelski, A., Wagner, S.: Model checking of hybrid systems: from reachability towards stability. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 507\u2013521. Springer, Heidelberg (2006). doi:10.\u200b1007\/\u200b11730637_\u200b38 CrossRef\n\n46.\n\nPodelski, A., Wagner, S.: Region stability proofs for hybrid systems. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 320\u2013335. Springer, Heidelberg (2007). doi:10.\u200b1007\/\u200b978-3-540-75454-1_\u200b23 CrossRef\n\n47.\n\nPodelski, A., Wagner, S.: A sound and complete proof rule for region stability of hybrid systems. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 750\u2013753. Springer, Heidelberg (2007). doi:10.\u200b1007\/\u200b978-3-540-71493-4_\u200b76 CrossRef\n\n48.\n\nPrabhakar, P., Garcia Soto, M.: Abstraction based model-checking of stability of hybrid systems. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 280\u2013295. Springer, Heidelberg (2013). doi:10.\u200b1007\/\u200b978-3-642-39799-8_\u200b20 CrossRef\n\n49.\n\nPrajna, S., Jadbabaie, A.: Safety verification of hybrid systems using barrier certificates. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 477\u2013492. Springer, Heidelberg (2004). doi:10.\u200b1007\/\u200b978-3-540-24743-2_\u200b32 CrossRef\n\n50.\n\nRatschan, S., She, Z.: Providing a basin of attraction to a target region of polynomial systems by computation of Lyapunov-like functions. SIAM J. Control Optim. 48(7), 4377\u20134394 (2010)MathSciNetCrossRefMATH\n\n51.\n\nRichardson, D.: Some undecidable problems involving elementary functions of a real variable. J. Symb. Logic 33(4), 514\u2013520 (1968)MathSciNetCrossRefMATH\n\n52.\n\nSankaranarayanan, S.: Automatic invariant generation for hybrid systems using ideal fixed points. In: HSCC, pp. 221\u2013230 (2010)\n\n53.\n\nSankaranarayanan, S., Sipma, H.B., Manna, Z.: Constructing invariants for hybrid systems. FMSD 32(1), 25\u201355 (2008)MATH\n\n54.\n\nSogokon, A., Ghorbal, K., Jackson, P.B., Platzer, A.: A method for invariant generation for polynomial continuous systems. In: Jobstmann, B., Leino, K.R.M. (eds.) VMCAI 2016. LNCS, vol. 9583, pp. 268\u2013288. Springer, Heidelberg (2016). doi:10.\u200b1007\/\u200b978-3-662-49122-5_\u200b13 CrossRef\n\n55.\n\nSogokon, A., Jackson, P.B.: Direct formal verification of liveness properties in continuous and hybrid dynamical systems. In: Bj\u00f8rner, N., de Boer, F. (eds.) FM 2015. LNCS, vol. 9109, pp. 514\u2013531. Springer, Cham (2015). doi:10.\u200b1007\/\u200b978-3-319-19249-9_\u200b32 CrossRef\n\n56.\n\nSogokon, A., Jackson, P.B., Johnson, T.T.: Verifying safety and persistence properties of hybrid systems using flowpipes and continuous invariants. Technical report, Vanderbilt University (2017)\n\n57.\n\nStrzebo\u0144ski, A.W.: Cylindrical decomposition for systems transcendental in the first variable. J. Symb. Comput. 46(11), 1284\u20131290 (2011)MathSciNetCrossRefMATH\n\n58.\n\nTaly, A., Tiwari, A.: Deductive verification of continuous dynamical systems. In: Kannan, R., Kumar, K.N. (eds.) FSTTCS. LIPIcs, vol. 4, pp. 383\u2013394. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik, Wadern (2009)\n\n59.\n\nTiwari, A.: Generating box invariants. In: Egerstedt, M., Mishra, B. (eds.) HSCC 2008. LNCS, vol. 4981, pp. 658\u2013661. Springer, Heidelberg (2008). doi:10.\u200b1007\/\u200b978-3-540-78929-1_\u200b58 CrossRef\n\n60.\n\nWang, S., Zhan, N., Zou, L.: An improved HHL prover: an interactive theorem prover for hybrid systems. In: Butler, M., Conchon, S., Za\u00efdi, F. (eds.) ICFEM 2015. LNCS, vol. 9407, pp. 382\u2013399. Springer, Cham (2015). doi:10.\u200b1007\/\u200b978-3-319-25423-4_\u200b25 CrossRef\n\n61.\n\nXue, B., Easwaran, A., Cho, N.J., Fr\u00e4nzle, M.: Reach-avoid verification for nonlinear systems based on boundary analysis. IEEE Trans. Autom. Control (2016)\n\n62.\n\nZhao, H., Yang, M., Zhan, N., Gu, B., Zou, L., Chen, Y.: Formal verification of a descent guidance control program of a lunar lander. In: Jones, C., Pihlajasaari, P., Sun, J. (eds.) FM 2014. LNCS, vol. 8442, pp. 733\u2013748. Springer, Cham (2014). doi:10.\u200b1007\/\u200b978-3-319-06410-9_\u200b49 CrossRef\n\n63.\n\nZhao, H., Zhan, N., Kapur, D.: Synthesizing switching controllers for hybrid systems by generating invariants. In: Liu, Z., Woodcock, J., Zhu, H. (eds.) Theories of Programming and Formal Methods. LNCS, vol. 8051, pp. 354\u2013373. Springer, Heidelberg (2013). doi:10.\u200b1007\/\u200b978-3-642-39698-4_\u200b22 CrossRef\n\nFootnotes\n\n1\n\nMetric Temporal Logic; see e.g. [22].\n\n2\n\nThe system exhibits sliding behaviour on a portion of this surface known as the sliding set. See [34].\n\n3\n\nFiles for the case study are available online. http:\/\/\u200bwww.\u200bverivital.\u200bcom\/\u200bnfm2017.\n\n4\n\nHere denotes the gradient of V, i.e. the vector of partial derivatives .\n\n5\n\nE.g. those featured in the right-hand side of the ODE, i.e. .\n\n6\n\nIntel i5-2520M CPU @ 2.50 GHz, 4 GB RAM, running Arch Linux kernel 4.2.5-1.\n\n7\n\nE.g. numerical solution computation with \"qualitative\" features, such as invariance of certain regions.\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_15\n\n# A Relational Shape Abstract Domain\n\nHugo Illous1, 2 , Matthieu Lemerre1 and Xavier Rival2\n\n(1)\n\nCEA, LIST, Software Reliability and Security Laboratory, P.C. 174, 91191 Gif-sur-Yvette, France\n\n(2)\n\nInria Paris\/CNRS\/\u00c9cole Normale Sup\u00e9rieure\/PSL Research University, Paris, France\n\nHugo Illous (Corresponding author)\n\nEmail: hugo.illous@cea.fr\n\nMatthieu Lemerre\n\nEmail: matthieu.lemerre@cea.fr\n\nXavier Rival\n\nEmail: xavier.rival@ens.fr\n\nAbstract\n\nStatic analyses aim at inferring semantic properties of programs. While many analyses compute an over-approximation of reachable states, some analyses compute a description of the input-output relations of programs. In the case of numeric programs, several analyses have been proposed that utilize relational numerical abstract domains to describe relations. On the other hand, designing abstractions for relations over memory states and taking shapes into account is challenging. In this paper, we propose a set of novel logical connectives to describe such relations, which are inspired by separation logic. This logic can express that certain memory areas are unchanged, freshly allocated, or freed, or that only part of the memory was modified. Using these connectives, we build an abstract domain and design a static analysis that over-approximates relations over memory states containing inductive structures. We implement this analysis and report on the analysis of a basic library of list manipulating functions.\n\n## 1 Introduction\n\nGenerally, static analyses aim at computing semantic properties of programs. Two common families of analyses are reachability analyses, that compute an over-approximation for the set of reachable states of programs, and relational analyses, that compute an over-approximation for the relations between input and output states. In general, sets of states are easier to abstract than state relations, which often makes reachability analyses simpler to design. On the other hand, abstracting relations brings several advantages:\n\n * First, state relations allow to make the analyses modular [3, 6, 10, 17, 22] and compositional. Indeed, to analyze a sequence of two sub-programs, relational analyses can simply analyze each sub-program separately, and compose the resulting state relations. When sub-programs are functions, relational analyses may analyze each function separately, and compute one summary per function, so that the analysis of a function call does not require re-analyzing the body of the function, which is an advantage for scalability.\n\n * Second, some properties can be expressed on state relations but not on sets of states, which makes relational analyses intrinsically more expressive. For example, contract languages [1, 21] let functions be specified by formulas that may refer both to the input and to the output states. Such properties cannot be expressed using abstractions of sets of states, thus are beyond the scope of reachability analyses.\n\nIn general, the increased expressiveness of relational analyses requires more expressive abstractions. Let us discuss, as an example the case of numeric programs. A common way to express relations between input and output states consists in defining for each variable a primed version that describes the value of in the output state whereas the non primed version denotes the value of in the input state. In this context, non-relational numerical abstract domain such as intervals [8] cannot capture any interesting relation between input and output states. On the other hand, relational numerical abstract domains such as convex polyhedra [7] can effectively capture relations between input and output states, as shown in [22]: for instance, when applied to a program that increments by one, this analysis can infer the relation .\n\nIn the context of programs manipulating complex data structures, relational analysis could allow to compute interesting classes of program properties. For instance, such analyses could express and verify that some memory areas were not physically modified by a program. Reachability analyses such as [5, 15, 24] cannot distinguish a program that inputs a list and leaves it unmodified from a program that inputs a list, copies it into an identical version and deallocates it, whereas a relational analysis could. More generally, it is often interesting to infer that a memory region is not modified by a program.\n\nSeparation logic [23] provides an elegant description for sets of states and is at the foundation of many reachability analyses for heap properties. In particular, the separating conjunction connective expresses that two regions are disjoint and allows local reasoning. On the other hand, it cannot describe state relations.\n\nIn this paper, we propose a logic inspired by separation logics and that can describe such properties. It provides connectives to describe that a memory region has been left unmodified by a program fragment, or that memory states can be split into disjoint sub-regions that undergo different transformations. We build an abstract domain upon this logic, and apply it to design an analysis for programs manipulating simple list or tree data structures. We make the following contributions:\n\n * In Sect. 2, we demonstrate the abstraction of state relations using a specific family of heap predicates;\n\n * In Sect. 4, we set up a logic to describe heap state relations and lift it into an abstract domain that describe concrete relations defined in Sect. 3;\n\n * In Sect. 5, we design static analysis algorithms to infer heap state relations from abstract pre-condition;\n\n * In Sect. 6, we report on experiments on basic linked data structures (lists and trees);\n\n * Finally, we discuss related works in Sect. 7 and conclude in Sect. 8.\n\n## 2 Overview and Motivating Example\n\nWe consider the example code shown in Fig. 1, which implements the insertion of an element inside a non empty singly linked list containing integer values. When applied to a pointer to an existing non empty list and an integer value, this function traverses it partially (based on a condition on the values stored in list elements \u2014that is elided in the figure). It then allocates a new list element, inserts it at the selected position and copies the integer argument into the field. For instance, Fig. 2(a) shows an input list containing elements and an output list where value is inserted as a new element in the list. We observe that all elements of the input list are left physically unmodified except the element right before the insertion point. We now discuss abstractions of the behaviors of this program using abstractions for sets of states and abstractions for state relations.\n\nFig. 1.\n\nA list insertion program\n\nReachability Analysis. First, we consider an abstraction based on separation logics with inductive predicates as used in [5, 15]. We assume that the predicate describes heap regions that consist of a well-formed linked list starting at address ( is a symbolic variable used in the abstraction to denote a concrete address). This predicate is intuitively defined by induction as follows: it means either the region is empty and is the null pointer, or the region is not empty, and consists of a list element of address and with a field containing a value described by symbolic variable and a region that can be described by . Thus, the valid input states for the insertion function can be abstracted by the abstract state shown in the top of Fig. 2(b). The analysis of the function needs to express that the insertion occurs somewhere in the middle of the list. This requires a list segment predicate , that is defined in a similar way as for : it describes region that stores a sub list starting at address and the last element of which has a field pointing to address (note that the empty region can be described by ). Using this predicate, we can now also express an abstraction for the output states of the insertion function: the abstract state shown in the bottom of Fig. 2(b) describes the states where the new element was inserted in the middle of the structure (the list starts with a segment, then the predecessor of the inserted element, then the inserted element, and finally the list tail). We observe that this abstraction allows to express and to verify that the function is memory safe, and returns a well-formed list. Indeed, it captures the fact that no null or dangling pointer is ever dereferenced. Moreover, all states described by the abstract post-condition consist of a well-formed list, made of a segment, followed by two elements and a list tail. On the other hand, it does not say anything about the location of the list in the output state with respect to the list in the input state. More precisely, it cannot capture the fact that the elements of addresses are left unmodified physically. This is a consequence of the fact that each abstract state in Fig. 2(b) independently describes a set of concrete heaps.\n\nFig. 2.\n\nAbstractions (Color figure online)\n\nRelational Analysis. To abstract state relations instead of sets of states, we now propose to define a new structure in Fig. 2(c), that partially overlays the abstractions of input and output states. First, we observe that the tail of the list is not modified at all, thus, we describe it with a single predicate , that denotes pairs made of input state and an output state, that are physically equal and can both be described by . The same kind of predicate can be used to describe that the initial segment has not changed between the two states. Second, we need to define a counterpart for separating conjunction at the relation level. Indeed, the effect of the insertion function can be decomposed as its effect on the initial segment (which is left unchanged), its effect on the tail (which is also left unchanged) and its effect on the insertion point (where a new element is allocated and a pointer is modified). This relation separating conjunction is noted . To avoid confusion, from now on, we write for the usual separating conjunction. Last, the insertion function allocates a new element and modifies the value of the field of an existing element. To account for this, we need a new connective which is applied to two abstract states: if are abstract heaps (described by formulas in the usual separation logic with inductive predicates), then describes the transformation of an input state described by into an output state described by . This is presented with different colors in the figure. In Sect. 4, we formalize this logics and the abstraction that it defines. The analysis by forward abstract interpretation [8] starts with the identity relation at function entry, and computes relations between input and output states step by step. The analysis algorithms need to unfold inductive predicates to materialize cells (for instance to analyze the test at line 4), and to fold inductive predicates in order to analyze loops. In addition to this, it also needs to reason over , and predicates, and perform operations similar to unfolding and folding on them. Section 5 describes the analysis algorithms.\n\n## 3 Concrete Semantics\n\nBefore defining the abstraction, we fix notations for concrete states and programs.\n\nWe let denote the set of program variables and denote the set of values (that includes the set of numeric addresses). A field (noted as ) denotes both field names and offsets. A memory state is a partial function from addresses to values. We write for the domain of , that is the set of addresses for which it is defined. Additionally, if are such that , we let be the memory state obtained by merging and (its domain is ). If is an address and a value, we write the memory state where contains (with ).\n\nIn the following, we consider simple imperative programs, that include basic assignments, allocation and deallocation statements and loops (although our analysis supports a larger language, notably with conditionals and unstructured control flow). Programs are described by the grammar below:\n\nWe assume the semantics of a program is defined as a function that maps a set of input states into a set of output states (thus ). We do not provide a full formal definition for as it is classical. Given a program , we define its relational semantics by:\n\nIn the following, we define an analysis to compute an over-approximation for .\n\n## 4 Abstraction\n\nIn this section, we first define abstract states, that describe sets of memory states (as in [5]), and then we set up abstract state relations, that describe binary relations over memory states. Although our analysis and implementation support more general inductive predicates (such as trees and others), we consider only list inductive predicates in the body of the paper, for the sake of simplicity.\n\nAbstract States. We assume a countable set of symbolic addresses that abstract values and heap addresses. An abstract state consists of an abstract heap with a conjunction of numerical constraints such as equalities and disequalities. An abstract heap is a separating conjunction of region predicates that abstract separate memory regions [23] (as mentioned above, separating conjunction is denoted by ). A node is either a variable address or a symbolic address . A region predicate is either describing an empty region, or a points-to predicate (that describes a heap memory cell at the base address with the possibly null offset and with the content ), or a summary predicate describing a list structure or for a (possibly empty) list segment from address to . The predicate is defined by induction as follows:\n\nSegment predicate stands for the segment version of and describes a list without a tail; it can also be defined by induction. We write for the unfolding relation that syntactically transforms an instance of an inductive predicate into any of the disjuncts of that predicate.\n\nDefinition 1\n\n(Abstract state). Abstract heaps and abstract states are defined by the grammar below:\n\nWe now define the meaning of abstract heaps and abstract states using concretization functions [8], that associate to abstract elements the set of concrete elements they describe. To concretize an abstract heap, we also need to define how the nodes are bound into concrete values in concrete memories. We call valuation a function that maps nodes into concrete values and addresses.\n\nDefinition 2\n\n(Concretization of abstract states). The concretization function maps a numeric constraint into a set of valuations whereas and respectively map an abstract heap and an abstract state into a set of pairs made of memory state and a valuation. They are defined by induction as follows:\n\nExample 1\n\n(Abstract state). The abstract pre-condition of the program of Fig. 1 is .\n\nAbstract Relations. An abstract heap relation describes a set of pairs made of an input memory state and an output memory state . Abstract heap relations are defined by the following connectives:\n\n * the identity relation describes pairs of memory states that are equal and are both abstracted by ; this corresponds to the identity transformation;\n\n * the transformation relation describes pairs corresponding to the transformation of a memory state abstracted by into a memory state abstracted by ;\n\n * the relation separating conjunction of two heap relations denotes a transformation that can be described by combining independently the transformations described by and on disjoint memory regions.\n\nDefinition 3\n\n(Abstract relations). The syntax of abstract heap relations and abstract state relations are defined by the grammar below:\n\nThe concretization of relations also requires using valuations as it also needs to define the concrete values that nodes denote. It thus returns triples made of two memory states and a valuation.\n\nDefinition 4\n\n(Concretization of abstract relations). The concretization functions respectively map an abstract heap relation and an abstract state relation into elements of . They are defined by:\n\nWe remark that is commutative and associative.\n\nExample 2\n\n(Expressiveness). Let and . We observe that describes only the identity transformation applied to a pre-condition where is the address of a well-formed list, whereas describes any transformation that inputs such a list and also outputs such a list, but may modify its content, add or remove elements, or may modify the order of list elements (except for the first one which remains at address ). This means that .\n\nMore generally, we have the following properties:\n\nTheorem 1\n\n(Properties). Let be abstract heaps. Then, we have the following properties\n\n 1. 1.\n\n 2. 2.\n\n (the opposite inclusion may not hold, as observed in Example 2);\n\n 3. 3.\n\n (the opposite inclusion may not hold).\n\nExample 3\n\n(Abstract state relation). The effect of the insertion function of Fig. 1 can be described by the abstract state relation , where (preserved region), , (modified region) and (new region).\n\n## 5 Analysis Algorithms\n\nWe now propose a static analysis to compute abstract state relations as described in Definition 3. It proceeds by forward abstract interpretation [8], starting from the abstract relation where is a pre-condition, supplied by the user.\n\nMore generally, the analysis of a program is a function that inputs an abstract state relation describing a previous transformation done on the input before running and returns a relation describing that transformation followed by the execution of . Thus, should meet the following soundness condition:\n\n### 5.1 Basic Abstract Post-conditions\n\nWe start with the computation of abstract post-condition for assignments, allocation and deallocation, on abstract relations that do not contain inductive predicates. As an example, we consider the analysis of an assignment , starting from an abstract pre-condition relation . To compute the effect of this assignment on , the analysis should update it so as to reflect the modification of in the output states of the pairs denoted by . We first consider the case where is a transformation relation.\n\nCase of a Transformation Relation. We assume . Then, if is an abstract state that describes the memory states after the assignment , when it is executed on a state that is in , then a valid definition for is . An algorithm for computing such a can be found in [5]. It first evaluates into a points-to predicate describing the cell that represents, then evaluates into a node describing the value of the right hand side and finally replaces with . As a consequence, we have the following definitions for the two main cases of assignments:\n\nCase of a Separating Conjunction Relation. We now assume that . If the assignment can be fully analyzed on (i.e., it does not read or modify ), then the following definition provides a sound transfer function, that relies on the same principle as the Frame rule [23] for separation logic:\n\nWhen writes in and reads in , we get a similar definition as above. For instance:\n\nCase of an Identity Relation. We now assume that . As observed in Theorem 1, . We derive from the previous two paragraphs and from this principle the following definitions:\n\nOther Transfer Functions. Condition tests boil down to numeric constraints intersections. The analysis of allocation needs to account for the creation of cells in the right side of relations whereas deallocation needs to account for the deletion of cells that were present before. Thus, for instance:\n\n### 5.2 Materialization and General Abstract Post-conditions\n\nIn Sect. 5.1, we considered only abstract states without inductive predicates, to first provide a simpler definition of abstract post-conditions. We now lift this restriction. For example, the analysis of the program in Fig. 1 starts with , and then has to analyze a reading of .\n\nIf we consider an abstract state relation of the form , and an assignment that reads or writes a field at base address , the inductive predicate should first be unfolded [5]: before the post-condition operators of Sect. 5.1 can be applied, this predicate first needs to be substituted with the disjunction of cases it is made of, as defined in Sect. 4. This process is known in reachability shape analyses as a technique to materialize cells [5, 15, 24]. It results in disjunctive abstract states. For instance, the concretization of the abstract state relation is included in the union of the concretizations of and . This disjunctive abstract states allows to analyze a read or write into a field at address .\n\nHowever, this naive extension of unfolding may be imprecise here. Let us consider the unfolding at node in the abstract state relation . The above technique will generate two disjuncts, including one where . However, cannot be equal to the null pointer here, since is the base address of a regular list element in the left side of the abstract relation. Therefore, unfolding should take into account information in both sides of abstract relations for the sake of analysis precision.\n\nIn the following, we let denote the set of disjuncts produced by unfolding an inductive predicate at node in abstract state , if any. For instance, is . If there is no inductive predicate attached to node in , we let . This operator is sound in the sense that, is included in .\n\nUsing , we define the function that performs unfolding at a given node and in an abstract state relation as follows:\n\n * ;\n\n * if the node carries inductive predicate in then ;\n\n * ;\n\n * .\n\nWe note that conjunctions of numerical constraints over node may yield to unfeasible elements being discarded in the last two cases: for instance, in the case, unfolding will only retain disjuncts where both sides of the arrow express compatible conditions over .\n\nWe can prove by case analysis that this unfolding operator is sound:\n\nExample 4\n\n(Abstract state relation unfolding and post-condition). Let us consider the analysis of the insertion function of Fig. 1. This function should be applied to states where is a non null list pointer (the list should have at least one element), thus, the analysis should start from (in this example, we omit for the sake of concision). Before the loop entry, the analysis computes the abstract state relation . To deal with the test (and the assignment ), the analysis should materialize the cell at node . This unfolding is performed under the connective, and produces:\n\nIn turn, the effect of the condition test and of the assignment in the loop body can be precisely analyzed from this abstract state relation.\n\n### 5.3 Folding and Lattice Operations\n\nLike classical shape analyses [5, 15], our analysis needs to fold inductive predicates so as to (conservatively) decide inclusion and join abstract states. We present folding algorithms in the following paragraphs.\n\nConservative Inclusion Checking. Inclusion checking is used to verify logical entailment, to check the convergence of loop iterates, and to support the join\/widening algorithm. It consists of a conservative function over abstract states and a conservative function over abstract state relations, that either return (meaning that the inclusion of concretizations holds) or (meaning that the analysis cannot conclude whether inclusion holds).\n\nFig. 3.\n\nInclusion checking rules\n\nTheir definition relies on a conservative algorithm, that implements a proof search, based on the rules shown in Fig. 3 (for clarity, we omit the numerical constraints inclusion checking). In this system of rules, if (resp., ), then (resp., ). The rules and are specific to reasoning of abstract states, and are directly inspired from [5] (they allow to reason over equal abstract regions, over segments, and over separating conjunction). The rule allows to reason by unfolding of inductive predicates, at the level of relations. Finally, the rules and allow to derive inclusion over abstract state relations, and implement the properties observed in Theorem 1. The proof search algorithm starts from the goal to prove and attempt to apply these rules so as to complete an inclusion derivation. We observe that abstract states are equivalent up to a renaming of the internal nodes (the nodes that are not of the form ), thus, the implementation also takes care of this renaming, although the rules of Fig. 3 do not show it, as this issue is orthogonal to the reasoning over abstract state relations which is the goal of this paper (indeed, this requires complex renaming functions that are made fully explicit in [5]). The rules can be proved sound one by one, thus they define a sound inclusion checking procedure:\n\nTheorem 2\n\n(Soundness of inclusion checking). If and then:\n\nExample 5\n\n(Inclusion checking). Let us consider the following abstract state relations, and discuss the computation of :\n\nUsing first rule then rule , this goal gets reduced into checking the inclusion , where and . In turn, this inclusion follows from rule .\n\nJoin\/Widening Operators. In the following, we define abstract operators , that respectively operate over abstract states and abstract state relations, and compute an over-approximation for concrete unions. They also ensure termination and serve as widening. The algorithm to compute these two functions heavily relies on the inclusion checking that was discussed in the previous paragraph. Indeed, the widening functions compute results that are more approximate than their arguments. To achieve this, they search for syntactic patterns in their arguments and produce outputs that inclusion checking proves more general. This process is performed region by region on both arguments of the widening, as formalized in [5, Fig. 7]. We discuss in the following a list of such widening rules:\n\n * when both arguments of widening are equal to a same base predicate, widening is trivial, and returns the same base predicate, thus for instance:\n\n * when applied to two abstract relations that consist of the same connective, the widening functions simply calls themselves recursively on the sub-components:\n\n * when applied to an predicate and another abstract relation, widening first tries to maintain the predicate, and, if this fails, tries to weaken it into an predicate:\n\n * when applied to an predicate, the widening tries to weaken the other argument accordingly:\n\nEach of these operations is sound, and the results computed by widening are also sound:\n\nTheorem 3\n\n(Soundness of widening). If and then:\n\nFurthermore, termination of widening follows from an argument similar to [5].\n\nExample 6\n\n(Widening). We consider the analysis of the program of Fig. 1, and more specifically, the widening after the first abstract iteration over the loop:\n\nThis abstract widening performs some generalization and introduces a list segment inductive predicate, that over-approximates an empty segment in the left argument, and a segment of length one. It also involves some renaming of symbolic nodes (as observed in the previous paragraph, the concretization of an abstract states is unchanged under symbolic nodes renaming).\n\n### 5.4 Analysis\n\nThe abstract semantics relies on the abstract operations defined in Sect. 5.1, on the unfolding of Sect. 5.2 to analyze basic statements, and on the folding operations defined in Sect. 5.3 to cope with control flow joins and loop invariants computation. Soundness follows from the soundness of the basic operations.\n\nTheorem 4\n\n(Soundness). The analysis is sound in the sense that, for all program and for all abstract state relation :\n\n## 6 Experimental Evaluation\n\nIn this section, we report on the implementation of our analysis and try to evaluate:\n\n 1. 1.\n\nwhether it can prove precise and useful relational properties, and\n\n 2. 2.\n\nhow it compares with a more classical reachability shape analysis.\n\nOur implementation supports built-in inductive predicates to describe singly linked lists and binary trees. It provides both the analysis described in this paper, and a basic reachability shape analysis in the style of [5], and supporting the same inductive predicates. It was implemented as a Frama-C [19] plugin consisting of roughly 7800 lines of OCaml. We have ran both the reachability shape analysis and relational shape analysis on series of small programs manipulating lists and trees listed in Table 1. These tests are selected to test specifically the relational domain (and not a full analysis). This allows us to not only assess the results of the analysis computing abstract state relations, but also to compare them with an analysis that infers abstract states.\n\nTable 1.\n\nExperiment results (sll: singly linked lists; tree: binary trees; time in milliseconds averaged over 1000 runs on a laptop with Intel Core i7 running at 2.3 GHz, with 16 GB RAM, for the reachability and relational analyses; the last column states whether the relational shape analysis computed the expected abstract relation)\n\nStructure | Function | Time (in ms) | Loop iterations | Relational property\n\n---|---|---|---|---\n\nReach | Relat.\n\nsll | allocation | 0.53 | 1.27 | 2 | Yes\n\nsll | deallocation | 0.34 | 0.99 | 2 | Yes\n\nsll | traversal | 0.53 | 0.83 | 2 | Yes\n\nsll | insertion (head) | 0.32 | 0.33 | 0 | Yes\n\nsll | insertion (random pos) | 1.98 | 2.75 | 2 | Yes\n\nsll | insertion (random) | 2.33 | 3.94 | 2 | Yes\n\nsll | reverse | 0.52 | 2.36 | 2 | Partial\n\nsll | map | 0.66 | 1.17 | 2 | Partial\n\ntree | allocation | 0.94 | 2.21 | 2 | Yes\n\ntree | search | 1.06 | 1.76 | 2 | Yes\n\nFirst, we discuss whether the analysis computing abstract state relations computes the expected relations, that describes the most precisely the transformation implemented by the analyzed function. As an example, in the case of an insertion at the head of a list, we expect the abstract relation below, that expresses that the body of the list was not modified:\n\nWe observe that the state relation computed in all test cases except the list reverse and map are the most precise. For example, with the function map that traverses a list and modifies only its fields, the relation obtained is:\n\nThis relation shows that both input and output lists start at the address and end at the address . This is not enough to prove that the lists contain the same addresses linked in the same order.\n\nSecond, we compare the runtime of the relational analysis and of the reachability analysis. We observe that the slow-down is at most (reverse), and is about in most cases. An exception is the list head insertion, which incurs no slowdown. This is due to the fact this analysis does not require computing an abstract join. While these test cases are not large, these results show that the analysis computing abstract state relations has a reasonable overhead compared to a classical analysis, yet it computes stronger properties. Furthermore, it would be more adapted to a modular interprocedural analysis.\n\n## 7 Related Works\n\nOur analysis computes an abstraction of the relational semantics of programs so as to capture the effect of a function or other blocks of code using an element of some specifically designed abstract domain. This technique has been applied to other abstractions in the past, and often applied to design modular static analyses [10], where program components can be analyzed once and separately. For numerical domains, it simply requires duplicating each variable into two instances respectively describing the old and the new value, and using a relational domain to the inputs and outputs. For instance, [22] implements this idea using convex polyhedra and so as to infer abstract state relations for numerical programs. It has also been applied to shape analyses based on Three Valued Logic [24] in [17]. This work is probably the closest to ours, but it relies on a very different abstraction using a TVLA whereas we use a set of abstract predicates based on separation logic. It uses the same variable duplication trick as mentioned above. Our analysis also has a notion of overlaid old\/new predicates, but these are described heap regions, inside separation logic formulas. Desynchronized separation [11] also introduces a notion of overlaid state in separation logic, but does not support inductive predicates as our analysis does. Instead, it allows to reason on abstractions of JavaScript open objects seen as dictionaries. Also, [13, 14] can express relations between heaps in different states using temporal logic extensions and automatas. In the context of functional languages, [18] allows to write down relations between function inputs and outputs, and relies on a solver to verify that constraints hold and [25] computes shape specifications by learning. Modular analyses that compute invariants by separate analysis of program components [4, 6, 12] use various sorts of abstractions for the behavior of program components. A common pattern is to use tables of couples made of an abstract pre-condition and a corresponding abstract post-condition, effectively defining a sort of cardinal power abstraction [9]. This technique has been used in several shape analyses based on separation logic [2, 3, 16, 20]. We believe this tabular approach could benefit from abstractions of relations such as ours to infer stronger properties, and more concise summaries.\n\n## 8 Conclusion\n\nIn this paper, we have introduced a set of logical connectives inspired by separation logic, to describe state relations rather than states. We have built upon this logic an abstract domain, and a static analysis based on abstract interpretation that computes conservative state relations. Experiments prove it effective for the analysis of basic data structure library functions.\n\nAcknowledgements\n\nWe thank Arlen Cox for fruitful discussions, and Francois Berenger, Huisong Li, Jiangchao Liu and the anonymous reviewers for their comments on an earlier version of this paper. This work has received funding from the European Research Council under the EU's seventh framework programme (FP7\/2007-2013), grant agreement 278673, Project MemCAD, and from Bpifrance, grant agreement P3423-189738, FUI Project P-RC2.\n\nReferences\n\n1.\n\nBaudin, P., Filli\u00e2tre, J.-C., March\u00e9, C., Monate, B., Moy, Y., Prevosto, V.: ACSL: ANSI C specification language (2008)\n\n2.\n\nCalcagno, C., Distefano, D., O'Hearn, P.W., Yang, H.: Footprint analysis: a shape analysis that discovers preconditions. In: Nielson, H.R., Fil\u00e9, G. (eds.) SAS 2007. LNCS, vol. 4634, pp. 402\u2013418. Springer, Heidelberg (2007). doi:10.\u200b1007\/\u200b978-3-540-74061-2_\u200b25 CrossRef\n\n3.\n\nCalcagno, C., Distefano, D., O'Hearn, P., Yang, H.: Compositional shape analysis by means of bi-abduction. In: Symposium on Principles of Programming Languages (POPL), pp. 289\u2013300. ACM (2009)\n\n4.\n\nCastelnuovo, G., Naik, M., Rinetzky, N., Sagiv, M., Yang, H.: Modularity in lattices: a case study on the correspondence between top-down and bottom-up analysis. In: Blazy, S., Jensen, T. (eds.) SAS 2015. LNCS, vol. 9291, pp. 252\u2013274. Springer, Heidelberg (2015). doi:10.\u200b1007\/\u200b978-3-662-48288-9_\u200b15 CrossRef\n\n5.\n\nChang, B.-Y.E., Rival, X.: Relational inductive shape analysis. In: Symposium on Principles of Programming Languages (POPL), pp. 247\u2013260. ACM (2008)\n\n6.\n\nChatterjee, R., Ryder, B.G., Landi, W.A.: Relevant context inference. In: Symposium on Principles of Programming Languages (POPL), pp. 133\u2013146. ACM (1999)\n\n7.\n\nCousot, P., Halbwachs, N.: Automatic discovery of linear restraints among variables of a program. In: Symposium on Principles of Programming Languages (POPL), pp. 84\u201397. ACM (1978)\n\n8.\n\nCousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Symposium on Principles of Programming Languages (POPL) (1977)\n\n9.\n\nCousot, P., Cousot, R.: Systematic design of program analysis frameworks. In: Symposium on Principles of Programming Languages (POPL). ACM (1979)\n\n10.\n\nCousot, P., Cousot, R.: Modular static program analysis. In: Horspool, R.N. (ed.) CC 2002. LNCS, vol. 2304, pp. 159\u2013179. Springer, Heidelberg (2002). doi:10.\u200b1007\/\u200b3-540-45937-5_\u200b13 CrossRef\n\n11.\n\nCox, A., Chang, B.-Y.E., Rival, X.: Desynchronized multi-state abstractions for open programs in dynamic languages. In: Vitek, J. (ed.) ESOP 2015. LNCS, vol. 9032, pp. 483\u2013509. Springer, Heidelberg (2015). doi:10.\u200b1007\/\u200b978-3-662-46669-8_\u200b20 CrossRef\n\n12.\n\nDillig, I., Dillig, T., Aiken, A., Sagiv, M.: Precise and compact modular procedure summaries for heap manipulating programs. In: Conference on Programming Language Design and Implementation (PLDI), pp. 567\u2013577. ACM (2011)\n\n13.\n\nDistefano, D., Katoen, J.-P., Rensink, A.: Who is pointing when to whom? In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2004. LNCS, vol. 3328, pp. 250\u2013262. Springer, Heidelberg (2004). doi:10.\u200b1007\/\u200b978-3-540-30538-5_\u200b21 CrossRef\n\n14.\n\nDistefano, D., Katoen, J.-P., Rensink, A.: Safety and liveness in concurrent pointer programs. In: Boer, F.S., Bonsangue, M.M., Graf, S., Roever, W.-P. (eds.) FMCO 2005. LNCS, vol. 4111, pp. 280\u2013312. Springer, Heidelberg (2006). doi:10.\u200b1007\/\u200b11804192_\u200b14 CrossRef\n\n15.\n\nDistefano, D., O'Hearn, P.W., Yang, H.: A local shape analysis based on separation logic. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 287\u2013302. Springer, Heidelberg (2006). doi:10.\u200b1007\/\u200b11691372_\u200b19 CrossRef\n\n16.\n\nGulavani, B.S., Chakraborty, S., Ramalingam, G., Nori, A.V.: Bottom-up shape analysis. In: Palsberg, J., Su, Z. (eds.) SAS 2009. LNCS, vol. 5673, pp. 188\u2013204. Springer, Heidelberg (2009). doi:10.\u200b1007\/\u200b978-3-642-03237-0_\u200b14 CrossRef\n\n17.\n\nJeannet, B., Loginov, A., Reps, T., Sagiv, M.: A relational approach to interprocedural shape analysis. ACM Trans. Program. Lang. Syst. (TOPLAS) 32(2), 5 (2010)CrossRefMATH\n\n18.\n\nKaki, G., Jagannathan, S.: A relational framework for higher-order shape analysis. In: International Colloquium on Function Programming, pp. 311\u2013324. ACM (2014)\n\n19.\n\nKirchner, F., Kosmatov, N., Prevosto, V., Signoles, J., Yakobowski, B.: Frama-C: a software analysis perspective. Form. Asp. Comput. 27(3), 573\u2013609 (2015)MathSciNetCrossRef\n\n20.\n\nLe, Q.L., Gherghina, C., Qin, S., Chin, W.-N.: Shape analysis via second-order bi-abduction. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 52\u201368. Springer, Cham (2014). doi:10.\u200b1007\/\u200b978-3-319-08867-9_\u200b4\n\n21.\n\nLeavens, G.T., Baker, A.L., Ruby, C.: JML: a java modeling language. In: Formal Underpinnings of Java Workshop (at OOPSLA 1998), pp. 404\u2013420 (1998)\n\n22.\n\nPopeea, C., Chin, W.-N.: Inferring disjunctive postconditions. In: Okada, M., Satoh, I. (eds.) ASIAN 2006. LNCS, vol. 4435, pp. 331\u2013345. Springer, Heidelberg (2007). doi:10.\u200b1007\/\u200b978-3-540-77505-8_\u200b26 CrossRef\n\n23.\n\nReynolds, J.: Separation logic: a logic for shared mutable data structures. In: Symposium on Logics in Computer Science (LICS), pp. 55\u201374. IEEE (2002)\n\n24.\n\nSagiv, M., Reps, T., Wilhelm, R.: Parametric shape analysis via 3-valued logic. ACM Trans. Program. Lang. Syst. (TOPLAS) 24(3), 217\u2013298 (2002)CrossRef\n\n25.\n\nZhu, H., Petri, G., Jagannathan, S.: Automatically learning shape specifications. In: Conference on Programming Language Design and Implementation (PLDI), pp. 491\u2013507. ACM (2016)\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_16\n\n# Floating-Point Format Inference in Mixed-Precision\n\nMatthieu Martel1\n\n(1)\n\nLaboratoire de Math\u00e9matiques et Physique (LAMPS), Universit\u00e9 de Perpignan Via Domitia, Perpignan, France\n\nMatthieu Martel\n\nEmail: matthieu.martel@univ-perp.fr\n\nAbstract\n\nWe address the problem of determining the minimal precision on the inputs and on the intermediary results of a program containing floating-point computations in order to ensure a desired accuracy on the outputs. The first originality of our approach is to combine forward and backward static analyses, done by abstract interpretation. The backward analysis computes the minimal precision needed for the inputs and intermediary values in order to have a desired accuracy on the results, specified by the user. The second originality is to express our analysis as a set of constraints made of first order predicates and affine integer relations only, even if the analyzed programs contain non-linear computations. These constraints can be easily checked by an SMT Solver. The information collected by our analysis may help to optimize the formats used to represent the values stored in the floating-point variables of programs. Experimental results are presented.\n\n## 1 Introduction\n\nIssues related to numerical accuracy are almost as old as computer science. An important step towards the design of more reliable numerical software was the definition, in the 1980's, of the IEEE754 Standard for floating-point arithmetic [2]. Since then, work has been carried out to determine the accuracy of floating-point computations by dynamic [3, 17, 29] or static [11, 13, 14] methods. This work has also been motivated by a few disasters due to numerical bugs [1, 15].\n\nWhile existing approaches may differ strongly each other in their way of determining accuracy, they have a common objective: to compute approximations of the errors on the outputs of a program depending on the initial errors on the data and on the roundoff of the arithmetic operations performed during the execution. The present work focuses on a slightly different problem concerning the relations between precision and accuracy. Here, the term precision refers to the number of bits used to represent a value, i.e. its format, while the term accuracy is a bound on the absolute error between the represented value and the exact value x that we would have in the exact arithmetic.\n\nWe address the problem of determining the minimal precision on the inputs and on the intermediary results of a program performing floating-point computations in order to ensure a desired accuracy on the outputs. This allows compilers to select the most appropriate formats (for example IEEE754 half, single, double or quad formats [2, 23]) for each variable. It is then possible to save memory, reduce CPU usage and use less bandwidth for communications whenever distributed applications are concerned. So, the choice of the best floating-point formats is an important compile-time optimization in many contexts. Our approach is also easily generalizable to the fixed-point arithmetic for which it is important to determine data formats, for example in FPGAs [12, 19].\n\nThe first originality of our approach is to combine a forward and a backward static analysis, done by abstract interpretation [8, 9]. The forward analysis is classical. It propagates safely the errors on the inputs and on the results of the intermediary operations in order to determine the accuracy of the results. Next, based on the results of the forward analysis and on assertions indicating which accuracy the user wants for the outputs at some control points, the backward analysis computes the minimal precision needed for the inputs and intermediary results in order to satisfy the assertions. Not surprisingly, the forward and backward analyses can be applied repeatedly and alternatively in order to refine the results until a fixed-point is reached.\n\nThe second originality of our approach is to express the forward and backward transfer functions as a set of constraints made of propositional logic formulas and relations between affine expressions over integers (and only integers). Indeed, these relations remain linear even if the analyzed program contains non-linear computations. As a consequence, these constraints can be easily checked by a SMT solver (we use Z3 in practice [4, 21]). The advantage of the solver appears in the backward analysis, when one wants to determine the precision of the operands of some binary operation between two operands a and b, in order to obtain a certain accuracy on the result. In general, it is possible to use a more precise a with a less precise b or, conversely, to use a more precise b with a less precise a. Because this choice arises at almost any operation, there is a huge number of combinations on the admissible formats of all the data in order to ensure a given accuracy on the results. Instead of using an ad-hoc heuristic, we encode our problem as a set of constraints and we let a well-known, optimized solver generate a solution.\n\nThis article is organized as follows. We briefly introduce some elements of floating-point arithmetic, a motivating example and related work in Sect. 2. Our abstract domain as well as the forward and backward transfer functions are introduced in Sect. 3. The constraint generation is presented in Sect. 4 and experimental results are given in Sect. 5. Finally, Sect. 6 concludes.\n\n## 2 Preliminary Elements\n\nIn this section we introduce some preliminary notions helpful to understand the rest of the article. Elements of floating-point arithmetic are introduced in Sect. 2.1. Further, an illustration of what our method does is given in Sect. 2.2. Related work is discussed in Sect. 2.3.\n\n### 2.1 Elements of Floating-Point Arithmetic\n\nWe introduce here some elements of floating-point arithmetic [2, 23]. First of all, a floating-point number x in base is defined by\n\n(1)\n\nwhere is the sign, is the significand, is the precision and e is the exponent, .\n\nA floating-point number x is normalized whenever . Normalization avoids multiple representations of the same number. The IEEE754 Standard also defines denormalized numbers which are floating-point numbers with and . Denormalized numbers make underflow gradual [23]. The IEEE754 Standard defines binary formats (with ) and decimal formats (with ). In this article, without loss of generality, we only consider normalized numbers and we always assume that (which is the most common case in practice). The IEEE754 Standard also specifies a few values for and which are summarized in Fig. 1. Finally, special values also are defined: nan (Not a Number) resulting from an invalid operation, corresponding to overflows, and and (signed zeros).\n\nFig. 1.\n\nBasic binary IEEE754 formats.\n\nThe IEEE754 Standard also defines five rounding modes for elementary operations over floating-point numbers. These modes are towards , towards , towards zero, to the nearest ties to even and to the nearest ties to away and we write them and , respectively. The semantics of the elementary operations is then defined by\n\n(2)\n\nwhere denotes the rounding mode. Equation (2) states that the result of a floating-point operation done with the rounding mode returns what we would obtain by performing the exact operation and next rounding the result using . The IEEE754 Standard also specifies how the square root function must be rounded in a similar way to Eq. (2) but does not specify the roundoff of other functions like sin, log, etc.\n\nWe introduce hereafter two functions which compute the unit in the first place and the unit in the last place of a floating-point number. These functions are used further in this article to generate constraints encoding the way roundoff errors are propagated throughout computations. The of a number x is\n\n(3)\n\nThe of a floating-point number which significand has size p is defined by\n\n(4)\n\nThe of a floating-point number corresponds to the binary exponent of its most significant digit. Conversely, the of a floating-point number corresponds to the binary exponent of its least significant digit. Note that several definitions of the have been given [22].\n\nFig. 2.\n\nTop left: initial program. Top right: annotations after analysis. Bottom left: forward analysis (one iteration). Bottom right: backward analysis (one iteration).\n\n### 2.2 Overview of Our Method\n\nLet us consider the program of Fig. 2 which implements a simple linear filter. At each iteration t of the loop, the output is computed as a function of the current input and of the values and of the former iteration. Our program contains several annotations. First, the statement on the last line of the code informs the system that the programmer wants to have 10 accurate binary digits on at this control point. In other words, let for some , the absolute error between the value v that would have if all the computations where done with real numbers and the floating-point value of is less than .\n\nNote that accuracy is not a property of a number but a number that states how closely a particular floating-point number matches some ideal true value. For example, using the basis for the sake of simplicity, the floating-point value 3.149 represents with an accuracy of 3. It itself has a precision of 4. It represents the real number 3.14903 with an accuracy of 4.\n\nAn abstract value represents the set of floating-point values with p accurate bits ranging from a to b. For example, in the code of Fig. 2, the variables and are initialized to the abstract value thanks to the annotation [1.0,3.0]#16. Let be the of set of all floating-point numbers with accuracy p. This means that, compared to exact value v computed in infinite precision, the value of is such that . By definition, using the function ufp introduced in Eq. (3), for any the roundoff error on x is bounded by . Concerning the abstract values, intuitively we have the concretization function\n\n(5)\n\nThese abstract values are special cases of the values used in other work [18] in the sense that, in the present framework, the errors attached to floating-point numbers have form for some integer u instead of arbitrary intervals with real bounds. Restricting the form of the errors enables one to simplify drastically the transfer functions for the backward analysis and the generation of constraints in Sect. 4. In this article, we focus on the accuracy of computations and we omit other problems related to runtime-errors [3, 5]. In particular, overflows are not considered and we assume that any number with p accurate digits belongs to . In practice, a static analysis computing the ranges of the variables and rejecting programs which possibly contain overflows is done before our analysis.\n\nFig. 3.\n\nExample of forward addition: 3.0#16 \\+ 1.0#16 = 4.0#17.\n\nIn our example, and belong to which means, by definition, that these variables have a value ranging in [1.0, 3.0] and such that the error between and the value v that we would have in the exact arithmetic is bounded by . Typically, in this example, this information would come from the specification of the sensor related to x. By default, the values for which no accuracy annotation is given (for instance the value of in the example of Fig. 2) are considered as exact numbers rounded to the nearest in double precision. In this format numbers have 53 bits of significand (see Fig. 1). The last bit being rounded, these numbers have 52 accurate bits in our terminology and, consequently, by default values belong to in our framework. Based on the accuracy of the inputs, our forward analysis computes the accuracy of all the other variables and expressions. The program in the left bottom corner of Fig. 2 displays the result of the forward analysis on the first iteration of the loop. Let denote the forward addition (all the operations used in the current example are formally defined in Sect. 3). For example, the result of has 16 accurate digits since\n\nThis is illustrated in Fig. 3 where we consider the addition of these values at the bit level. For the result of the addition between intervals, we take the most pessimistic accuracy: .\n\nThe backward analysis is performed after the forward analysis and takes advantage of the accuracy requirement at the end of the code (see the right bottom corner of Fig. 2 for an unfolding of the backward analysis on the first iteration of the loop). Since, in our example, 10 bits only are required for , the result of the addition also needs 10 accurate bits only. By combining this information with the result of the forward analysis, it is then possible to lower the number of bits needed for one of the operands. Let be the backward addition. For example, for in the assignment of v, we have:\n\nConversely to the forward function, the interval function now keeps the largest accuracy arising in the computation of the bounds:\n\nFig. 4.\n\nFinal program with generated data types for the example of Fig. 2.\n\nBy processing similarly on all the elementary operations and after computation of the loop fixed point, we obtain the final result of the analysis displayed in the top right corner of Fig. 2. This information may be used to determine the most appropriate data type for each variable and operation, as shown in Fig. 4. To obtain this result we generate a set of constraints corresponding to the forward and backward transfer functions for the operations of the program. There exists several ways to handle a backward operation: when the accuracy on the inputs x and y computed by the forward analysis is too large wrt. the desired accuracy on the result, one may lower the accuracy of either x or y or both.\n\nSince this question arises at each binary operation, we would face to a huge number of combinations if we decided to enumerate all possibilities. Instead, we generate a disjunction of constraints corresponding to the minimization of the accuracy of each operand and we let the solver search for a solution. The control flow of the program is also encoded with constraints. For a sequence of statements, we relate the accuracy of the former statements to the accuracy of the latter ones. Each variable x has three parameters: its forward, backward and final accuracy, denoted , and respectively. We must always have\n\n(6)\n\nFor the forward analysis, the accuracy of some variable may decrease when passing to the next statement (we may only weaken the pre-conditions). Conversely, in the backward analysis, the accuracy of a given variable may increase when we jump to a former statement in the control graph (the post-conditions may only be strengthened). For a loop, we relate the accuracy of the variables at the beginning and at the end of the body, in a standard way.\n\nThe key point of our technique is to generate simple constraints made of propositional logic formulas and of affine expressions among integers (even if the floating-point computations in the source code are non-linear). A static analysis computing safe ranges at each control point is performed before our accuracy analysis. Then the constraints depend on two kinds of integer parameters: the ufp of the values and their accuracies and . For instance, given control points and , the set C of constraints generated for , assuming that we require 10 accurate bits for the result are:\n\nFor the sake of conciseness, the constraints corresponding to Eq. (6) have been omitted in C. For example, for the forward addition, the accuracy of the result is the number of bits between and the u of the error which is\n\nwhere or depending on some condition detailed later. The constraints generated for each kind of expression and command are detailed in Sect. 4.\n\n### 2.3 Related Work\n\nSeveral approaches have been proposed to determine the best floating-point formats as a function of the expected accuracy on the results. Darulova and Kuncak use a forward static analysis to compute the propagation of errors [11]. If the computed bound on the accuracy satisfies the post-conditions then the analysis is run again with a smaller format until the best format is found. Note that in this approach, all the values have the same format (contrarily to our framework where each control-point has its own format). While Darulova and Kuncak develop their own static analysis, other static techniques [13, 29] could be used to infer from the forward error propagation the suitable formats. Chiang et al. [7] have proposed a method to allocate a precision to the terms of an arithmetic expression (only). They use a formal analysis via Symbolic Taylor Expansions and error analysis based on interval functions. In spite of our linear constraints, they solve a quadratically constrained quadratic program to obtain annotations.\n\nOther approaches rely on dynamic analysis. For instance, the Precimonious tool tries to decrease the precision of variables and checks whether the accuracy requirements are still fulfilled [24, 27]. Lam et al. instrument binary codes in order to modify their precision without modifying the source codes [16]. They also propose a dynamic search method to identify the pieces of code where the precision should be modified. Finally, another related research axis concerns the compile-time optimization of programs in order to improve the accuracy of the floating-point computation in function of given ranges for the inputs, without modifying the formats of the numbers [10, 26].\n\n## 3 Abstract Semantics\n\nIn this section, we give a formal definition of the abstract domain and transfer functions presented informally in Sect. 2. The domain is defined in Sect. 3.1 and the transfer functions are given in Sect. 3.2.\n\n### 3.1 Abstract Domain\n\nLet be the set floating-point numbers with accuracy p (we assume that the error between and the value that we would have in the exact arithmetic is less than ) and let be the set of all intervals of floating-point numbers with accuracy p. As mentioned in Sect. 2.2, we assume that no overflow arises during our analysis and we omit to specify the lower and upper bounds of . An element , denoted , is then defined by two floating-point numbers and an accuracy p. We have\n\n(7)\n\nOur abstract domain is the complete lattice where elements are ordered by . In other words, is more precise than if it is an included interval with a greater accuracy. Let denote the rounding of x at precision r using the rounding mode m. Then the join and meet operators are defined by\n\n(8)\n\nand\n\n(9)\n\nIn addition, we have and we have whenever . Let be the abstraction function which maps a set of floating-point numbers X with different accuracies , to a value of . Let , and the minimal accuracy in X. We have,\n\n(10)\n\nLet and . The concretization function is defined as:\n\n(11)\n\nUsing the functions and of Eqs. (10) and (11), we define the Galois connection [8].\n\n### 3.2 Transfer Functions\n\nIn this section, we introduce the forward and backward transfer functions for the abstract domain of Sect. 3.1. These functions are defined using the unit in the first place of a floating-point number introduced in Sect. 2.1. First, we introduce the forward transfer functions corresponding to the addition and product of two floating-point numbers and . The addition and product are defined by\n\n(12)\n\n(13)\n\nIn Eqs. (12) and (13), and denote the exact sum and product of the two values. In practice, this sum must be done with enough accuracy in order to ensure that the result has accuracy r, for example by using more precision than the accuracy of the inputs. The errors on the addition and product may be bounded by and , respectively. Then the most significant bits of the errors have weights and and the accuracies of the results are and , respectively.\n\nFig. 5.\n\nForward and backward transfer functions for the addition and product on .\n\nWe introduce now the backward transfer functions and . We consider the operation between and whose result is . Here, and are known while is unknown. We have\n\n(18)\n\n(19)\n\nThe correctness of the backward product relies on the following arguments. Let and be the exact errors on x, y and z respectively. We have and then Finally, we conclude that .\n\nWe end this section by extending the operations to the values of the abstract domain of Sect. 3.1. First, let , let be a rounding mode and let be the rounding function which returns the roundoff of a number at precision p using the rounding mode m. We write and the forward and backward addition and and the forward and backward products on . These functions are defined in Fig. 5. The forward functions and take two operands and and return the resulting abstract value . The backward functions take three arguments: the operands and known from the forward pass and the result computed by the backward pass [20]. Then and compute the backward value of the first operand. The backward value of the second operand can be obtained by inverting the operands and . An important point in these formulas is that, in forward mode, the resulting intervals inherit from the minimal accuracy computed for their bounds while, in backward mode, the maximal accuracy computed for the bounds is assigned to the interval.\n\n## 4 Constraint Generation\n\nIn this section, we introduce our system of constraints. The transfer functions of Sect. 3 are not directly translated into constraints because the resulting system would be too difficult to solve, containing non-linear constraints among non-integer quantities. Instead, we reduce the problem to a system of constraints made of linear relations between integer elements only. Sections 4.1 and 4.2 introduce the constraints for arithmetic expressions and programs, respectively.\n\n### 4.1 Constraints for Arithmetic Expressions\n\nIn this section, we introduce the constraints generated for arithmetic expressions. As mentioned in Sect. 2, we assume that a range analysis is performed before the accuracy analysis and that a bounding interval is given for each variable and each value at any control point of the input programs.\n\nLet us start with the forward operations. Let and and let us consider the operation . We know from Eq. (12) that with . We need to over-approximate in order to ensure . Let and . We have and and, consequently, We introduce the function defined by . We have\n\nand we conclude that\n\n(20)\n\nNote that, since we assume that a range analysis has been performed before the accuracy analysis, , a and b are known at constraint generation time. For the forward product, we know from Eq. (13) that with . Again, let and . We have, by definition of , . Then may be bound by\n\nSince and , we may get rid of the last term of the former equation and we obtain that\n\nWe conclude that\n\n(21)\n\nNote that, by reasoning on the exponents of the values, the constraints resulting from a product become linear. We consider now the backward transfer functions. If then we know from Eq. (18) that with . Let , we over-approximate using the relations and . So, and\n\n(22)\n\nFinally, for the backward product, using Eq. (19) we know that if then with Using the relations , , and , we deduce that and that . Consequently, and it results that\n\n(23)\n\nFig. 6.\n\nConstraint generation for arithmetic expressions.\n\nFig. 7.\n\nConstraint generation for commands.\n\n### 4.2 Systematic Constraint Generation\n\nTo explain the constraint generation, we use the simple imperative language of Eq. (24) in which a unique label is attached to each expression and command to identify without ambiguity each node of the syntactic tree.\n\n(24)\n\nAs in Sect. 2, denotes a constant c with accuracy p and the statement indicates that x must have at least accuracy n at control point . The set of identifiers occurring in the source program is denoted . Concerning the arithmetic expressions, we assign to each label of the expression three variables in our system of constraints, , and respectively corresponding to the forward, backward and final accuracies and we systematically generate the constraints .\n\nFor each control point in an arithmetic expression, we assume given a range , computed by static analysis and which bounds the values possibly occurring at Point at run-time. Our constraints use the unit in the first place and of these ranges. Let be an environment which relates each identifier x to its last assignment : Assuming that is the last assignment of x, the environment maps x to (we will use join operators when control flow branches will be considered). Then generates the set of constraints for the expression e in the environment . These constraints, defined in Fig. 6, are derived from equations of Sect. 4.1. For commands, labels are used to distinguish many assignments of the same variable or to implement joins in conditions and loops. Given a command c and an environment , returns a pair made of a set C of constraints and of a new environment . is defined by induction on the structure of commands in Fig. 7. These constraint join values at control flow junctions and propagate the accuracies as described in Sect. 2. In forward mode, accuracy decreases while in backward mode accuracy increases (we weaken pre-conditions and strengthen post-conditions).\n\n## 5 Experimental Results\n\nIn this section we present some experimental results obtained with our prototype. Our tool generates the constraints defined in Sect. 4 and calls the Z3 SMT solver [21] in order to obtain a solution. Since, when they exist, solutions are not unique in general, we add an additional constraint related to a cost function to the constraints of Figs. 6 and 7. The cost function of a program c computes the sum of all the accuracies of the variables and intermediary values stored in the control points of the arithmetic expressions, . Then, by binary search, our tool searches the smallest integer P such that the system of constraints admits a solution (we aim at using an optimizing solver in future work [6, 25, 28]). In our implementation we assume that, in the worst case, all the values are in double precision, consequently we start the binary search with where n is the number of variables and intermediary values stored in the control points. When a solution is found for some P, a new iteration of the binary search is run with a smaller P. Otherwise, a new iteration is run with a larger P.\n\nFig. 8.\n\nExamples of mixed-precision inference. Source programs, inferred accuracies and formats. Top: determinant. Middle: Horner's scheme. Bottom: a PD controller.\n\nFig. 9.\n\nMeasures of efficiency of the analysis on the codes of Figs. 2 and 8.\n\nWe consider three sample codes displayed in Fig. 8. The first program computes the determinant of a matrix . We have The matrix coefficients belong to the ranges and we require that the variable det containing the result has accuracy 10 which corresponds to a fairly rounded half precision number. By default, we assume that in the original program all the variables are in double precision. Our tool infers that all the computations may be carried out in half precision.\n\nThe second example of Fig. 8 concerns the evaluation of a degree 9 polynomial using Horner's scheme: . The coefficients belong to and . Initially all the variables are in double precision and we require that the result is fairly rounded in single precision. Our tool then computes that all the variables may be in single precision but p which must remain in double precision. Our last example is a proportional differential controller. Initially the measure m is given by a sensor which sends values in and which ensures an accuracy of 32. All the other variables are assumed to be in double precision. As shown in Fig. 8, many variables may fit inside single precision formats.\n\nFor each program, we give in Fig. 9 the number of variables of the constraint system as well as the number of constraints generated. Next, we give the total execution time of the analysis (including the generation of the system of constraints and the calls to the SMT solver done by the binary search). Then we give the number of bits needed to store all the values of the programs, assuming that all the values are stored in double precision (column #Bits-Init.) and as computed by our analysis (column #Bits-Optim.) Finally, the number of calls to the SMT solver done during the binary search is displayed. Globally, we can observe that the numbers of variables and constraints are rather small and very tractable for the solver. This is confirmed by the execution times which are very short. The improvement, in the number of bits needed to fulfill the requirements, compared to the number of bits needed if all the computations are done in double precision, ranges from to which is very important.\n\n## 6 Conclusion\n\nWe have defined a static analysis which determines the floating-point formats needed to ensure a given accuracy. This analysis is done by generating a set of linear constraints between integer variables only, even if the programs contain non-linear computations. These constraints are easy to solve by a SMT solver.\n\nOur technique can be easily extended to other language structures. For example, since all the elements of an array must have the same type, we just need to join all the elements in a same abstract value to obtain a relevant result. Similarly, functions are also easy to manage since only one type per argument and returned value need. Our analysis is built upon a range analysis performed before. Obviously, the precision of this analysis impacts the precision of the floating-point format determination and the inference of sharp ranges given by relational domains, improves the quality of the results. In future work, we aim at exploring the use a solver based on optimization modulo theories [6, 25, 28] instead of the non-optimizing solver coupled to a binary search used presently.\n\nReferences\n\n1.\n\nPatriot missile defense: Software problem led to system failure at Dhahran, Saudi Arabia. Technical Report GAO\/IMTEC-92-26, General Accounting office (1992)\n\n2.\n\nANSI\/IEEE: IEEE Standard for Binary Floating-Point Arithmetic (2008)\n\n3.\n\nBarr, E.T., Vo, T., Le, V., Su, Z.: Automatic detection of floating-point exceptions. In: POPL 2013, pp. 549\u2013560. ACM (2013)\n\n4.\n\nBarrett, C.W., Sebastiani, R., Seshia, S.A., Tinelli, C.: Satisfiability modulo theories. In: Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185, pp. 825\u2013885. IOS Press (2009)\n\n5.\n\nBertrane, J., Cousot, P., Cousot, R., Feret, J., Mauborgne, L., Min\u00e9, A., Rival, X.: Static analysis by abstract interpretation of embedded critical software. ACM SIGSOFT Softw. Eng. Notes 36(1), 1\u20138 (2011)CrossRef\n\n6.\n\nBj\u00f8rner, N., Phan, A.-D., Fleckenstein, L.: \\- an optimizing SMT solver. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 194\u2013199. Springer, Heidelberg (2015). doi:10.\u200b1007\/\u200b978-3-662-46681-0_\u200b14\n\n7.\n\nChiang, W., Baranowski, M., Briggs, I., Solovyev, A., Gopalakrishnan, G., Rakamaric, Z.: Rigorous floating-point mixed-precision tuning. In: POPL, pp. 300\u2013315. ACM (2017)\n\n8.\n\nCousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Principles of Programming Languages, pp. 238\u2013252. ACM Press (1977)\n\n9.\n\nCousot, P., Cousot, R.: A gentle introduction to formal verification of computer systems by abstract interpretation. NATO Science Series III: Computer and Systems Sciences, pp. 1\u201329. IOS Press (2010)\n\n10.\n\nDamouche, N., Martel, M., Chapoutot, A.: Intra-procedural optimization of the numerical accuracy of programs. In: N\u00fa\u00f1ez, M., G\u00fcdemann, M. (eds.) FMICS 2015. LNCS, vol. 9128, pp. 31\u201346. Springer, Cham (2015). doi:10.\u200b1007\/\u200b978-3-319-19458-5_\u200b3 CrossRef\n\n11.\n\nDarulova, E., Kuncak, V.: Sound compilation of reals. In: Symposium on Principles of Programming Languages, POPL 2014, pp. 235\u2013248. ACM (2014)\n\n12.\n\nGao, X., Bayliss, S., Constantinides, G.A.: SOAP: structural optimization of arithmetic expressions for high-level synthesis. In: International Conference on Field-Programmable Technology, pp. 112\u2013119. IEEE (2013)\n\n13.\n\nGoubault, E.: Static analysis by abstract interpretation of numerical programs and systems, and FLUCTUAT. In: Logozzo, F., F\u00e4hndrich, M. (eds.) SAS 2013. LNCS, vol. 7935, pp. 1\u20133. Springer, Heidelberg (2013). doi:10.\u200b1007\/\u200b978-3-642-38856-9_\u200b1 CrossRef\n\n14.\n\nGoubault, E., Putot, S.: Static analysis of finite precision computations. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol. 6538, pp. 232\u2013247. Springer, Heidelberg (2011). doi:10.\u200b1007\/\u200b978-3-642-18275-4_\u200b17 CrossRef\n\n15.\n\nHalfhill, T.R.: The truth behind the Pentium bug. Byte, March 1995\n\n16.\n\nLam, M.O., Hollingsworth, J.K., de Supinski, B.R., LeGendre, M.P.: Automatically adapting programs for mixed-precision floating-point computation. In: Supercomputing, ICS 2013, pp. 369\u2013378. ACM (2013)\n\n17.\n\nLamotte, J.L., Chesneaux, J.M., J\u00e9z\u00e9quel, F.: CADNA_C: a version of CADNA for use with C or C++ programs. Comput. Phys. Commu. 181(11), 1925\u20131926 (2010)CrossRef\n\n18.\n\nMartel, M.: Semantics of roundoff error propagation in finite precision calculations. High.-Order Symb. Comput. 19(1), 7\u201330 (2006)CrossRefMATH\n\n19.\n\nMartel, M., Najahi, A., Revy, G.: Code size and accuracy-aware synthesis of fixed-point programs for matrix multiplication. In: Pervasive and Embedded Computing and Communication Systems, pp. 204\u2013214. SciTePress (2014)\n\n20.\n\nMin\u00e9, A.: Inferring sufficient conditions with backward polyhedral under-approximations. Electr. Notes Theor. Comput. Sci. 287, 89\u2013100 (2012)CrossRefMATH\n\n21.\n\nMoura, L., Bj\u00f8rner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337\u2013340. Springer, Heidelberg (2008). doi:10.\u200b1007\/\u200b978-3-540-78800-3_\u200b24 CrossRef\n\n22.\n\nMuller, J.M.: On the definition of ulp(x). Technical report 2005\u201309, Laboratoire d'Informatique du Parall\u00e9lisme, Ecole Normale Sup\u00e9rieure de Lyon (2005)\n\n23.\n\nMuller, J.M., Brisebarre, N., de Dinechin, F., Jeannerod, C.P., Lef\u00e8vre, V., Melquiond, G., Revol, N., Stehl\u00e9, D., Torres, S.: Handbook of Floating-Point Arithmetic. Birkh\u00e4user Boston, Boston (2010)\n\n24.\n\nNguyen, C., Rubio-Gonzalez, C., Mehne, B., Sen, K., Demmel, J., Kahan, W., Iancu, C., Lavrijsen, W., Bailey, D.H., Hough, D.: Floating-point precision tuning using blame analysis. In: International Conference on Software Engineering (ICSE). ACM (2016)\n\n25.\n\nNieuwenhuis, R., Oliveras, A.: On SAT modulo theories and optimization problems. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 156\u2013169. Springer, Heidelberg (2006). doi:10.\u200b1007\/\u200b11814948_\u200b18 CrossRef\n\n26.\n\nPanchekha, P., Sanchez-Stern, A., Wilcox, J.R., Tatlock, Z.: Automatically improving accuracy for floating point expressions. In: PLDI, pp. 1\u201311. ACM (2015)\n\n27.\n\nRubio-Gonzalez, C., Nguyen, C., Nguyen, H.D., Demmel, J., Kahan, W., Sen, K., Bailey, D.H., Iancu, C., Hough, D.: Precimonious: tuning assistant for floating-point precision. In: International Conference for High Performance Computing, Networking, Storage and Analysis, pp. 27:1\u201327:12. ACM (2013)\n\n28.\n\nSebastiani, R., Tomasi, S.: Optimization modulo theories with linear rational costs. ACM Trans. Comput. Log. 16(2), 12:1\u201312:43 (2015)MathSciNetCrossRefMATH\n\n29.\n\nSolovyev, A., Jacobsen, C., Rakamari\u0107, Z., Gopalakrishnan, G.: Rigorous estimation of floating-point round-off errors with symbolic Taylor expansions. In: Bj\u00f8rner, N., de Boer, F. (eds.) FM 2015. LNCS, vol. 9109, pp. 532\u2013550. Springer, Cham (2015). doi:10.\u200b1007\/\u200b978-3-319-19249-9_\u200b33 CrossRef\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_17\n\n# A Verification Technique for Deterministic Parallel Programs\n\nSaeed Darabi1 , Stefan C. C. Blom1 and Marieke Huisman1\n\n(1)\n\nUniversity of Twente, Enschede, The Netherlands\n\nSaeed Darabi (Corresponding author)\n\nEmail: s.darabi@utwente.nl\n\nStefan C. C. Blom\n\nEmail: s.c.c.blom@utwente.nl\n\nMarieke Huisman\n\nEmail: M.Huisman@utwente.nl\n\nAbstract\n\nA commonly used approach to develop parallel programs is to augment a sequential program with compiler directives that indicate which program blocks may potentially be executed in parallel. This paper develops a verification technique to prove correctness of compiler directives combined with functional correctness of the program. We propose syntax and semantics for a simple core language, capturing the main forms of deterministic parallel programs. This language distinguishes three kinds of basic blocks: parallel, vectorized and sequential blocks, which can be composed using three different composition operators: sequential, parallel and fusion composition. We show that it is sufficient to have contracts for the basic blocks to prove correctness of the compiler directives, and moreover that functional correctness of the sequential program implies correctness of the parallelized program. We formally prove correctness of our approach. In addition, we define a widely-used subset of OpenMP that can be encoded into our core language, thus effectively enabling the verification of OpenMP compiler directives, and we discuss automated tool support for this verification process.\n\n## 1 Introduction\n\nA common approach to handle the complexity of parallel programming is to write a sequential program augmented with parallelization compiler directives that indicate which part of code might be parallelized. A parallelizing compiler consumes the annotated sequential program and automatically generates a parallel version. This approach is often called deterministic parallel programming, as the parallelization of a deterministic sequential program augmented with correct compiler directives is always deterministic. Deterministic parallel programming is supported by different languages and libraries such as OpenMP [18] and is often used for financial and scientific applications [3, 11, 16, 19].\n\nAlthough it is relatively easy to write parallel programs in this way, careless use of compiler directives can easily introduce data races and consequently non-deterministic program behaviour. This paper proposes a static technique to prove that parallelization as indicated by the compiler directives does not introduce such non-determinism. Moreover it also shows how our technique reduces functional verification of the parallelized program to functional verification of the sequential program. We develop our verification technique over a core deterministic parallel programming language called PPL (for Parallel Programming Language). To show practical usability of our approach, we present how a commonly used subset of OpenMP can be encoded into PPL and then be verified in our approach. We also discuss tool support for this process.\n\nIn essence, PPL is a language for the composition of code blocks. We identify three kinds of basic blocks: a parallel block, a vectorized block and a sequential block. Basic blocks are composed by three binary block composition operators: sequential composition, parallel composition and fusion composition where the fusion composition allows two parallel basic blocks to be merged into one. An operational semantics for PPL is presented.\n\nOur verification technique requires each basic block to be specified by an iteration contract [6] that describes which memory locations are read and written by a thread. Moreover, the program itself should be specified by a global contract. To verify the program, we show that the block compositions are memory safe (i.e. data race free) by proving that for all independent iterations (i.e. the iterations that might run in parallel) all accesses to shared memory are non-conflicting, meaning that they are disjoint or they are read accesses. If all block compositions are memory safe, then it is sufficient to prove that the sequential composition of all the basic blocks w.r.t. program order is memory safe and functionally correct, to conclude that the parallelized program is functionally correct.\n\nThe main contributions of this paper are the following:\n\n * A core language, PPL, and an operational semantics which captures the main forms of parallelization constructs in deterministic parallel programming.\n\n * A verification approach for reasoning about data race freedom and functional correctness of PPL programs.\n\n * A soundness proof that all verified PPL programs are indeed data race free and functionally correct w.r.t. their contracts.\n\n * Tool support that addresses the complete process of encoding of OpenMP into PPL and verification of PPL programs.\n\nThis paper is organized as follows. After some background information, Sect. 3 explains syntax and semantics of PPL. Section 4 presents our verification technique for reasoning about PPL programs and also discusses soundness of our verification approach. Section 5 explains how our approach is applied to verification of OpenMP programs. Finally, we conclude with related and future work.\n\n## 2 Background\n\nWe present some background information on OpenMP, Permission-based Separation Logic and the notion of iteration contract.\n\n### 2.1 OpenMP\n\nThis section illustrates the most important OpenMP features by an example. We verify this example later in Sect. 5 where the program contract and the iteration contracts are added. The example in Fig. 1 is a sequential C program augmented by OpenMP compiler directives (pragmas). The pivotal parallelization annotation in OpenMP is omp parallel which determines the parallelizable code block (called parallel region). Threads are forked upon entering a parallel region and joined back into a single thread at the end of the region.\n\nThe example shows a parallel region with three for-loops , and . The loops are marked as omp for meaning that they are parallelizable (i.e. their iterations are allowed to be executed in parallel). To precisely define the behaviour of threads in the parallel region, omp for annotations are extended by clauses. For example the combined use of the nowait and schedule(static) clauses indicates that it is safe to fuse the parallel loops and , meaning that the corresponding iterations of and are executed by the same thread without waiting. The clause nowait implies that it is safe to eliminate the implicit barrier at the end of omp for. The clause schedule(static) ensures that the OpenMP compiler assigns the same thread to corresponding iterations of the loops. In OpenMP all variables which are not local to a parallel region are considered as shared by default unless they are explicitly declared as private (using private clause) when they are passed to a parallel region.\n\nFig. 1.\n\nOpenMP example\n\n### 2.2 Permission-Based Separation Logic\n\nOur verification technique is based on Permission-based Separation Logic [7, 10]. Separation logic [21] is an extension of Hoare logic [14], originally proposed to reason about pointer programs. Separation logic is also suited for modular verification of concurrent programs [17]: two threads working on disjoint parts of the heap do not interfere and thus can be verified in isolation.\n\nThe basis of our specification language is a separation logic for C [22], extended with fractional permissions [7, 10] to denote the right to either read from or write to a location. Any fraction in the interval denotes a read permission, while 1 denotes a write permission. Permissions can be split and combined, but soundness of the logic prevents the sum of the permissions for a location over all threads to exceed 1. This guarantees that if permission specifications can be verified, the program is data race free. The set of permissions that a thread holds are often called its resources. In earlier work, we have shown that this logic is suitable to reason about kernel programs [5] and parallel loops [6].\n\nFormulas F in our logic are built from first-order logic formulas b, permission predicates , conditional expressions ( ), separating conjunction , and universal separating conjunction over a finite set I. The syntax of formulas is formally defined as follows:\n\nwhere b is a side-effect free boolean expression, l is a side-effect free expression of type location, and f is a side-effect free expression of type fraction. The semantics of formulas is given in the extended version of this paper [12].\n\n### 2.3 Iteration Contract\n\nAn iteration contract specifies the variables read and written by one iteration of the loop. In [6], we prove that if the iteration contract can be proven correct without any further specifications, the iterations are independent and the loop is parallelizable. If a loop has dependences, we can add additional specifications that capture these dependences, and describe how resources are transferred to another iteration of the loop. For example the iteration contract of consists of: a precondition and a post-condition .\n\n## 3 Syntax and Semantics of Deterministic Parallelism\n\nThis section presents the abstract syntax and semantics of PPL, our core language for deterministic parallelism.\n\nFig. 2.\n\nAbstract syntax for parallel programming language\n\n### 3.1 Syntax\n\nFigure 2 presents the PPL syntax. The basic building block of a PPL program is a block. Each block has a single entry point and a single exit point. Blocks are composed using three binary composition operators: parallel composition , fusion composition and sequential composition . The entry block of the program is the outermost block. Basic blocks are: a parallel block ( ) ; a vectorized block ( ) ; and a sequential block , where is a positive integer variable that denotes the number of parallel threads, i.e., the block's parallelization level, is a sequence of statements and is a sequence of guarded assignments . We assume a restricted syntax for fusion composition such that its operands are parallel basic blocks with the same parallelization levels. Each basic block has a local read-only variable called thread identifier where is the block's parallelization level. We generalize the term iteration to refer to the computations of a single thread in a basic block. So a parallel or vectorized block with parallelization level has iterations. For simplicity, but without loss of generality, threads have access to a single shared array which we refer to as heap. We assume all memory locations in the heap are allocated initially. A thread may update its local variables by performing a local computation ( ), or by reading from the heap ( ). A thread may update the heap by writing one of its local variables to it ( ).\n\n### 3.2 Semantics\n\nThe behaviour of PPL programs is described using a small step operational semantics. Throughout, we assume existence of the finite domains: , the set of variable names, , the set of all values, which includes the memory locations, , the set of memory locations and for thread identifiers. We write to concatenate two statement sequences ( ). To define the program state, we use the following definitions.\n\nNow we define . We distinguish various kinds of block states: an initial state , composite block states and , a state in which a parallel basic block should be executed , a local state in which a vectorized or a sequential basic block should be executed, and a terminated block state .\n\nThe state consists of a block statement . The state consists of two block states, and the state contains a block state and a block statement ; they capture all the states that a parallel composition and a sequential composition of two blocks might be in, respectively. The basic block state captures all the states that a parallel basic block ( ) might be in during its execution. It contains a mapping , that maps each thread to its local state, which models the parallel execution of the threads. There are three kinds of local states: a vectorized state , a sequential state , and a terminated sequential state .\n\nThe block state captures all states that a vectorized basic block ( ) might be in during its execution. It consists of , which maps each thread to its private memory, the body to be executed , a private memory , and a statement . As vectorized blocks may appear inside a sequential block, keeping and allows continuation of the sequential basic block after termination of the vectorized block. To model vectorized execution, the state contains an auxiliary set that models which threads have already executed the current instruction. Only when equals , the next instruction is ready to be executed. Finally, the block state consists of private memory and a statement .\n\nFig. 3.\n\nOperational semantics for program execution\n\nFig. 4.\n\nOperational semantics for thread execution\n\nWe model the program state as a triple of block state, program store and heap and thread state as a pair of local state and heap . The program store is constant within a block and it contains all global variables (e.g. the initial address of arrays). To simplify our notation, each thread receives a copy of the program store as part of its private memory when it initializes. The operational semantics is defined as a transition relation between program states: , (Fig. 3), using an auxiliary transition relation between thread local states , (Fig. 4), and a standard transition relation to evaluate assignments, (Fig. 5). The semantics of expression e and boolean expression b over private memory , written and respectively, is standard and not discussed any further. We use the standard notation for function update: given a function , , and :\n\nProgram execution starts in a program state where is the program's entry block. Depending on the form of , a transition is made into an appropriate block state, leaving the heap unchanged. The evaluation of a state non-deterministically evaluates one of its block states (i.e. or ), evaluation of a sequential block is done by evaluating the local state. The evaluation of a state evaluates its block state step by step when this evaluation is done, the subsequent block is initiated.\n\nThe evaluation of a parallel basic block is defined by the rules Par Step and Par Done. To allow all possible interleavings of the threads in the block's thread pool, each thread has its own local state , which can be executed independently, modeled by the mapping . A thread in the parallel block terminates if there is no more statement to be executed and a parallel block terminates if all threads executing the block are already terminated.\n\nThe evaluation of sequential basic block's statements as defined in Fig. 4 is standard except when it contains a vectorized basic block. A sequential basic block terminates if there is no instruction left to be executed (Seq Done). The execution of a vectorized block (defined by the rules Init Vec, Vec Step, Vec Sync and Vec Done in Fig. 4) is done in lock-step, i.e. all threads execute the same instruction and no thread can proceed to the next instruction until all are done, meaning that they all share the same program counter. As explained, we capture this by maintaining an auxiliary set, , which contains the identifier of the threads that have already executed the vector instruction (i.e. the guarded assignment ). When a thread executes a vector instruction, its thread identifier is added to (rules Vec Step). The semantics of vector instructions (i.e. guarded assignments) is the semantics of assignments if the guard evaluates to true and it does nothing otherwise. When all threads have executed the current vector instruction, the condition holds, and execution moves on to the next vector instruction of the block (with an empty auxiliary set) (rule Vec Sync). The semantics of assignments as defined in Fig. 5 is standard and does not require further discussion.\n\nFig. 5.\n\nOperational semantics for assignments\n\n## 4 Verification Approach\n\nThis section discusses our verification technique for reasoning about PPL programs, as well as soundness of our verification approach.\n\n### 4.1 Verification\n\nFor the verification of PPL programs, we assume that each basic block is specified by an iteration contract. We distinguish two kinds of formulas in an iteration contract: resource formulas (in permission-based separation logic) and functional formulas (in first-order logic). For an individual basic block if its iteration contract is proven correct, then the basic block is data race free and it is functionally correct w.r.t. its iteration contract. To verify the correctness of the program, using standard permission-based separation logic rules, the contracts of all composite blocks should be given. However, our verification approach requires only the basic blocks to be specified at the cost of an extra proof obligation that ensures that the heap accesses of all iterations which are not ordered sequentially are non-conflicting (i.e. they are disjoint or they are read accesses). If this condition holds, correctness of the PPL program can be derived from the correctness of a linearised variant of the program. The rest of this section discusses the formalization of our approach.\n\nTo verify a program, we require each basic block of the program to be specified by an iteration contract which consists of: a resource contract , and a functional contract , where i is the block's iteration variable. The functional contract consists of a precondition , and a postcondition . We also require the program to be globally specified by a contract which consists of the program's resource contract and the program's functional contract with the program's precondition and the program's postcondition .\n\nLet be the set of all PPL programs and be an arbitrary PPL program assuming that each basic block in is identified by a unique label. We define , as the finite set of basic block labels of the program . For a basic block with parallelization level , we define a finite set of iteration labels where indicates the iteration of the block . Let be the finite set of all iterations of the program .\n\nTo state our proof rule, we first define the set of all iterations which are not ordered sequentially, the incomparable iteration pairs, as:\n\nwhere is the least partial order which defines an extended happens-before relation. The extension addresses the iterations which are happens-before each other because their blocks are fused. We define based on two partial orders over the program's basic blocks: and . The former is the standard happens-before relation of blocks where they are sequentially composed by and the latter is an happens-before relation w.r.t. fusion composition . They are defined by means of an auxiliary partial order generator function such that: and . We define as follows:\n\nwhere .\n\nThe function computes the set of all iteration pairs of the input program which are in relation w.r.t. the given composition operator . This computation is basically a syntactical analysis over the input program. Now we define the extended partial order as:\n\nThis means that the iteration happens-before the iteration if happens-before (i.e. is sequentially composed with ) or if is fused with and and are corresponding iterations in and .\n\nFig. 6.\n\nProof rule for b-linearisation reduction of PPL programs.\n\nWe extend the program logic that we introduced in [6] with the proof rule b-linearise. We first define the block level linearisation (b-linearisation for short) as a program transformation which substitutes all non-sequential compositions by a sequential composition. We define as a subset of in which only sequential composition is allowed as composition operator.\n\nFigure 6 presents the rule b-linearise. In the rule, and are the resource contracts of two different basic blocks b and where and . Application of the rule results in two new proof obligations. The first ensures that all heap accesses of all incomparable iteration pairs (the iterations that may run in parallel) are non-conflicting (i.e. all block compositions in are memory safe). This reduces the correctness proof of to the correctness proof of its b-linearised variant (the second proof obligation). Then the second proof obligation is discharged in two steps: (1) proving the correctness of each basic block against its iteration contract (using the proof rule introduced in [6]) and (2) proving the correctness of against the program contract.\n\n### 4.2 Soundness\n\nNext we show that a PPL program with provably correct iteration contracts and a global contract that is provable in our logic extended with the rule b-linearise is indeed data race free and functionally correct w.r.t. its specifications. To show this, we prove soundness of the b-linearise rule, as well as data race freedom of all verified programs.\n\nFor the soundness proof, we show that for each program execution there exists a corresponding b-linearised execution with the same functional behaviour (i.e. they end in the same terminal state if they start in the same initial state) if all independent iterations are non-conflicting. From the rule's assumption, we know that if the precondition holds for the initial state of the b-linearised execution (which is also the initial state of the program execution) then its terminal state satisfies the postcondition. As both executions end in the same terminal state, the postcondition thus also holds for the program execution. To prove that there exists a matching b-linearised execution for each program execution, we first show that any valid program execution can be normalized w.r.t. program order and second that any normalized execution can be mapped to a b-linearised execution. To formalize this argument, we first define: an execution, an instrumented execution, and a normalized execution.\n\nWe assume all program's blocks including basic and composite blocks have a block label and program's statements are labelled by the label of the block to which they belong. Also there exists a total order over the block labels.\n\nDefinition 1\n\n(Execution). An execution of a program is a finite sequence of state transitions .\n\nTo distinguish between valid and invalid executions, we instrument our operational semantics with heap masks. A heap mask models the access permissions to every heap location. It is defined as a map from locations to fractions where is the set of fractions ([0, 1]). Any fraction (0, 1) is read and 1 is write permission. The instrumented semantics ensures that each transition has sufficient access permissions to the heap locations that it accesses. We first add a heap mask to all block state constructors ( , , and so on) and local state constructors ( , and ). Then we extend the operational semantics rules such that in each block initialization state with heap mask an extra premise should be discharged, which states that there are heap masks , one for each newly initialized state such that . The heap masks are carried along by the computation and termination transitions without any extra premises, while in the termination transitions heap masks of the terminated blocks are forgotten as they are not required after termination. As an example, we provide the instrumented versions of the rules Init ParC, ParC Done, rdsh, and wrsh.\n\nwhere and denote program and assignment transition relations in the instrumented semantics respectively. If a transition cannot satisfy its premises it blocks.\n\nDefinition 2\n\n(Instrumented Execution). An instrumented execution of a program is a finite sequence of state transitions where the set of all instrumented executions of is written as .\n\nLemma 1\n\nAssuming that (1) and (2) are valid for a program (i.e. every basic block in respects its iteration contract), for any execution E of the program , there exists a corresponding instrumented execution.\n\nProof\n\nGiven an execution E, we assign heap masks to all program states that the execution E might be in. The program's initial state is assigned by a heap mask . Assumption (1) implies that all iterations which might run in parallel are non-conflicting which implies that for all Init ParC transitions, there exist and such that where is the heap mask of the state in which Init ParC evaluates. In all computation transitions the successor state receives a copy of the heap mask of its predecessor. Assumption (2) implies that all iterations of all parallel and vectorized basic blocks are non-conflicting. This implies that for an arbitrary Init Par or Init Vec transition which initializes a basic block b, there exists such that holds in b's initialization transition and in all computation transitions of an arbitrary iteration i of the block b the premises of rdsh and wrsh transitions is satisfiable by .\n\nLemma 2\n\nAll instrumented executions of a program are data race free.\n\nProof\n\nThe proof proceeds by contradiction. Assume that there exists an instrumented execution that has a data race. Thus, there must be two parallel threads such that one writes to and the other one reads from or writes to a shared heap location e. Because all instrumented executions are non-blocking, the premises of all transitions hold. Therefore, holds for the first thread, and for the second thread either it writes or reads. Also because the program starts with one single main thread, both threads should have a single common ancestor thread z such that where x and y are the ancestors of the first and the second thread respectively. A thread only gains permission from its parent; therefore holds. Permission fractions are in the range [0, 1] by definition, therefore holds. This implies that if , then which is a contradiction.\n\nA normalized execution is an instrumented execution that respects the program order, which is defined using an auxiliary labelling function where is the set of all transitions, is the set of labels , and is the set of block labels (including both composite and basic block labels).\n\nwhere returns the label of each block or statement in the program. We assume the precedence order over . We say transition t with label (b, l) is less than with label if where returns the label set of all blocks of which b is composed.\n\nDefinition 3\n\n(Normalized Execution). An instrumented execution labelled by is normalized if the labels of its transitions are in non-decreasing order.\n\nWe transform an instrumented execution to a normalized one by safely commuting the transitions whose labels do not respect the program order.\n\nLemma 3\n\nFor each instrumented execution of a program , there exists a normalized execution such that they both end in the same terminal state.\n\nLemma 4\n\nFor each normalized execution of a program , there exists a b-linearised execution , such that they both end in the same terminal state.\n\nThe extended version of this paper [12] presents the proofs of Lemmas 3 and 4.\n\nDefinition 4\n\n(Validity of Hoare Triple). The Hoare triple is valid if for any execution (i.e. ) if is valid in the initial state of , then is valid in its terminal state.\n\nThe validity of and is defined by the semantics of formulas presented in the extended version of this paper [12].\n\nTheorem 1\n\nThe rule b-linearise is sound.\n\nProof\n\nAssume (1). and (2). . From assumption (2) and the soundness of the program logic used to prove it [6], we conclude (3). . Given a program , implication (3), assumption (1) and, Lemma 1 imply that there exists an instrumented execution for . Lemma 3 and Lemma 4 imply that there exists an execution for the b-linearised variant of , , such that both and end in the same terminal state. The initial states of both and satisfy the precondition . From assumption (2) and the soundness of the program logic used to prove it [6], holds in the terminal state of which thus also holds in the terminal state of as they both end in the same terminal state.\n\nFinally, we show that a verified program is indeed data race free.\n\nProposition 1\n\nA verified program is data race free.\n\nProof\n\nGiven a program , with the same reasoning steps mentioned in the Theorem 1, we conclude that there exists an instrumented execution for . From Lemma 2 all instrumented executions are data race free. Thus, all executions of a verified program are data race free.\n\n## 5 Verification of OpenMP Programs\n\nFinally, this section discusses the practical applicability of our approach, by showing how it can be used for verification of OpenMP programs. We demonstrate this in detail on the OpenMP program presented in Sect. 2.1. More OpenMP examples are available online1. Below we precisely identify a commonly used subset of OpenMP programs that can be verified in our approach.\n\nFig. 7.\n\nRequired contracts for verification of the running OpenMP example\n\nWe verify OpenMP programs in the following three steps: (1) specifying the program (i.e. providing an iteration contract for each loop and writing the program contract for the outermost OpenMP parallel region), (2) encoding of the specified OpenMP program into its PPL counterpart (carrying along the original OpenMP specifications), (3) checking the PPL program against its specifications. Steps two and three have been implemented as part of the VerCors toolset [4, 23]. The details of the encoding algorithm are discussed in the extended version of this paper [12].\n\nFigure 7 shows the required contracts for the example discussed in Sect. 2.1. There are four specifications. The first one is the program contract which is attached to the outermost parallel block. The others are the iteration contracts of the loops and . The requires and ensures keywords indicate pre and post-conditions of each contract and the context keyword is a shorthand for both requiring and ensuring the same predicate. We use and to denote separating conjunction and universal separating conjunction receptively. Before verification, we encode the example into the following PPL program :\n\nProgram contains three parallel basic blocks and and is verified by discharging two proof obligations: (1) ensures that all heap accesses of all incomparable iteration pairs (i.e. all iteration pairs except the identical iterations of and ) are non-conflicting implying that the fusion of and and parallel composition of and are memory safe (2) consists of first proving that each parallel basic block by itself satisfies its iteration contract , and second proving the correctness of the b-linearised variant of against its program contract .\n\nWe have implemented a slightly more general variant of PPL in the tool that supports variable declarations and method calls. To check the first proof obligation in the tool we quantify over pairs of blocks which allows the number of iterations in each block to be a parameter rather than a fixed number.\n\nFig. 8.\n\nOpenMP core grammar\n\nCaptured Subset of OpenMP. We define a core grammar which captures a commonly used subset of OpenMP [1]. This defines also the OpenMP programs that can be encoded into PPL and then verified using our approach. Figure 8 presents the OMP grammar which supports the OpenMP annotations: omp parallel, omp for, omp simd, omp for simd, omp sections, and omp single. An OMP program is a finite and non-empty list of Jobs enclosed by omp parallel. The body of omp for, omp simd, and omp for simd, is a for-loop. The body of omp single is either an OMP program or it is a sequential code block . The omp sections block is a finite list of omp section sub-blocks where the body of each omp section is either an OMP program or it is a sequential code block .\n\n## 6 Related Work\n\nBotincan et al. propose a proof-directed parallelization synthesis which takes as input a sequential program with a proof in separation logic and outputs a parallelized counterpart by inserting barrier synchronizations [8, 9]. Hurlin uses a proof-rewriting method to parallelize a sequential program's proof [15]. Compared to them, we prove the correctness of parallelization by reducing the parallel proof to a b-linearised proof. Moreover, our approach allows verification of sophisticated block compositions, which enables reasoning about state-of-the-art parallel programming languages (e.g. OpenMP) while their work remains rather theoretical.\n\nRaychev et al. use abstract interpretation to make a non-deterministic program (obtained by naive parallelization of a sequential program) deterministic by inserting barriers [20]. This technique over-approximates the possible program behaviours which ends up in a determinization whose behaviour is implied by a set of rules which decide between feasible schedules rather than the behaviour of the original sequential program. Unlike them, we do not generate any parallel program. Instead we prove that parallelization annotations can safely be applied and the parallelized program is functionally correct and exhibits the same behaviour as its sequential counterpart. Barthe et al. synthesize SIMD code given pre and postconditions for loop kernels in C++ STL or C# BCL [2]. We alternatively enable verification of SIMD loops, by encoding them into vectorized basic blocks. Moreover, we address the parallel or sequential composition of those loops with other forms of parallelized blocks.\n\nDodds et al. introduce a higher-order variant of Concurrent Abstract Predicates (CAP) to support modular verification of synchronization constructs for deterministic parallelism [13]. Their proofs use nested region assertions and higher-order protocols, but they do not address the semantic difficulties introduced by these features which make their reasoning unsound.\n\n## 7 Conclusion and Future Work\n\nWe have presented the PPL language which captures the main forms of deterministic parallel programming. Then, we proposed a verification technique to reason about data race freedom and functional correctness of PPL programs. We illustrated the practical applicability of our technique by discussing how a commonly used subset of OpenMP can be encoded into PPL and then verified.\n\nAs future work, we plan to look into adapting annotation generation techniques to automatically generate iteration contracts, including both resource formulas and functional properties. This will lead to fully automatic verification of deterministic parallel programs. Moreover, our technique can be extended to address a larger subset of OpenMP programs by supporting more complex OpenMP patterns for scheduling iterations and omp task constructs. We also plan to identify the subset of atomic operations that can be combined with our technique that allows verification of the widely-used reduction operations.\n\nReferences\n\n1.\n\nAviram, A., Ford, B.: Deterministic OpenMP for race-free parallelism. In: HotPar 2011, Berkeley, CA, USA, p. 4 (2011)\n\n2.\n\nBarthe, G., Crespo, J.M., Gulwani, S., Kunz, C., Marron, M.: From relational verification to SIMD loop synthesis. In: ACM SIGPLAN Notices, vol. 48, pp. 123\u2013134 (2013)\n\n3.\n\nBerger, M.J., Aftosmis, M.J., Marshall, D.D., Murman, S.M.: Performance of a new CFD flow solver using a hybrid programming paradigm. J. Parallel Distrib. Comput. 65(4), 414\u2013423 (2005)CrossRefMATH\n\n4.\n\nBlom, S., Huisman, M.: The VerCors tool for verification of concurrent programs. In: Jones, C., Pihlajasaari, P., Sun, J. (eds.) FM 2014. LNCS, vol. 8442, pp. 127\u2013131. Springer, Cham (2014). doi:10.\u200b1007\/\u200b978-3-319-06410-9_\u200b9 CrossRef\n\n5.\n\nBlom, S., Huisman, M., Mihel\u010di\u0107, M.: Specification and verification of GPGPU programs. Sci. Comput. Program. 95, 376\u2013388 (2014)CrossRef\n\n6.\n\nBlom, S., Darabi, S., Huisman, M.: Verification of loop parallelisations. In: Egyed, A., Schaefer, I. (eds.) FASE 2015. LNCS, vol. 9033, pp. 202\u2013217. Springer, Heidelberg (2015). doi:10.\u200b1007\/\u200b978-3-662-46675-9_\u200b14\n\n7.\n\nBornat, R., Calcagno, C., O'Hearn, P., Parkinson, M.: Permission accounting in separation logic. In: POPL, pp. 259\u2013270 (2005)\n\n8.\n\nBotincan, M., Dodds, M., Jagannathan, S.: Resource-sensitive synchronization inference by abduction. In: POPL, pp. 309\u2013322 (2012)\n\n9.\n\nBotin\u010dan, M., Dodds, M., Jagannathan, S.: Proof-directed parallelization synthesis by separation logic. ACM Trans. Program. Lang. Syst. 35, 1\u201360 (2013)CrossRef\n\n10.\n\nBoyland, J.: Checking interference with fractional permissions. In: Cousot, R. (ed.) SAS 2003. LNCS, vol. 2694, pp. 55\u201372. Springer, Heidelberg (2003). doi:10.\u200b1007\/\u200b3-540-44898-5_\u200b4 CrossRef\n\n11.\n\nChe, S., Boyer, M., Meng, J., Tarjan, D., Sheaffer, J.W., Lee, S.-H., Skadron, K.: Rodinia: a benchmark suite for heterogeneous computing. In: Workload Characterization, IISWC 2009, pp. 44\u201354 (2009)\n\n12.\n\nDarabi, S., Blom, S.C.C., Huisman, M.: A verification technique for deterministic parallel programs (extended version). Technical report TR-CTIT-17-01, Centre for Telematics and Information Technology, University of Twente (2017)\n\n13.\n\nDodds, M., Jagannathan, S., Parkinson, M.J.: Modular reasoning for deterministic parallelism. In: ACM SIGPLAN Notices, pp. 259\u2013270 (2011)\n\n14.\n\nHoare, C.: An axiomatic basis for computer programming. Commun. ACM 12(10), 576\u2013580 (1969)CrossRefMATH\n\n15.\n\nHurlin, C.: Automatic parallelization and optimization of programs by proof rewriting. In: Palsberg, J., Su, Z. (eds.) SAS 2009. LNCS, vol. 5673, pp. 52\u201368. Springer, Heidelberg (2009). doi:10.\u200b1007\/\u200b978-3-642-03237-0_\u200b6 CrossRef\n\n16.\n\nJin, H.-Q., Frumkin, M., Yan, J.: The OpenMP implementation of NAS parallel Benchmarks and its performance (1999)\n\n17.\n\nO'Hearn, P.W.: Resources, concurrency and local reasoning. Theoret. Comput. Sci. 375(1\u20133), 271\u2013307 (2007)MathSciNetCrossRefMATH\n\n18.\n\nOpenMP Architecture Review Board: OpenMP API specification for parallel programming. http:\/\/\u200bopenmp.\u200borg\/\u200bwp\/\u200b. Accessed 28 Nov 2016\n\n19.\n\nLLNL OpenMP Benchmarks. https:\/\/\u200basc.\u200bllnl.\u200bgov\/\u200bCORAL-benchmarks\/\u200b. Accessed 28 Nov 2016\n\n20.\n\nRaychev, V., Vechev, M., Yahav, E.: Automatic synthesis of deterministic concurrency. In: Logozzo, F., F\u00e4hndrich, M. (eds.) SAS 2013. LNCS, vol. 7935, pp. 283\u2013303. Springer, Heidelberg (2013). doi:10.\u200b1007\/\u200b978-3-642-38856-9_\u200b16 CrossRef\n\n21.\n\nReynolds, J.: Separation logic: a logic for shared mutable data structures. In: Logic in Computer Science, pp. 55\u201374. IEEE Computer Society (2002)\n\n22.\n\nTuch, H., Klein, G., Norrish, M.: Types, bytes, and separation logic. In: Hofmann, M., Felleisen, M. (eds.) POPL, pp. 97\u2013108. ACM (2007)\n\n23.\n\nVerCors project homepage, 28 September 2016. http:\/\/\u200bwww.\u200butwente.\u200bnl\/\u200bvercors\/\u200b\n\nFootnotes\n\n1\n\nSee the online version of the VerCors toolset at http:\/\/\u200bwww.\u200butwente.\u200bnl\/\u200bvercors\/\u200b.\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_18\n\n# Systematic Predicate Abstraction Using Variable Roles\n\nYulia Demyanova1 , Philipp R\u00fcmmer2 and Florian Zuleger1\n\n(1)\n\nVienna University of Technology, Vienna, Austria\n\n(2)\n\nUppsala University, Uppsala, Sweden\n\nYulia Demyanova\n\nEmail: demy@forsyte.at\n\nPhilipp R\u00fcmmer (Corresponding author)\n\nEmail: philipp.ruemmer@it.uu.se\n\nAbstract\n\nHeuristics for discovering predicates for abstraction are an essential part of software model checkers. Picking the right predicates affects the runtime of a model checker, or determines if a model checker is able to solve a verification task at all. In this paper we present a method to systematically specify heuristics for generating program-specific abstractions. The heuristics can be used to generate initial abstractions, and to guide abstraction refinement through templates provided for Craig interpolation. We describe the heuristics using variable roles, which allow us to pick domain-specific predicates according to the program under analysis. Variable roles identify typical variable usage patterns and can be computed using lightweight static analysis, for instance with the help of off-the-shelf logical programming engines. We implemented a prototype tool which extracts initial predicates and templates for C programs and passes them to the Eldarica model checker in the form of source code annotations. For evaluation, we defined a set of heuristics, motivated by Eldarica's previous built-in heuristics and typical verification benchmarks from the literature and SV-COMP. We evaluate our approach on a set of more than 500 programs, and observe an overall increase in the number of solved tasks by 11.2%, and significant speedup on certain benchmark families.\n\nY. Demyanova and F. Zuleger were supported by the Austrian National Research Network S11403-N23 (RiSE) of the Austrian Science Fund (FWF).\n\n## 1 Introduction\n\nAnalysis tools, in particular software model checkers, achieve automation by mapping systems with infinite state space to finite-state abstractions that can be explored exhaustively. One of the most important classes of abstraction is predicate abstraction [13], defined through a set of predicates capturing relevant data or control properties in a program. Picking the right predicates, either upfront or dynamically during analysis [5], is essential in this setting to ensure rapid convergence of a model checker, and is in practice achieved through a combination of \"systematic\" methods (for CEGAR, in particular through Craig interpolation) and heuristics. For instance, SLAM extracts refinement predicates from counterexamples using domain-specific heuristics [16]; YOGI uses machine learning to choose the default set of heuristics for picking predicates [19]; CPAchecker uses domain types to decide whether to represent variables explicitly or using BDDs [2], and to choose refinement predicates [4]; and Eldarica uses heuristics to guide the process of Craig interpolation [18]. Similar heuristics can be identified in tools based on abstract interpretation, among others.\n\nThe goal of the present paper is to systematise the definition of abstraction heuristics, and this way enable easier and more effective adaptation of analysis tools to specific domains. In order to effectively construct program abstractions, it is essential for an analysis tool to have (semantic) information about variables and data-structures used in the program. We propose a methodology in which heuristics are defined with the help of variable roles [9], which are features capturing typical variable usage patterns and which can be computed through lightweight static analysis. Knowledge about roles of variables can be used to generate problem-specific parameters for model checkers, or other analysis tools, and thus optimise the actual later analysis process.\n\nAs a case study, we describe how variable roles can be used to infer code annotations for the CEGAR-based model checker Eldarica [20]. Eldarica has two main parameters controlling the analysis process: initial predicates for predicate abstraction, and templates guiding Craig interpolation during counterexample-based refinement [18]. Both parameters can be provided in the form of source-code annotations. We focus on the analysis of C programs defined purely over integer scalar variables, i.e., not containing arrays, pointers, heap-based data structures and bitvectors. By manually inspecting a (small) sample of such programs from SV-COMP [3], we were able to identify a compact set of relevant variable roles, and of heuristics for choosing predicates and templates based on those roles. To evaluate the effectiveness of the heuristics, we compared the performance of Eldarica (with and without the heuristics), and of other model checkers on a set of over 500 programs taken from the literature and SV-COMP. We observe an increase in the number of solved tasks by 11.2% when using our heuristics, and speedups on certain benchmark families.\n\nContributions of the paper are: 1. We introduce a methodology for defining abstraction heuristics using variable roles; 2. we define 8 roles and corresponding heuristics for efficiently analysing C programs with scalar variables; 3. we implement our approach and perform an extensive experimental evaluation.\n\nRelated Work. Patterns of variable usage were studied in multiple disciplines, e.g. in teaching programming languages [21] (where the patterns were called variable roles), in type systems for inferring equivalence relations for types [22], and others. In [9] a set of patterns, also called variable roles, was defined using data-flow analysis, based on a set of C benchmarks1. In [7, 8] variable roles were used to build a portfolio solver for software verification. Similarly to variable roles, code patterns recognised with light-weight static analyses are used in the bug-finding tool Coverity [11] to devise heuristics for ranking possible bugs. Domain types in CPAChecker [4] can be viewed as a restricted class of variable roles. Differently from this work, where variable roles guide the generation of interpolants, the domain types are used in [4] to choose the \"best\" interpolant from a set of generated interpolants. In addition, our method generates role-based initial predicates, while the method of [4] does not.\n\nThere has been extensive research on tuning abstraction refinement techniques, in such a way that convergence of model checkers is ensured or improved. This research in particular considers various methods of Craig interpolation, and controls features such as interpolant strength, interpolant size, the number of distinct symbols in interpolants, or syntactic features like the magnitude of coefficients; for a detailed survey we refer the reader to our previous work [18].\n\n### 1.1 Introductory Examples of Domain-Specific Abstraction\n\nWe introduce our approach on two examples. These and all further examples in this paper are taken from the benchmarks of the software competition SV-COMP'16 [3]. We simplified some of the examples for demonstration purposes.\n\nFig. 1.\n\nMotivation examples illustrating variable roles.\n\nMotivation Example 1. The code in Fig. 1.1 initializes variables max1, max2 and max3 to id1, id2 and id3 respectively, which are in turn initialized non-deterministically. The assume statement at lines 9\u201310 is an Eldarica-specific directive, which puts a restriction that control reaches line 12 only if id1!=id2&& id1!=id3&& id2!=id3 evaluates to true. In the loop the value max{id1,id2,id3}, which is the maximum of id1, id2 and id3 is calculated: At the first iteration, max1 is assigned the value max{id1,id3}, and max2 and max3 are assigned the value max{id1,id2,id3}. After the second iteration max1, max2 and max3 all store the value max{id1,id2,id3}. Since id1, id2 and id3 have distinct values, only one of the conditions in lines 18\u201320 evaluates to true. The assertion checks that the value of exactly one of variables max1, max2 and max3 remains unchanged after two iterations, namely max , where .\n\nIt takes Eldarica 27 CEGAR iterations and 19 sec to prove the program safe. However, for 88 out of 108 original programs from SV-COMP with this pattern in category \"Integers and Control Flow\", of which the code in Fig. 1.1 is a simplified form2, Eldarica does not give an answer within the time limit of 15 min. Predicate abstraction needs to generate for these programs from 116 to 996 predicates, depending on the number of values, for which the maximum is calculated. Since predicates are added step-wise in the CEGAR loop, checking these benchmarks is time consuming. We therefore suggest a method of generating the predicates upfront.\n\nIn order to prove that exactly one condition in lines 18\u201320 evaluates to true and cnt is incremented by one, predicate abstraction needs to track the values assigned to variables max1, max2 and max3 with 9 predicates: max1==id1, max1==id2, max1==id3, etc. Additionally, in order to precisely evaluate conditions in lines 13\u201315, abstraction needs to track the ordering of variables id1, id2 and id3 with 6 predicates which compare variables id1, id2 and id3 pairwise: , and so on.\n\nTo generate the above mentioned 15 predicates our algorithm uses the following variable roles. Variable is input if it is assigned a return value of an external function call. This pattern is often used in SV-COMP to initialize variables non-deterministically, e.g. id1=nondet_char(), where variables id1, id2, id3 are inputs. Variables which are assigned only inputs are run-time analogues of compile-time enumerations. A variable is dynamic enumeration if it is assigned only constant values or input variables, i.e. variables max1, max2 and max3 are dynamic enumerations. For each dynamic enumeration x which takes values v1, ,vn, our algorithm generates n equality predicates: x==v1, , x==vn.\n\nVariable x is extremum if it is used in the pattern if(comp_expr)x = y, where comp_expr is a comparison operator or applied to y and some expression expr, e.g. . For every variable x which is both dynamic enumeration and extremum, our algorithm generates pairwise comparisons for all pairs of input values v1, ,vn assigned to x, e.g. , and so on.\n\nEldarica proves the program in Fig. 1.1 annotated with the 15 predicates in 8 sec and 0 CEGAR iterations, and it takes Eldarica from 21 to 858 sec (and from 0 to 4 CEGAR iterations) to prove 53 programs from SV-COMP with this pattern annotated analogously. For the remaining 55 benchmarks with this pattern from SV-COMP the number of abstract states becomes too large for Eldarica to be checked within the time limit.\n\nMotivation Example 2. The code in Fig. 1.2 increments variables i and k in the loop at line 6 until i reaches n, and decrements variables j and k in the loop at lines 7\u20139 until j reaches 0. The assertion checking that the value of variable k remains positive in the loop can be proven using the predicates and . These predicates are difficult to find, e.g., the baseline version of Eldarica [20] keeps generating a sequence of pairs of predicates , etc. As demonstrated by this example, heuristics are needed to guide interpolation towards finding suitable refinement predicates. The community has suggested various heuristics for the above example, e.g., the most recent version of Eldarica [18] proves the program safe in 5 sec and 6 CEGAR iterations.\n\nWe suggest to generate predicate templates demand-driven from the code under analysis. For the above example, we propose a heuristic which tracks the dependencies between loop counters: The heuristic searches for variables x assigned in a loop in a statement matching the pattern x=x+expr, where expr is an arbitrary expression. For each pair x1 and x2 of such variables the heuristic generates a predicate template x1-x2. This template restricts the search space of the interpolation solver to predicates of the form . To formalise the heuristic we introduce the following role: local counter is a variable assigned in a loop in a statement x=x+expr, where expr is an arbitrary expression. Note that we do not restrict expr to be a constant, in contrast to induction variables [1], since the heuristic is a trade-off between generality and computational cost and performs well in practice.\n\nMethodology for Choosing Roles. To choose roles and role-based predicates and templates, we investigated benchmarks of the competition SV-COMP'16 from categories \"Integers and Control Flow\" and \"Loops\" and loop invariant generation benchmarks (appr. 30 benchmarks altogether) on which Eldarica did not give an answer within the time limit of 15 min. We manually inspected the code of these benchmarks and annotated the benchmarks with a minimum set of predicates and templates so that Eldarica checks the benchmarks within the time limit. We then derived new variable roles which captured specific code patterns in which the annotated variables were used.\n\n## 2 Predicate Abstraction and Refinement\n\nWe outline the algorithm implemented by predicate abstraction-based software model checkers, in particular the Eldarica tool [20] used as test-bed. As the core procedure, Eldarica applies predicate abstraction [13] and counterexample-guided abstraction refinement [5] to check the satisfiability of Horn constraints expressing safety properties of a software program [14, 15, 20]. The procedure has two main parameters that can be used to tune the abstraction process:\n\n * initial predicates for predicate abstraction (see Sect. 2.1);\n\n * interpolation templates T that guide Craig interpolation towards meaningful predicates during abstraction refinement (see Sect. 2.2).\n\nThe pair can be computed with the help of variable roles, as outlined in the previous section. It is important to note that neither parameter has any effect on soundness of a model checker, only termination is affected.\n\n### 2.1 Solving Horn Clauses with Predicate Abstraction\n\nA Horn clause is a formula of the form , with constraint , body literals containing uninterpreted relation symbols, and head literal H. Eldarica has a C\/C++ front-end that translates software programs to sets of Horn clauses. In this setting, relation symbols represent state invariants associated with a control location c of a program, and Horn clauses express 1. pre-conditions for program entry points c; 2. Floyd-style inductiveness conditions , for transitions between control locations ; and 3. safety assertions for control locations c. The translation from software programs to Horn clauses is defined such that the program is safe if and only if the clauses are satisfiable, i.e., if and only if the predicates can be interpreted in such a way that all clauses become valid.\n\nModel checkers like HSF [14] or Eldarica [20] construct solutions of Horn clauses in disjunctive normal form by building an abstract reachability graph (ARG) over a set of given predicates. For this, a Horn solver maintains a mapping from relation symbols to finite sets of predicates. The solver starts from some initial mapping ; for instance, mapping every relation symbol to an empty set of predicates. The solver will then attempt to construct a closed ARG by means of fixed-point computation, which can either succeed (in which case a solution of the Horn clauses has been derived), or fail because some assertion clause is violated during the construction. In the latter case, a connected acyclic ARG fragment can be extracted that leads from entry clauses (clauses without relation symbols in the body) to the violated assertion clause. A theorem prover is then used to verify that the counterexample is genuine; spurious counterexamples are eliminated by generating additional predicates by means of Craig interpolation, leading to an extended mapping and refined abstraction.\n\n### 2.2 Craig Interpolation with Templates\n\nPredicate abstraction-based model checkers rely on theorem provers to find suitable interpolants, or interpolants containing the right predicates, in a generally infinite lattice of interpolants for every extracted counterexample (represented as acyclic ARG fragments). Eldarica uses interpolation abstraction [18] as a semantic way to guide the interpolation procedure towards \"good\" interpolants; in this method, interpolation queries are instrumented to restrict the symbols that can occur in interpolants, ranking the interpolants with the help of templates. It has previously been shown that interpolation abstraction can significantly improve the performance of Horn solvers [18].\n\nIn the scope of this paper, we focus on templates in the form of terms. As an example, consider the binary interpolation query with and . The interpolation problem has multiple solutions I (with the property that and ), including and . In a software model checker, clearly is preferable, since it abstracts from concrete values of the variables. Interpolation abstraction can be used to distinguish between and , by preventing theorem provers, e.g., to compute as an interpolant. For this, template terms are used to capture the expressions that an interpolant might contain. In the example, given templates , a theorem prover could compute either of ; with the template , a theorem prover could return , but no longer .\n\nIn Eldarica, software programs can be annotated to express preference of certain interpolants. For instance, line 4 of the code in Fig. 1.2 can be annotated to express that the differences i-k and j-k are preferred templates:\n\nAnnotations are attached to variable declarations, and are then applied when computing interpolants at control points in the scope of the variable. If no interpolant can be constructed using this template, a conventional interpolant will be used. Besides manual annotation, Eldarica also has a set of inbuilt heuristics to choose meaningful templates automatically [18].\n\n## 3 Role-Based Predicates and Templates\n\nSpecification Language for Roles. In this section we describe a framework for the specification and computation of role-based initial predicates and predicate templates. Roles are usage patterns of variables, we introduce and formalize them as data-flow analyses in our previous work [9]. Here we re-formulate roles as logic queries on the control-flow graph (CFG) of a program. We choose logic programming as a formalism for two reasons: first, its notation is well known, and second, we can use of-the-shelf logic engines for the computation of roles. Specifically, we use the syntax and standard fixed point semantics of Datalog.\n\nPreliminaries on Datalog. A rule in Datalog is of the form . The head of a rule A is an atom. The body of a rule is a set of literals, and each literal L is of the form A or not A for an atom A, where the connective not corresponds to default negation. An atom takes boolean values and is of the form 1. , or 2. , or 3. , where p is a predicate symbol, f is a function symbol, t are term symbols and op is a comparison operator (e.g. , etc.). Atom always evaluates to true and assigns to term t the result of function . Each term t is a constant symbol (i.e. a function symbol with arity 0), a variable, or an integer. Predicate and function symbols start with a small letter, and variables start with a capital letter. A rule is evaluated as follows: if every literal L in the body evaluates to true, then the atom A in the head evaluates to true. A rule with empty body is called a fact.\n\nFig. 2.\n\nTranslation of C code to a logic program\n\nTranslation of C Code to a Logic Program. We assume a C program to be given as a logic program, where each node and edge in the control-flow graph is translated to one or more facts in the logic program. For example, the code in Fig. 2a is translated to a logic program in Fig. 2b (see the CFG in Fig. 2c). In particular, the loop condition is represented with nodes 6, 3 and 7 in the CFG and lines 7\u20138 and 14\u201319 in the logic program. Below we will denote a node corresponding to variable x in the control-flow graph with node .\n\nFig. 3.\n\nSimplified specification of roles and role-based templates and initial predicates.\n\nWe define roles local counter, extremum, input and dynamic enumeration in Fig. 3. Specifically, in Fig. 3a we define role local counter which is used to generate templates, and in Fig. 3b we define roles which are used to generate initial predicates. Due to the lack of space we introduce the remaining roles and the generated predicates and templates informally in Table 1. We explain the definitions of roles in Sect. 3.1, and the generation of predicates and templates for these roles in Sect. 3.2.\n\n### 3.1 Definition of Roles\n\nRole Local Counter. Role local counter (line 2\u20134 in Fig. 3) is defined in the scope of one loop. The set of variables to which this role is ascribed is encoded with a binary relation local_cnt with a parameter corresponding to the resp. loop statement WhileStmt. The parameter is needed, because we later define a template for pairs of local counters, such that the counters have the same parameter. A variable X is ascribed role local counter if there is a loop statement WhileStmt, in the body of which X is assigned the sum of X and some other expression. Term sub_stmt(Stmt,SubStmt) encodes that in the control flow graph SubStmt is a descendant of Stmt. Term assigned(X,Expr,AsgnStmt) encodes that variable X is assigned expression Expr in statement AsgnStmt. Term operand(Expr,Bop) encodes that Expr is an operand of binary operator Bop. For example, for code in Fig. 2a the evaluation of the rule derives the fact local_cnt(3) for node . For clarity we omit rules for terms sub_stmt, assigned, operand and a rule for the case when the counter is decremented.\n\nTable 1.\n\nInformal description of remaining roles with examples.\n\nRole name | # | Description of role | \/ T | Example\n\n---|---|---|---|---\n\nCode | Generated predicates \/templates T\n\nAssertion condition | 1 | Variable is used in pattern assert(expr) | | assert( cnt==1) | {cnt==1}\n\n2 | Statement assert(expr) is nested in an if statement with condition cond | | |\n\nParity variable | 3 | Variable x is used in remainder operator x%c | | x%2 | {x%2}\n\n4 | Variable x is incremented in a loop by constant c, s.t. c!=1 | | | {x%2}\n\nLoop iterator | 5 | Variable x is modified in a loop and is used in the loop condition cond | | |\n\n6 | In addition to 5), cond matches pattern expr1!=expr2 | | for(i=0; i!=n;i++) |\n\n7 | In addition to 5), cond matches pattern (resp. ) and loop iterator is changed by 1 in the loop | (resp. ) | |\n\nLoop bound | 8 | Variable bnd is compared to loop iterator it in loop condition: , where ; and bnd is assigned in statement bnd=expr | | |\n\nRole Extremum. Role extremum (lines 2\u20134) is ascribed to variable X, denoted with term extremum(X), if there is an if statement IfStmt, the condition Cond of which is a binary operator greater-than or less-than (encoded with term strict_rel_opcode(Opcode)), s.t. Cond contains a variable Y which is assigned to X in the body of IfStmt. For example, for code (line 13 in Fig. 1.1), the result of evaluating the rule is . Relation strict_rel_opcode(Opcode) encodes that its parameter is a greater-than or less-than operator.\n\nRole Input. Role input (lines 7\u20138) is ascribed to variable X if X is assigned the result of a call CallExpr to a function Func, the body of which is not defined (encoded with atom not body(Func)). For example, for the C code id1=nondet_char() where nondet_char() is defined as an external function (lines 1 and 3 in Fig. 1.1), evaluation of the rule derives fact input(node ).\n\nRole Dynamic Enumeration. Role dynamic enumeration (lines 11\u201318) is defined via its complement not_dyn_enum (line 11). Fact not_dyn_enum(X) is generated if variable X is assigned an expression Expr which does not belong to relation dyn_enum_expr (lines 14\u201315). The unary relation dyn_enum_expr includes constant literals and input variables (lines 17\u201318). For example, for code in Fig. 1.1 evaluation of rules derives facts dyn_enum(node ), dyn_enum(node ) and dyn_enum(node ).\n\n### 3.2 Role-Based Predicates and Templates\n\nOur algorithm generates initial predicates and templates , where pred(p) and tpl(t) are the facts derived by the logic program (see line 7 in Fig. 3a and lines 21\u201322 and 25\u201327 in Fig. 3b). We now describe the role-based initial predicates and templates in detail.\n\nLocal Counter. For every pair of local counters X and Y s,t. X and Y are modified in loop WhileStmt, a template X-Y is derived (lines 7\u20138). For example, for code in Fig. 1.2 the evaluation of the rule derives templates i-k and j-k.\n\nDynamic Enumeration. For every pair of a dynamic enumeration X and input Y, s.t. Y is assigned to X, predicate X==Y is derived (lines 21\u201322). Term @concat encodes a call to a function which concatenates its parameters. For example, for code in Fig. 1.1 the evaluation of the rule derives predicates max1==id1, max2==id2 and max3==id3.\n\nInput Variables. For every pair of input variables Y and Z, s.t. both Y and Z are assigned to dynamic enumeration and extremum X, predicate is derived (lines 25\u201327). For example, for code in Fig. 1.1 the evaluation of rules derives predicates and .\n\n## 4 Evaluation\n\nWe implemented our approach in a prototype tool and evaluated the tool on altogether 549 C benchmarks3.\n\nTable 2.\n\nCharacteristics of the benchmarks\n\n# | Name | Number of files | Size, KLOC\n\n---|---|---|---\n\nTotal | Safe | Unsafe\n\n1 | SV-COMP CFI | 234 | 91 | 143 | 226.4\n\n2 | SV-COMP Loops | 95 | 68 | 27 | 6.5\n\n3 | VeriMAP | 153 | 133 | 20 | 13.2\n\n4 | Llreve | 21 | 16 | 5 | 0.6\n\n5 | HOLA | 46 | 46 | 0 | 1.4\n\nTotal | 549 | 354 | 195 | 248.0\n\nTable 3.\n\nEldarica configurations. denotes the templates generated by built-in heuristics of Eldarica.\n\nName | | T\n\n---|---|---\n\nEld | |\n\nEld+B | |\n\nEld+R | |\n\nEld+BR | |\n\nBenchmarks. Table 2 lists the benchmarks and gives their characteristics. Specifically, the benchmarks contain (listed in the same order as in Table 2):\n\n 1. 1.\n\nBenchmarks of the competition SV-COMP'16 from the \"Integers and Control Flow\" category. We excluded the Recursive sub-category and 75 benchmarks which contain C structures and arrays;\n\n 2. 2.\n\nBenchmarks from the Loops category of SV-COMP'16 (we excluded 50 benchmarks for same reasons);\n\n 3. 3.\n\nBenchmarks of the verification tool VeriMAP 4. We excluded 234 duplicate benchmarks contained in SV-COMP CFI, and 2 benchmarks, for which the transition relations cannot be expressed with Presburger arithmetic;\n\n 4. 4.\n\nSimplified versions5 of the benchmarks of tool llr\u00eave for automated program equivalence checking [12];\n\n 5. 5.\n\nLoop invariant generation benchmarks of the verication tool HOLA [10].\n\nTools for Comparison. We evaluate the following configurations of Eldarica: without interpolation abstraction (to which we refer by Eld), with templates (Eld+B), with roles (Eld+R), and with a combination of templates and roles (Eld+BR). Table 3 lists different choices for the parameters and T described in Sect. 2. As a baseline we also compare Eldarica to SMT solvers Z3 [6] and Spacer [17]. We could not compare to the duality engine of Z3 because of a bug in duality, which was not fixed by the time of paper submission. Finally, we compare Eldarica to the model checker CPAchecker, which is not based on Horn clauses. CPAchecker has very successfully participated in the software competition in the recent years and thus provides an interesting choice for comparison.\n\nExperimental Setup. We performed our experiments on 2.0GHz AMD Opteron PC (31GB RAM, 64KB L1 cache, 512KB L2 cache). We did not restrict the number of cores on which the tasks were performed. We report the wall-clock time measured using the date shell utility. For evaluation we set the value of timeout for all tools to 15 min, which is the value of the timeout in the SV-COMP competition. We put no memory limit on the tools.\n\nOverall Improvement of Eldarica. The results of our evaluation are represented in Fig. 4, which shows the number of solved and unsolved tasks, with safe and unsafe tasks counted separately. Specifically, Fig. 4a gives a summary for all benchmarks, and Figs. 4b-4f show detailed results for each benchmark. In the bar plots on top of each bar is the mean runtime of the respective tool, calculated without timeouts. The times for Eld+R include the times for computing roles: the mean and median time of annotating a program for all benchmarks amount to 3.8 sec and 0.8 sec resp. We observe that the best configuration of Eldarica is Eld+R, which solves the highest number of tasks for every benchmark separately and for all benchmarks. The second best configuration for most benchmarks is Eld+B. Overall Eld+R solves 11.2% more tasks than Eld+B: 4.6% more safe and 6.6% more unsafe tasks. We conclude that the configuration Eld+R improves on the previous configurations of Eldarica (Eld and Eld+B).\n\nFig. 4.\n\nBar plots comparing the percentage of proved tasks for CPAchecker, Z3, Spacer and different Eldarica configurations. Inside each bar is the percentage of the resp. answers. On top of each bar is the mean runtime computed without timeouts (for solved tasks).\n\nComparison of Runtimes. Overall, the runtime of Eld+R is comparable to the runtime of other Eldarica's configurations, but for the benchmarks SV-COMP CFI we observe a significant speedup of Eld+R, as shown in Fig. 5. SV-COMP CFI is a specific family of benchmarks because of their big size and a large number of enumeration variables, see e.g. the code in Fig. 1.1. Note that in Fig. 5 we compare Eld+R to Eld, which is the second best configuration, because for these benchmarks no heuristics are needed. The speedup of Eld+R for SV-COMP CFI is caused by a considerable decrease in the number of CEGAR iterations. To demonstrate this, we evaluate the configuration Eld+B with the timeout value of one hour (denoted as Eld+BH in Fig. 4c). We observe that Eld+BH solves 12.8% more unsafe and 9.0% more safe tasks than Eld+B. To conclude, Eld+R does not increase the runtime on all benchmarks, and even shows a significant speedup for the family of benchmarks from SV-COMP CFI.\n\nFig. 5.\n\nScatter plots comparing the number of CEGAR iterations and runtime, both in logarithmic scale, of configurations Eld+R and Eld for benchmark SV-COMP CFI. The mean runtime of Eld+R is 1.5 times smaller than that of Eld, and the average number of CEGAR iterations of Eld+R is 19.0 times smaller than that of Eld, the four values calculated on the tasks solved by both Eld and Eld+R.\n\nComparison of Roles with Eldarica's Previous Heuristics. A comparison of Eld+R to Eld+B shows that all but one benchmarks solved by old configurations of Eldarica can also be solved by Eld+R. The one benchmark not solved by Eld+R requires a predicate relating three variables in an equality, which according to our experience does not fall into frequently used patterns. Moreover, as Fig. 4 shows, the configuration Eld+BR, which combines roles and old heuristics of Eldarica, solves 3% less tasks than Eld+R. One possible reason for the slowdown (and consequently the lower number of solved benchmarks) of Eld+BR are redundant predicates generated by built-in heuristics of Eldarica. These results confirm that our framework not only describes new heuristics but also captures all previous heuristics of Eldarica.\n\nImprovement on Unsafe Benchmarks. Surprisingly, the initial predicates also help to solve more unsafe benchmarks, as Fig. 4c shows. In principle, these predicates can be found by Eld+B with a higher value of runtime, as demonstrated by the configuration Eld+BH. We conclude that when variable roles are used, the number of solved unsafe tasks does not decrease in general and even increases for SV-COMP CFI benchmarks.\n\nComparison of Eldarica to SMT Solvers. We compare Eldarica to SMT solvers Z3 and Spacer6. We note that a small number of tasks in benchmarks SV-COMP Loops and HOLA cannot be processed by Z3 and Spacer because of existential quantifiers in the SMT translation, which is not in the fragment handled by the PDR engine of Z3. We denote these benchmarks as \"Not Supported\" in Fig. 4. We observe that, on one hand, all configurations of Eldarica outperform both Z3 and Spacer in the number of solved tasks, in particalar Eld+R solves 30% more tasks than Z3. We note, however, that our method for guiding predicate abstraction uses the structure of a program, which is not preserved on the level of SMT formulae. On the other hand, the mean runtime of Z3 is 2.0 times lower than the mean runtime of Eld+R. To conclude, Eldarica outperforms Z3 and Spacer in the number of solved tasks, but loses in speed.\n\nComparison of Eldarica to CPAChecker. Finally, we compare Eldarica to the model checker CPAchecker. We observe that on safe and unsafe tasks the tools show complementary strengths. In particular, CPAchecker proves more tasks unsafe than Eldarica on CFI benchmarks, and on other benchmark sets shows comparable to Eldarica results. For safe benchmarks, however, on all benchmark sets CPAchecker can prove fewer programs safe than the Eldarica configurations Eld+B, Eld+R and Eld+BR. To conclude, Eldarica with interpolation abstraction outperforms CPAchecker on safe benchmarks, while CPAchecker performs better on a family of unsafe benchmarks.\n\nReferences\n\n1.\n\nAho, A.V., Sethi, R., Ullman, J.D.: Compilers, Principles. Techniques. Addison Wesley, Boston (1986)\n\n2.\n\nApel, S., Beyer, D., Friedberger, K., Raimondi, F., Rhein, A.: Domain types: abstract-domain selection based on variable usage. In: Bertacco, V., Legay, A. (eds.) HVC 2013. LNCS, vol. 8244, pp. 262\u2013278. Springer, Cham (2013). doi:10.\u200b1007\/\u200b978-3-319-03077-7_\u200b18 CrossRef\n\n3.\n\nBeyer, D.: Reliable and reproducible competition results with benchexec and witnesses (report on SV-COMP 2016). In: Chechik, M., Raskin, J.-F. (eds.) TACAS 2016. LNCS, vol. 9636, pp. 887\u2013904. Springer, Heidelberg (2016). doi:10.\u200b1007\/\u200b978-3-662-49674-9_\u200b55 CrossRef\n\n4.\n\nBeyer, D., L\u00f6we, S., Wendler, P.: Refinement selection. In: Fischer, B., Geldenhuys, J. (eds.) SPIN 2015. LNCS, vol. 9232, pp. 20\u201338. Springer, Cham (2015). doi:10.\u200b1007\/\u200b978-3-319-23404-5_\u200b3 CrossRef\n\n5.\n\nClarke, E.M., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement for symbolic model checking. J. ACM 50(5), 752\u2013794 (2003)MathSciNetCrossRefMATH\n\n6.\n\nMoura, L., Bj\u00f8rner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337\u2013340. Springer, Heidelberg (2008). doi:10.\u200b1007\/\u200b978-3-540-78800-3_\u200b24 CrossRef\n\n7.\n\nDemyanova, Y., Pani, T., Veith, H., Zuleger, F.: Empirical software metrics for benchmarking of verification tools. In: Kroening, D., P\u0103s\u0103reanu, C.S. (eds.) CAV 2015. LNCS, vol. 9206, pp. 561\u2013579. Springer, Cham (2015). doi:10.\u200b1007\/\u200b978-3-319-21690-4_\u200b39 CrossRef\n\n8.\n\nDemyanova, Y., Pani, T., Veith, H., Zuleger, F.: Empirical software metrics for benchmarking of verification tools. Int. J. Form. Methods Syst. Des., 1\u201328 (2017). doi:10.\u200b1007\/\u200bs10703-016-0264-5. http:\/\/\u200blink.\u200bspringer.\u200bcom\/\u200barticle\/\u200b10.\u200b1007%2Fs10703-016-0264-5\n\n9.\n\nDemyanova, Y., Veith, H., Zuleger, F.: On the concept of variable roles and its use in software analysis. In: Formal Methods in Computer-Aided Design (FMCAD), pp. 226\u2013230. IEEE (2013)\n\n10.\n\nDillig, I., Dillig, T., Li, B., McMillan, K.: Inductive invariant generation via abductive inference. ACM SIGPLAN Not. 48, 443\u2013456 (2013). ACMCrossRefMATH\n\n11.\n\nEngler, D., Chen, D.Y., Hallem, S., Chou, A., Chelf, B.: Bugs as deviant behavior: a general approach to inferring errors in systems code. In: Operating Systems Principles (SOSP), vol. 35. ACM (2001)\n\n12.\n\nFelsing, D., Grebing, S., Klebanov, V., R\u00fcmmer, P., Ulbrich, M.: Automating regression verification. In: Automated software engineering (ASE), pp. 349\u2013360. ACM (2014)\n\n13.\n\nGraf, S., Saidi, H.: Construction of abstract state graphs with PVS. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 72\u201383. Springer, Heidelberg (1997). doi:10.\u200b1007\/\u200b3-540-63166-6_\u200b10 CrossRef\n\n14.\n\nGrebenshchikov, S., Lopes, N.P., Popeea, C., Rybalchenko, A.: Synthesizing software verifiers from proof rules. In: Programming Language Design and Implementation (PLDI), pp. 405\u2013416. ACM (2012)\n\n15.\n\nHoder, K., Bj\u00f8rner, N.: Generalized property directed reachability. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 157\u2013171. Springer, Heidelberg (2012). doi:10.\u200b1007\/\u200b978-3-642-31612-8_\u200b13 CrossRef\n\n16.\n\nJhala, R., Majumdar, R.: Software model checking. ACM Comput. Surv. (CSUR) 41(4), 21 (2009)CrossRef\n\n17.\n\nKomuravelli, A., Gurfinkel, A., Chaki, S., Clarke, E.M.: Automatic abstraction in SMT-based unbounded software model checking. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 846\u2013862. Springer, Heidelberg (2013). doi:10.\u200b1007\/\u200b978-3-642-39799-8_\u200b59 CrossRef\n\n18.\n\nLeroux, J., R\u00fcmmer, P., Suboti\u0107, P.: Guiding craig interpolation with domain-specific abstractions. Acta Inform. 53, 1\u201338 (2016)MathSciNetCrossRefMATH\n\n19.\n\nNori, A.V., Rajamani, S.K.: An empirical study of optimizations in YOGI. In: Software Engineering (ICSE), vol. 1, pp. 355\u2013364. ACM (2010)\n\n20.\n\nR\u00fcmmer, P., Hojjat, H., Kuncak, V.: Disjunctive interpolants for horn-clause verification. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 347\u2013363. Springer, Heidelberg (2013). doi:10.\u200b1007\/\u200b978-3-642-39799-8_\u200b24 CrossRef\n\n21.\n\nSajaniemi, J.: An empirical analysis of roles of variables in novice-level procedural programs. In: Human-Centric Computing Languages and Environments (HCC), pp. 37\u201339. IEEE (2002)\n\n22.\n\nVan Deursen, A., Moonen, L.: Type inference for COBOL systems. In: Reverse Engineering (RE), pp. 220\u2013230. IEEE (1998)\n\nFootnotes\n\n1\n\nhttp:\/\/\u200bctuning.\u200borg\/\u200bwiki\/\u200bindex.\u200bphp\/\u200bCTools:\u200bCBench.\n\n2\n\nE.g. seq-mthreaded\/pals_opt-floodmax.3_true-unreach-call.ufo.BOUNDED-6.pals.c.\n\n3\n\nThe tool, the set of used benchmarks and the results of our evaluation are available at http:\/\/\u200bforsyte.\u200bat\/\u200bsoftware\/\u200bdemy\/\u200bnfm17.\u200btar.\u200bgz.\n\n4\n\nhttp:\/\/\u200bmap.\u200buniroma2.\u200bit\/\u200bvcgen\/\u200bbenchmark320.\u200btar.\u200bgz.\n\n5\n\nOriginal benchmarks are accessible at http:\/\/\u200bformal.\u200biti.\u200bkit.\u200bedu\/\u200bprojects\/\u200bimprove\/\u200breve and https:\/\/\u200bwww.\u200bmatul.\u200bde\/\u200breve.\n\n6\n\nWe evaluate the default configuration of Z3 without command-line options. To execute Spacer, we use the command-line option fixedpoint.xform.slice=false.\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_19\n\n# specgen: A Tool for Modeling Statecharts in CSP\n\nBrandon Shapiro1 and Chris Casinghino2\n\n(1)\n\nBrandeis University, Waltham, Massachusetts 02453, USA\n\n(2)\n\nDraper Laboratory, Cambridge, Massachusetts 02140, USA\n\nBrandon Shapiro\n\nEmail: bts8394@brandeis.edu\n\nChris Casinghino (Corresponding author)\n\nEmail: ccasinghino@draper.com\n\nAbstract\n\nWe present specgen, a tool for translating statecharts to the Communicating Sequential Processes language (CSP), where they may be explored and verified using FDR, the CSP model checker. We build on earlier algorithms for translating statecharts to CSP by supporting additional features, simplifying the generated models, and implementing a practical tool for statecharts built in Enterprise Architect, a commercially available modeling environment. We demonstrate the tool on a standard example.\n\nThis work was sponsored by DARPA\/AFRL Contract FA8750-12-C-0261. The views, opinions and\/or findings expressed are those of the authors and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S. Government.\n\n## 1 Introduction\n\nStatecharts are a widely-used technique for graphically representing the high-level behavior of complex systems. Since their introduction by Harel [5], support for various versions of statecharts has been implemented in many commercial tools, including Enterprise Architect and Simulink Stateflow. As the use of statecharts has become widespread, so too have techniques for formally verifying their behavior. Classic examples include modeling via translation to SPIN [10] or to SMV [2].\n\nThis paper presents specgen, a tool for translating statecharts to Communicating Sequential Processes (CSP). This makes it possible to explore and verify the behavior of a statechart using FDR, the CSP model checker [4]. CSP and FDR have been used for modeling and formal verification for decades, in both academia and industry [8, 9, 11].\n\nTranslating statecharts to CSP has two main advantages. First, CSP is a rich, expressive language for writing specifications. We may leverage FDR to check these specifications and to interactively explore the behavior of the translated systems. Second, statecharts are themselves a convenient way to represent specifications for more complex systems already implemented in CSP. For example, the second author has also implemented a tool, called cspgen, to translate imperative programs from C source or LLVM IR to CSP [1]. The typical use of cspgen involves taking code written by a domain expert and translating it to CSP, then developing specifications to be checked by FDR. As the domain expert is typically unfamiliar with CSP, statecharts provide an intuitive, graphical common language for these specifications. Having a tool like specgen to automatically convert the graphical specification to CSP makes this possible.\n\nThe specgen tool builds on previous work for modeling statecharts in CSP [12]. We have added support for several additional statechart features and designed a new, simplified algorithm by using new CSP language constructs, as described in Sect. 3. The tool supports statecharts developed with Enterprise Architect and is the first practical implementation of any such translation. The specgen distribution also includes several examples, described in Sect. 2, and is available freely under a permissive open-source license [14].\n\n## 2 The Dining Philosophers: An Example\n\nTo illustrate the use of specgen, we consider the classic dining philosophers problem [7]. Our distribution of specgen includes this example, implemented as a statechart in Enterprise Architect, for 2, 3 and 4 philosophers [14]. Figure 1 shows statecharts representing Philosopher 2 and Fork 2 from the four philosopher system. We elide the full system for space\u2014it consists of four philosophers and forks, similar to those shown, as parallel substates of one top-level node.\n\nFig. 1.\n\nStatecharts for one philosopher and fork\n\nWe begin our explanation with the statechart for Fork 2. Conceptually, it keeps track of which philosopher has permission to use the fork at any time. It begins in the state Free, indicating that the fork is not in use and may be claimed by either philosopher. Transitions to the Phil2Holds2 and Phil3Holds2 states are guarded by the constraints In(WaitingRight2) and In(WaitingLeft3) respectively. This ensures these transitions are not taken until the relevant philosopher is in the state where he is waiting on this fork, so the ownership of the fork is not given to a philosopher until he wants it.\n\nThe system also includes four variables, f1, ..., f4, one for each fork. Intuitively, the value in these variables indicates which philosopher, if any, currently has permission to use a given fork. Thus, the transition from state Free2 to state Phil3Holds2 sets variable f2 to 3. These variables are set by the forks, and used by guards in the philosophers. For example, consider node WaitingLeft2 in Phil2. This node models the state where Philosopher 2 is waiting to pick up his left fork (Fork 1). The guard on this transition prevents it from being taken unless f1 = 2, indicating that Philosopher 2 has permission to use Fork 1. Similarly, the transition from Eating2 to ReplacedRight2 is guarded by the requirement that f2 is not 2, indicating that Philosopher 2 no longer has permission to use his right fork. The semantics of statecharts require that all available transitions are taken immediately, ensuring that Fork 2 and Philosopher 2 remain synchronized here.\n\nFinally, we consider the edge from Sitting2 back to Standing2, which is labeled with the completion event complete(Sitting2). In statecharts, events are named triggers that are often used to represent external events. During execution, a set of enabled events is provided as input, and an edge labeled with an event may only be taken if the event is currently enabled. Completion events are special events that are enabled when a node terminates, rather than by input. A node is considered to have terminated when all of its concurrent subnodes have reached states with no out-edges. Here, the event label prevents the philosopher from standing until he is done eating.\n\nIt is worth noting that this example is not intended to represent the most efficient or natural implementation of the dining philosophers as a statechart. Rather, we have designed it to highlight several features supported by the tool.\n\n### 2.1 The Generated Model\n\nWhen run on an Enterprise Architect statechart like the one described above, specgen produces several files containing CSP definitions, including a top-level process that models the statechart's behavior. The behavior of a CSP process is most easily described by finite \"traces\" of observable events. In the case of , the relevant observable events include:\n\n * , indicating a transition between nodes. Here N is the name of the node that contains the transition, and E is the name of the edge itself. Typically, specgen will generate node names that match the name given in the statechart if all nodes have unique names, and will otherwise pick a name based on the full path of a node. Edges are given names like , indicating a transition from Node1 to Node2.\n\n * , indicating the completion of a \"step\" of the statechart. According to the semantics of statecharts, a step comprises a single transition in every currently-running subchart that can make one.\n\n * and , indicating reads or writes of a value n in variable x.\n\n * , indicating that the statechart has a race condition where two parallel subcharts attempted to write to the variable x in the same step.\n\n### 2.2 Finding the Deadlock\n\nThe most obvious property to check in the dining philosophers example is deadlock freedom. In our CSP scripts, this property is stated:\n\nThe (\"hiding\") operator here is used to hide the tock events of . A statechate continues to take \"steps\", represented by these events, even if no subchart can make a transition. Intuitively, to detect the deadlock, we must inform FDR that the mere passage of time does not count as progress.\n\nAsking FDR to check this property results in an assertion failure, as expected. Indeed, because the semantics of statecharts require each parallel process to make a transition in each step if able to, this system will always deadlock. FDR also displays the trace that leads to the deadlock. For the three philosopher system, this trace ends with the events:\n\nWe see that the last three events are each philosopher transitioning to his WaitingRight node, indicating that each philosopher has picked up his left fork and is waiting on his right fork.\n\n### 2.3 More Complicated Properties\n\nFDR, more generally, supports checking refinement between two CSP processes. This enables the use of CSP as a rich specification language for properties more interesting than deadlock. Our distribution of specgen includes many worked examples. For the dining philosophers system in particular, we show how to verify that changing the order in which a philosopher picks up his forks eliminates the deadlock, and include a detailed explanation of how to check the property \"after sitting, no philosopher stands without eating\". We also show how to check for race conditions in variable writes, and include several other statecharts to demonstrate a variety of properties.\n\n### 2.4 Performance\n\nThe time to find the deadlock in FDR is summarized in the table below, organized by the number of philosophers in the system:\n\nPhilosophers | 2 | 3 | 4\n\n---|---|---|---\n\nTime | 2.0 s | 6.0 s | 117 s\n\nThese times are the averages of 5 runs performed on an Intel Xeon E5-2630 v3. The machine had 32 GB of RAM, but all tests consumed less than 6 GB.\n\nPredictably, the time to find the deadlock grows exponentially with the number of philosophers. Checking these translated statecharts is slower than checking more natural implementations of the dining philosophers in CSP, because accurately modeling the semantics of statecharts involves substantial coordination overhead and additional features like per-node timers. As statecharts offer the advantage of wider accessibility, we believe this overhead is sometimes justified.\n\n## 3 Translation Enhancements\n\nAs mentioned in the introduction, specgen builds on an earlier algorithm for modeling statecharts in CSP, by Roscoe and Wu [12]. In addition to providing a practical implementation, we have improved on that paper's translation by including support for two additional statechart features (the \"in\" guards and completion events described in Sect. 2) and exploiting a newer FDR feature to simplify the generated models. The remainder of this section describes this simplification.\n\nThe biggest challenge in modeling statecharts in CSP is representing priority. In CSP, a process may select freely among its available actions, but in statecharts certain transitions may be favored over others. For example, nodes must be allowed to take an \"idle\" step if and only if no transitions are available. Also, transitions out of a state may be favored over transitions within that state when both are available, or vice versa\u2014classic Statemate semantics [6] favor outer transitions while UML favors inner ones [3]. (In specgen we have followed [12] in modeling Statemate, but it would be straightforward to prefer the alternate order, which is more common today).\n\nRoscoe and Wu's translation models these instances of priority with a subtle renaming and synchronization scheme [13]. Happily, modern versions of FDR include a new feature that specgen uses to simplify this: prioritise. This function takes as arguments a process P and an ordered list evs of sets of events. If P may perform events from different sets in evs, then prioritise(P,evs) may perform only events from the first set that contains any of P's events. Combining prioritise with interrupts, where a CSP process may be preempted by certain events, also allowed for a simplified encoding of \"promoted\" actions in statecharts. These actions allow an inner node to transition directly to an outer node, terminating its parallel siblings.\n\n## 4 Conclusion and Future Work\n\nThis paper has described specgen, a tool for translating statecharts to CSP. We demonstrated the use of the tool on a common example, illustrating how to analyze the behavior of a statechart by model-checking its translation with FDR (Sect. 2). Many more examples are available with the specgen distribution, which is available as open-source software [14]. The translation used by the tool is inspired by earlier work by Roscoe and Wu [12], which has been improved and extended (Sect. 3).\n\nWe are interested in expanding on this work in several directions. First, the generated model can likely be further optimized for model-checking speed in FDR. In particular, the use of inductive compression [13] to reduce the state space created by hidden control events seems particularly promising. Second, it would be interesting to compare our tool directly with other systems for verifying statecharts. Lastly, while the translation is intended to faithfully model one version of statechart semantics, it would be reassuring to formalize and mechanically verify this property with an interactive theorem prover like Coq or Isabelle\/HOL.\n\nWhile specgen is intended as a prototype, we have found it to work surprisingly well on a variety of examples. Readers are encouraged to download the implementation and give it a try.\n\nAcknowledgments\n\nThe authors thank Neil Brock, Thomas Gibson-Robinson, Colin O'Halloran and Cody Roux for their advice on this project, and the anonymous reviewers for their helpful feedback.\n\nReferences\n\n1.\n\nCasinghino, C.: cspgen (2016). https:\/\/\u200bgithub.\u200bcom\/\u200bdraperlaboratory\u200b\/\u200bcspgen\n\n2.\n\nChan, W., Anderson, R.J., Beame, P., Burns, S., Modugno, F., Notkin, D., Reese, J.D.: Model checking large software specifications. IEEE Trans. Softw. Eng. 24(7), 498\u2013520 (1998)CrossRef\n\n3.\n\nEshuis, R., Wieringa, R.: Requirements-level semantics for UML statecharts. In: Fourth International Conference on Formal Methods for Open Object-Based Distributed Systems, pp. 121\u2013140. Kluwer Academic Publishers (2000)\n\n4.\n\nGibson-Robinson, T., Armstrong, P., Boulgakov, A., Roscoe, A.W.: FDR3 \u2014 a modern refinement checker for CSP. In: \u00c1brah\u00e1m, E., Havelund, K. (eds.) TACAS 2014. LNCS, vol. 8413, pp. 187\u2013201. Springer, Heidelberg (2014). doi:10.\u200b1007\/\u200b978-3-642-54862-8_\u200b13 CrossRef\n\n5.\n\nHarel, D.: Statecharts: a visual formalism for complex systems. Sci. Comput. Programm. 8(3), 231\u2013274 (1987)MathSciNetCrossRef90035-9)MATH\n\n6.\n\nHarel, D., Naamad, A.: The statemate semantics of statecharts. ACM Trans. Softw. Eng. Methodol. 5(4), 293\u2013333 (1996)CrossRef\n\n7.\n\nHoare, C.A.R.: Communicating Sequential Processes. Prentice Hall Inc., Upper Saddle River (1985)MATH\n\n8.\n\nLawrence, J.: Practical application of CSP and FDR to software design. In: Abdallah, A.E., Jones, C.B., Sanders, J.W. (eds.) Communicating Sequential Processes. The First 25 Years. LNCS, vol. 3525, pp. 151\u2013174. Springer, Heidelberg (2005). doi:10.\u200b1007\/\u200b11423348_\u200b9 CrossRef\n\n9.\n\nLowe, G.: Casper: a compiler for the analysis of security protocols. J. Comput. Secur. 6(1\u20132), 53\u201384 (1998)CrossRef\n\n10.\n\nMikk, E., Lakhnech, Y., Siegel, M., Holzmann, G.J.: Implementing statecharts in PROMELA\/SPIN. In: Proceedings of the Second IEEE Workshop on Industrial Strength Formal Specification Techniques. IEEE Computer Society (1998)\n\n11.\n\nMota, A., Sampaio, A.: Model-checking CSP-Z: strategy, tool support and industrial application. Sci. Comput. Program. 40, 59\u201396 (2001)CrossRef00023-X)MATH\n\n12.\n\nRoscoe, A.W., Wu, Z.: Verifying statemate statecharts using CSP and FDR. In: Liu, Z., He, J. (eds.) ICFEM 2006. LNCS, vol. 4260, pp. 324\u2013341. Springer, Heidelberg (2006). doi:10.\u200b1007\/\u200b11901433_\u200b18 CrossRef\n\n13.\n\nRoscoe, A.: Understanding Concurrent Systems, 1st edn. Springer, New York (2010)CrossRefMATH\n\n14.\n\nShapiro, B., Casinghino, C.: specgen (2016). https:\/\/\u200bgithub.\u200bcom\/\u200bdraperlaboratory\u200b\/\u200bspecgen\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_20\n\n# HyPro: A C++ Library of State Set Representations for Hybrid Systems Reachability Analysis\n\nStefan Schupp1 , Erika \u00c1brah\u00e1m1, Ibtissem Ben Makhlouf1 and Stefan Kowalewski1\n\n(1)\n\nRWTH Aachen University, Aachen, Germany\n\nAbstract\n\nIn this tool paper we introduce HyPro, our free and open-source C++ programming library, which offers implementations for the most prominent state set representations used by flowpipe-construction-based reachability analysis techniques for hybrid systems.\n\nThis work was supported by the German Research Council (DFG) in the context of the HyPro project.\n\n## 1 Introduction\n\nAs hybrid systems with mixed discrete-continuous behaviour are often safety-critical applications, a rising interest in their safety verification resulted in the development of powerful tools implementing different approaches to determine the set of system states that are reachable from a given set of initial states. Besides approaches based on, e.g., theorem proving or SMT solving, flowpipe-construction-based reachability analysis is a well established method, which over-approximates the set of reachable states of a hybrid system by a union of state sets, each of them being represented by a geometric object of a certain shape (like boxes, polytopes, or zonotopes) or symbolically (like support functions or Taylor models). Hybrid systems reachability analysis tools like, e.g., Cora [1], Flow* [2], HyCreate [7], HyReach [8], SoapBox [5], and SpaceEx [3] implement different techniques using different geometric or symbolic state set representations, each of them having individual strengths and weaknesses.\n\nThe implementation of novel reachability analysis algorithms that use some geometric or symbolic state set representations is still effortful, as datatypes for the underlying state set representations need to be implemented first. In this paper we report on the first release of our free and open-source C++ library HyPro, providing implementations for the most prominent state set representations. Our aim is to offer assistance for the rapid implementation of new algorithms by encapsulating all representation-related issues and allowing the developers to focus on higher-level algorithmic aspects.\n\nThe HyPro library specifies a unified interface for different representations, which supports all operations required in reachability analysis as well as conversion methods between the different representations. Besides own implementations for state set representations, the library also offers approaches towards wrapping other existing libraries implementing a certain state set representation.\n\nAfter some preliminaries in Sect. 2, we describe in Sect. 3 the structure and usage of our library and provide some experimental evaluation in Sect. 4.\n\n## 2 Hybrid Systems Reachability Analysis\n\nReachability analysis aims at the computation of the set of states that are reachable in some system from a given set of initial states. Reachability analysis is often used for safety verification by showing that the set of reachable states does not intersect with a pre-defined set of unsafe states.\n\nWe are interested in reachability analysis for hybrid automata [6], a popular modelling formalism for hybrid systems. Intuitively, they extend discrete automata models, whose nodes resp. transitions model the states (control modi) resp. state changes (jumps) of the discrete part of the system, by additionally modelling the evolution of continuous quantities (flowpipe) between discrete state changes through ordinary differential equation (ODE) systems.\n\nAs the reachability problem for hybrid automata is in general undecidable, over-approximative bounded reachability analysis can be used to over-approximate reachability along such paths that satisfy some upper bounds on the time elapse between two consecutive jumps (time horizon) and on the number of jumps (jump depth). Due to the over-approximation, we can prove bounded safety in case of an empty intersection of the reachable state set with the unsafe state set, but no conclusive answer can be given if this intersection is not empty.\n\nFig. 1.\n\nFlowpipe-construction-based reachability analysis (guard satisfying sets in red, jump successor in green). (Color figure online)\n\nFlowpipe-construction-based reachability analysis approaches iteratively compute successors of a given initial state set. To over-approximate flowpipes, they divide a given time horizon into time segments and over-approximate the states reachable within each time segment by a state set, thus \"paving\" the flowpipe with state sets. For computing jump successors, they determine the intersections of those \"paving\" state sets with the guards of jumps that exit the current control modus, and apply the jumps' reset transformations to those intersections (see Fig. 1).\n\n## 3 The HyPro Library\n\nThe library is published at https:\/\/\u200bgithub.\u200bcom\/\u200bhypro\/\u200bhypro. In the following we describe its components (see Fig. 2) and its usage. For more details we refer to the online documentation and the user's guide accessible on the above page.\n\nFig. 2.\n\nHyPro class structure.\n\nArithmetic Computations. HyPro is templated in the number type and makes use of boost and the following external libraries:\n\n * cln, gmp (optional): exact number types cl_RA and mpq_class;\n\n * CArL: number-type-templated (cl_RA or mpq_class) exact arithmetic computations, number type conversion;\n\n * Eigen3: number-type-templated matrix computations; when instantiated with double, conservativeness is not assured;\n\n * PPL (optional): efficient but inexact computations with polytopes;\n\n * glpk: linear optimiser using either floating-point or exact arithmetic, however, its interface does not support the exchange of exact numbers, thus the results are not provably correct;\n\n * SMT-RAT, SoPlex and Z3 (optional): exact linear optimisers; SMT-RAT and SoPlex support mpq_class in their interfaces, but not Z3, therefore we need to convert mpq_class-numbers to strings when calling Z3;\n\n * log4cplus (optional): logger functionalities.\n\nCurrently, HyPro can be instantiated with inexact (double) or exact (cl_RA, mpq_class) number types; Eigen3 will be instantiated the same way. When inexact, all representations as well as Eigen3 use the double number type, thus we cannot guarantee over-approximative results; however, as exact optimisation is extremely important for meaningful results for most representations, we still guarantee exact optimisation through a combination of inexact glpk with an exact optimiser if available (see Fig. 3). When using an exact number type, HyPro assures conservative results if one of the modules SMT-RAT, SoPlex or Z3 are available and if PPL is not used; as glpk is faster than the other optimisers but its interface is inexact, we use the same approach as for the double representation shown in Fig. 3, but run glpk in exact modus.\n\nFig. 3.\n\nIncreased efficiency by combining inexact and exact computations.\n\nState Set Representations. To implement the computations described in the previous section, we need a suitable data type (representation) that supports the storage of state sets (subsets of ) and certain operations on them. The choice of the state set representation is highly relevant, as it strongly influences both computational effort and precision. Our library offers state-set representation by boxes, (convex) polytopes [10] in vertex ( ) as well as in halfspace ( ) representation, support functions [9] and zonotopes [4]. For these representations, we provide all operations needed for the reachability analysis of linear hybrid automata (hybrid automata specified using linear conditions and resets, and linear ODEs): linear transformation, Minkowski sum, intersection, union, and test for emptiness. All the above representations implement a common interface specifying these operations, extended with some additional convenience functions (e.g., functions for determining the dimension of a set or functionalities for output). Some representations also extend this interface with individual functions, only relevant for that representation (e.g., order reduction functions for zonotopes).\n\nWe additionally provide a module for orthogonal polyhedra, but it is partial as we found no proper way to compute the Minkowski sum and linear transformation. We thank Xin Chen who contributed with a further module for Taylor models; however, as Taylor-model-based reachability analysis requires different operations, this module does not implement the global HyPro interface.\n\nConversion. None of the state set representations is generally optimal in terms of both computational effort and precision in reachability analysis. Switching between representations, although mostly expensive, can pay off during the analysis, for instance to improve the precision of the computed state sets locally. This feature allows for the implementation of backtracking mechanisms and fast look-ahead strategies in a dynamic reachability analysis approach. HyPro implements easy-to-use (exact or over-approximating) conversion operations for all included state set representations; this converter is a template parameter and thus exchangeable by the user, if more specialised methods are desired.\n\nReduction Techniques. The size of state set representations usually strongly increases during the analysis due to more complex shapes (e.g., when computing Minkowski sum) and number representations (e.g., when computing linear transformation). For boxes and polytopes, HyPro provides efficient and conservative over-approximating number reduction techniques. For zonotopes we offer a conservative order-reduction algorithm to limit the number of generators. For support functions we reduce the operational tree of the object.\n\nAdditional Datastructures and Utility Functions. We provide a data type for hybrid automata, a parser for Flow*-like syntax, utility functions such as a plotter which creates gnuplot or TikZ output files for state set visualisation, logging mechanisms to trace executions, and an exemplary reachability analysis algorithm among various other examples showing how to use the library.\n\nUsage. We illustrate the usage of the HyPro library on some simple examples based on the double number type (where also Eigen3 objects are instantiated with double); for further details see the examples folder and the user's guide.\n\nWe can create a state set represented by an -polytope p by specifying an Eigen3 matrix A, representing the constraints (row-wise) and an Eigen3 vector b representing the constant parts, as follows:\n\nThe Minkowski sum p of two -polytopes p1 and p2 can be computed by:\n\nA box containing a set V of points of type can be converted to a polytope in the -representation using the Converter class:\n\nTo plot an object (per default in the first two dimensions), we can report its vertices to the singleton class Plotter, and create a gnuplot file using the method plot2d():\n\nFuture Work. Currently we focus on efficiency-related improvements for the presented representations, including the better exploitation of inexact arithmetic. Long-term plans address also extensions with further representations. Regarding efficiency, naturally, we cannot compete with well-established special-purpose libraries like PPL and polymake for polytope computations. Additionally to PPL, we work on the development of further wrappers for third-party libraries. Last but not least, as representation-related parameter settings are currently global and static, we work on the support of representation- and object-specific settings.\n\n## 4 Experimental Evaluation\n\nUsing our library we implemented a simple reachability analysis algorithm for linear hybrid systems, and used it to evaluate the efficiency of our library on three commonly known benchmarks: (1) the bouncing ball (BBall) models the bouncing of an elastic ball dropped from a predefined height (parameters: time step , time horizon ); (2) the rod reactor (Rod) models the temperature controller of a nuclear power plant and its cooling dynamics ( , ); (3) the switching 5D linear system (5D SW) is an artificially created benchmark in 5 dimensions with planar guards ( , ).\n\nTable 1.\n\nBenchmark results with runtimes in seconds (TO for minutes). Dashes indicate that a tool does not support this kind of state set representation. | mpq_class | double | SpaceEx\n\n---|---|---|---\n\nglpk | glpk+SMT-RAT | glpk+Z3 | glpk | glpk+SMT-RAT | glpk+Z3 | LGG | STC\n\nBox | BBall | 0.1 | 0.1 | 0.1 | 0.002 | 0.002 | 0.03 | 0.003 | 0.01\n\nRod | 63.8 | 64.8 | 65.1 | 0.01 | 0.06 | 0.02 | 0.02 | 0.2\n\n5D SW | 0.3 | 0.3 | 0.3 | 0.02 | 0.02 | 0.02 | 0.02 | 0.03\n\nHPoly | BBall | 1.2 | 1.1 | 8.7 | 0.2 | 0.7 | 4.9 | - | -\n\nRod | 24.3 | 21.3 | 136.5 | 4.8 | 16.1 | 131 | - | -\n\n5D SW | 54.8 | TO | TO | 4.3 | TO | TO | - | -\n\nVPoly | BBall | 1.8 | 1.5 | 6.0 | TO | (0.7) | (5.5) | - | -\n\nRod | 100.2 | 98.7 | 171.5 | TO | (0.3) | (2.6) | - | -\n\n5D SW | TO | TO | TO | TO | TO | TO | - | -\n\nPPL | BBall | 0.07 | 0.07 | 0.08 | 0.05 | 0.06 | 0.06 | - | -\n\nRod | 2.7 | 2.6 | 2.9 | 1.8 | 1.9 | 1.9 | - | -\n\n5D SW | TO | TO | TO | TO | TO | TO | - | -\n\nSF | BBall | 0.6 | 2.0 | 15.6 | 0.02 | 1.1 | 43.8 | 0.2 | 0.03\n\nRod | 72.8 | 101.6 | 1125.8 | 0.4 | 54.4 | 609.6 | 1.1 | 0.9\n\n5D SW | 270.6 | 279.8 | 411.1 | 0.04 | 2.6 | 319.3 | 0.8 | 0.2\n\nZono | BBall | TO | TO | TO | 0.006 | 0.007 | 0.006 | - | -\n\nRod | 4.8 | 4.9 | 4.9 | 0.02 | 0.02 | 0.02 | - | -\n\n5D SW | 3.8 | 3.9 | 3.9 | 0.004 | 0.004 | 0.004 | - | -\n\nAll experiments were carried on an Intel Core i7 ( GHz) CPU with 16 GB RAM. Table 1 shows the results when using mpq_class (exact) and double (inexact) number types, and as representations boxes (Box), -polytopes (HPoly), -polytopes which are converted to -polytopes for intersection computation (VPoly), polytope representation by the PPL library (PPL), support functions (SF) and zonotopes (Zono). For both mpq_class and double, we distinguish glpk only in exact resp. inexact modus, and glpk+SMT-RAT and glpk+Z3 combining glpk with an exact solver as in Fig. 3. Inexact-arithmetic results that we (manually) detected to be under-approximating are put in parenthesis; this occurred for VPoly due to inexact Eigen3computations. For comparison, we present SpaceEx results using support functions (SF) as well as SF with box templates (Box); note that SpaceEx uses double representation and glpk.\n\nDue to space limitation, we discuss only some timing issues. At least on these few examples, HyPro in inexact glpk-only modus is competitive with SpaceEx. A higher computational effort can be observed for exact arithmetic, most prominently for SF, which highly relies on optimisation; the longer running times for glpk+Z3 (wrt. SMT-RAT) are due to the string-based interface communication overhead. For 5D SW, the initial set is a single point. Zonotopes, performing well on small initial sets, deliver very good results here.\n\nReferences\n\n1.\n\nAlthoff, M., Dolan, J.M.: Online verification of automated road vehicles using reachability analysis. IEEE Trans.Robot. 30(4), 903\u2013918 (2014)CrossRef\n\n2.\n\nChen, X., \u00c1brah\u00e1m, E., Sankaranarayanan, S.: Flow*: an analyzer for non-linear hybrid systems. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 258\u2013263. Springer, Heidelberg (2013). doi:10.\u200b1007\/\u200b978-3-642-39799-8_\u200b18 CrossRef\n\n3.\n\nFrehse, G., et al.: SpaceEx: scalable verification of hybrid systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 379\u2013395. Springer, Heidelberg (2011). doi:10.\u200b1007\/\u200b978-3-642-22110-1_\u200b30 CrossRef\n\n4.\n\nGirard, A.: Reachability of uncertain linear systems using zonotopes. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 291\u2013305. Springer, Heidelberg (2005). doi:10.\u200b1007\/\u200b978-3-540-31954-2_\u200b19 CrossRef\n\n5.\n\nHagemann, W., M\u00f6hlmann, E., Rakow, A.: Verifying a PI controller using SoapBox and Stabhyli: experiences on establishing properties for a steering controller. In: Proceedings of ARCH 2014. EPiC Series in Computer Science, vol. 34. EasyChair (2014)\n\n6.\n\nHenzinger, T.: The theory of hybrid automata. In: Proceedings of LICS 1996, pp. 278\u2013292. IEEE Computer Society Press (1996)\n\n7.\n\nHyCreate. http:\/\/\u200bstanleybak.\u200bcom\/\u200bprojects\/\u200bhycreate\/\u200bhycreate.\u200bhtml\n\n8.\n\nHyReach. https:\/\/\u200bembedded.\u200brwth-aachen.\u200bde\/\u200bdoku.\u200bphp?\u200bid=\u200ben:\u200btools:\u200bhyreach\n\n9.\n\nLe Guernic, C., Girard, A.: Reachability analysis of linear systems using support functions. Nonlinear Anal.: Hybrid Syst. 4(2), 250\u2013262 (2010)MathSciNetMATH\n\n10.\n\nZiegler, G.M.: Lectures on Polytopes, vol. 152. Springer Science & Business Media, New York (1995)MATH\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_21\n\n# Asm2C++: A Tool for Code Generation from Abstract State Machines to Arduino\n\nSilvia Bonfanti1, 2 , Marco Carissoni1 , Angelo Gargantini1 and Atif Mashkoor2\n\n(1)\n\nUniversit\u00e0 degli Studi di Bergamo, Bergamo, Italy\n\n(2)\n\nSoftware Competence Center Hagenberg GmbH, Hagenberg im M\u00fchlkreis, Austria\n\nSilvia Bonfanti (Corresponding author)\n\nEmail: silvia.bonfanti@unibg.it\n\nMarco Carissoni\n\nEmail: m.carissoni1@studenti.unibg.it\n\nAngelo Gargantini\n\nEmail: angelo.gargantini@unibg.it\n\nAtif Mashkoor\n\nEmail: atif.mashkoor@scch.at\n\nAbstract\n\nThis paper presents Asm2C++, a tool that automatically generates executable C++ code for Arduino from a formal specification given as Abstract State Machines (ASMs). The code generation process follows the model-driven engineering approach, where the code is obtained from a formal abstract model by applying certain transformation rules. The translation process is highly configurable in order to correctly integrate the underlying hardware. The advantage of the Asm2C++ tool is that it is part of the Asmeta framework that allows to analyze, verify, and validate the correctness of a formal model.\n\nThis work is partially supported by the Austrian Ministry for Transport, Innovation and Technology, the Federal Ministry of Science, Research and Economy, and the Province of Upper Austria in the frame of the COMET center SCCH.\n\n## 1 Introduction\n\nThe Abstract State Machines (ASM) method [4] is a formal method that is used to guide the rigorous development of software and embedded systems seamlessly from their informal requirements. The ASM method follows a design process based on the refinement principle that allows to capture all details of the system design by a sequence of refined models till the desired level of detail. It combines validation (by simulation and testing) and verification methods at any desired level of detail. The final step of this refinement process consists in realizing the implementation, generally code that is compiled and deployed on the real system. Performing this last step manually increases costs, limits the reuse of a formal specification, is error prone as some faults can be introduced in the code writing process, and can be a barrier for a wider adoption of ASMs. For these reasons, we have devised a methodology supported by the Asm2C++ tool that is able to generate the desired source code from ASMs. In this paper, we target Arduino1 that is a widespread platform for rapid prototyping of embedded systems and supports C++. It is also suitable for learning the design of embedded systems due to its low cost.\n\nThe ultimate aim of the paper is to show the implementation of the model-driven engineering (MDE) paradigm through ASMs: requirements models are platform independent, there is a clear distinction between platform-specific details and original user and system requirements, the code generation process is seamless and automatic, and last but not least, the rigorous quality and correctness assurance is embedded in the development process. As an additional goal, we aim at producing a code which is readable such that the code instructions can be easily traced back to the specification concepts and constructs. Although this may decrease the code efficiency, we believe that it increases the maintainability and the usability of the Asm2C++ tool.\n\nThe paper is organized as follows: In Sect. 2, we present the ASM methodology. The process of code generation is presented in Sect. 3 and by means of a simple example, we illustrate some basic concepts of the proposed translation in Sect. 4. Section 5 presents some related work and Sect. 6 concludes the paper with some future work.\n\n## 2 Abstract State Machine Methodology\n\nThe ASM method guides the development of software from requirements capture to code generation through several steps. Figure 1 shows the process of the ASM-based development. This method is supported by the Asmeta (ASM mETAmodeling) framework2 [3] which provides a set of tools to help a developer in various development activities. The modelling process is based on refinement, i.e., it starts from an abstract model and adds further details to capture the complete system behaviour described in the requirements document. The correct refinement between two models is automatically proved using the ASMRefProver tool. If a model becomes complex, it is difficult to understand the behaviour only by the textual specification. For this reason, the visualizer AsmetaVis provides a visual notation that helps in the navigation of the model.\n\nFig. 1.\n\nASM process: from requirements to code\n\nThe validation and verification (V&V) activities are well-integrated in the process, as shown in Fig. 1, and can be applied to any refined machine. The validation of a model can be achieved in multiple ways: either through the model simulator AsmetaS, through the model validator AsmetaV or through the model reviewer AsmetaMA. The simulator AsmetaS allows to perform two type of simulations: interactive simulation (the user inserts the values of parameters by choice) and random simulation (the tool randomly chooses the values that depends on the environment). The model validator AsmetaV takes scenarios as input files that contain the expected system behaviours. The scenarios are executed to check whether the machine runs correctly. The model reviewer AsmetaMA performs static analysis, it determines whether a model has sufficient quality attributes (e.g., minimality, completeness, consistency). The verification tool AsmetaSMV verifies whether the properties, derived from the requirements document, comply with the behaviour of the model. When the final model is available, the Arduino code is automatically generated using the Asm2C++ tool (see Sect. 3). When an actual code of the system implementation is available, conformance checking is possible. It is divided in model-based testing (to check the conformance offline) and runtime verification (to check the conformance online). The former uses the ATGT tool that automatically generates from ASM models tests cases which can be used to test any programming language. The latter, using the CoMA tool, can be used to perform runtime verification: the machine code is checked during the execution.\n\nThe language used by Asm2C++ is UASM (Unified Syntax for Abstract State Machine) [2], the new ASM syntax developed by the ASM community to unify various ASMs dialects.\n\nFig. 2.\n\nTransformation process: from specification to code\n\n## 3 Code Generation Process\n\nThe translation process shown in Fig. 2 generates the runnable C++ code for Arduino starting from a UASM specification that we assume verified and validated. The first step of the transformation process consists in parsing the textual specification and producing the UASM model, which is given to the code generator. The code generator performs three activities: (1) Generate C++ Code (2) Generate ASM Runner Code (3) Integrate Hardware. The result is merged as an Arduino project.\n\nThe first activity translates the ASM model into C++ code. The code is composed of a header (.h) that contains the translation of the ASM signature and a source (.cpp) file that defines how the ASM evolves by translating each ASM rule to a C++ method.\n\nThe second activity generates the Arduino code that defines the running policy according to the ASM execution divided in four iterative steps: acquire inputs, perform the main rule, update state, and release outputs. The output, the ASM Runner, is an .ino file that is the default extension for the Arduino C++ code.\n\nThe third activity integrates all HW-related aspects into the project: Arduino board version, I\/O devices connections, Arduino-specific libraries that must be included, and any other HW-dependent information. The tool automatically generates a template configuration file (with .u2c extension). According to the HW configuration, the user edits this file which is used to generate the HW integration file. This is a C++ source file that works as an adapter between the generated code and the hardware. The output files are finally merged together to compose the Arduino project.\n\nAsm2C++ is built on top of Xtext [6], a framework for the development of domain-specific languages, which provides facilities for parsing and code generation and is fully compatible with the Eclipse Modeling Framework. The code generator has been developed as a model-to-text (M2T) transformation. The transformation was realized by means of Xtend, a Java dialect provided by the Xtext framework with features for code generation. The listing below shows the translation scheme for the SeqBlock rule of the ASM method. A SeqBlock is a list of rules which are executed sequentially and is translated as a list of C++ instructions enclosed by curly brackets. In Xtend syntax, the content within symbols is a template string, while the code inside brackets is a variable part of the template expression that will be translated according to the rules parameter.\n\nThe detailed information about the Asm2C++ tool can be found at http:\/\/\u200basmeta.\u200bsourceforge.\u200bnet\/\u200bdownload\/\u200basm2c++.\u200bhtml.\n\n## 4 Illustrative Example\n\nAsm2C++ has been used to implement a small case study. The system is a control panel to be placed on the car dashboard that enables the driver to interact with various car functionalities. The panel is responsible for controlling the following functionalities: 1. Switching on\/off the system 2. Climate control 3. Smart headlights activation 4. Radio system. Code examples 1 to 4 in Fig. 4 focus on functionality 1 to show some translation rules. The ASM is translated in the CarPanel class, where domains, functions and rules become respectively data types, properties and methods. As shown in Code 3, the runner cyclically calls four CarPanel methods: 1. Acquire inputs from sensors (getInputs) 2. Perform the main rule (r_Main) 3. Update the ASM state (updateState) 4. Set outputs to actuators (setOutputs). Parallel execution is translated as described in [7], where controlled functions are duplicated and the state is updated only after the main rule.\n\nFig. 3.\n\nCarPanel\n\nThe implementation process followed the methodology described in Sect. 2. We first defined a ground model that was progressively refined. When the model reached the last refinement step, we generated the runnable Arduino code. Along this process, we proved liveness properties with the model checker and executed some scenarios with the AsmetaV tool. In order to check the compliance between the specification and the code, we ran the same scenarios on the Arduino code, obtaining the same behavior as for the ASM simulation. The real system is shown in Fig. 3.\n\nFig. 4.\n\nSnippets from model and code\n\n## 5 Related Work\n\nAutomatic code generation from formal specifications is available as a part of tool support for several formal methods. SCADE3 and MATLAB\/Simulink4 provide this feature as a commercial off-the-shelf solution. The formal method B [1], on the other hand, provides this facility in the form of the Atelier B platform5, that comes with code generators for different target languages, including C, C++, Java, and Ada, and its Community Edition is freely available without any restriction. EventB2Java is another tool that generates executable code implemented as a plug-in of the Rodin platform [5].\n\nAs best of our knowledge, there is no state of the art, reusable and publicly available tool for the ASM method that is capable of automatically generating programming language code from formal specifications written in the ASM method. In the past, [7] introduced a compilation scheme to transform an ASM specification (written in ASM-SL) into C++ code, but this work was done within a company setting. Although some of the key results of the proposed compilation scheme were useful for our work as mentioned in Sect. 4.\n\n## 6 Conclusions and Future Work\n\nWe have presented Asm2C++, a tool that is able to generate C++ from formal specifications written as ASMs. This work follows the MDE paradigm: source code is obtained from requirements models by applying a set of M2T transformations. We have already successfully tried the tool with students of advanced programming courses to teach them rapid prototyping and designing of embedded devices.\n\nIn the future, we plan to extend the tool with an automatic test cases generator. From the ASM specification, a series of tests could be automatically generated which would be executed on the Arduino board. This would test both the system and the translation from the specification to the code. As, currently, the conformance relation between the specification and the code is coarsely defined, we also intend to formally specify and prove the correctness of the code transformation process.\n\nReferences\n\n1.\n\nAbrial, J.-R.: The B-book: Assigning Programs to Meanings. Cambridge University Press, New York (1996)CrossRefMATH\n\n2.\n\nArcaini, P., Bonfanti, S., Dausend, M., Gargantini, A., Mashkoor, A., Raschke, A., Riccobene, E., Scandurra, P., Stegmaier, M.: Unified syntax for abstract state machines. In: Butler, M., Schewe, K.-D., Mashkoor, A., Biro, M. (eds.) ABZ 2016. LNCS, vol. 9675, pp. 231\u2013236. Springer, Cham (2016). doi:10.\u200b1007\/\u200b978-3-319-33600-8_\u200b14 CrossRef\n\n3.\n\nArcaini, P., Gargantini, A., Riccobene, E., Scandurra, P.: A model-driven process for engineering a toolset for a formal method. Softw.: Pract. Exp. 41, 155\u2013166 (2011)\n\n4.\n\nB\u00f6rger, E., Stark, R.F.: Abstract State Machines: A Method for High-Level System Design and Analysis. Springer, New York (2003)CrossRefMATH\n\n5.\n\nCata\u00f1o, N., Rivera, V.: EventB2Java: a code generator for event-B. In: Rayadurgam, S., Tkachuk, O. (eds.) NFM 2016. LNCS, vol. 9690, pp. 166\u2013171. Springer, Cham (2016). doi:10.\u200b1007\/\u200b978-3-319-40648-0_\u200b13 CrossRef\n\n6.\n\nEysholdt, M., Behrens, H.: Xtext: implement your language faster than the quick and dirty way. In: Proceedings of the ACM International Conference Companion on OOPSLA, pp. 307\u2013309. ACM (2010)\n\n7.\n\nSchmid, J.: Compiling abstract state machines to C++. JUCS 7(11), 1068\u20131087 (2001)\n\nFootnotes\n\n1\n\nhttps:\/\/\u200bwww.\u200barduino.\u200bcc\/\u200b.\n\n2\n\nhttp:\/\/\u200basmeta.\u200bsourceforge.\u200bnet\/\u200b.\n\n3\n\nhttp:\/\/\u200bwww.\u200besterel-technologies.\u200bcom\/\u200bproducts\/\u200bscade-suite\/\u200b.\n\n4\n\nhttps:\/\/\u200bwww.\u200bmathworks.\u200bcom\/\u200bproducts\/\u200bsimulink\/\u200b.\n\n5\n\nhttp:\/\/\u200bwww.\u200batelierb.\u200beu\/\u200ben\/\u200b.\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_22\n\n# SPEN: A Solver for Separation Logic\n\nConstantin Enea1, Ond\u0159ej Leng\u00e1l2 , Mihaela Sighireanu1 and Tom\u00e1\u0161 Vojnar2\n\n(1)\n\nUniv. Paris Diderot, IRIF CNRS UMR 8243, Paris, France\n\n(2)\n\nFIT, Brno University of Technology, IT4Innovations Centre of Excellence, Brno, Czech Republic\n\nOnd\u0159ej Leng\u00e1l\n\nEmail: lengal@fit.vutbr.cz\n\nAbstract\n\nSpen is a solver for a fragment of separation logic (SL) with inductively-defined predicates covering both (nested) list structures as well as various kinds of trees, possibly extended with data. The main functionalities of Spen are deciding the satisfiability of a formula and the validity of an entailment between two formulas, which are essential for verification of heap manipulating programs. The solver also provides models for satisfiable formulas and diagnosis for invalid entailments. Spen combines several concepts in a modular way, such as boolean abstractions of SL formulas, SAT and SMT solving, and tree automata membership testing. The solver has been successfully applied to a rather large benchmark of various problems issued from program verification tools.\n\n## 1 Introduction\n\nFor analyzing programs with dynamic memory, separation logic (SL) is an established and fairly popular logic introduced by Reynolds et al. [11]. The high expressivity of SL, its ability to generate compact proofs, and its support for local reasoning motivated development of many tools for automatic reasoning about programs with complex dynamic linked data structures. These tools aim at establishing memory safety properties and\/or inferring shape properties of the heap. The tools often build on (semi-)decision procedures for checking satisfiability and entailment problems in SL.\n\nOur tool Spen 1 provides (semi-)decision procedures for the most commonly considered symbolic heaps fragment of SL, extended with user-defined inductive predicates to specify data structures of an unbounded size. Because unrestricted definitions of inductive predicates make the entailment problem for the fragment undecidable [3], only semi-decision procedures have been proposed, e.g., in [2, 4]. Iosif et al. [10] identified a rather large class of inductive definitions for which the entailment problem is decidable, although with a high complexity. Spen focuses on a smaller class of inductive definitions that is, however, expressive enough to specify complex dynamic data structures, such as skip lists, lists of circular lists, AVL trees, or binary search trees.\n\nThe chosen class of inductive definitions enables the design of efficient (semi-)decision procedures for satisfiability and entailment [6, 8]. The key idea used for satisfiability checking in Spen is to exploit the semantics of restricted inductive definitions and of separating conjunction to build an equisatisfiable boolean abstraction of the formula. For entailment checking, the idea is to reduce the problem of checking to the problem of checking a set of simple entailments where the right-hand side is an inductive predicate atom. The compositionality of this reduction leads to high efficiency (the simple entailments can be checked independently) and to a capability to provide fine diagnosis for invalid entailments.\n\nThe current version of Spen improves on the ones reported in [6, 8] in several directions. First, we introduced caching of constructions and results obtained from checking simple entailments in order to increase its efficiency. Second, the wrappers calling the SAT and SMT solvers have been refined to generate smaller formulas and to exploit the incrementality feature of underlying solvers. Third, we improved the diagnosis produced by Spen. For satisfiability checking, Spen now provides either a model of a satisfiable formula or an unsatisfiable core; for entailment checking, Spen provides a proof witness for valid entailments and a diagnostic information otherwise.\n\nSpen has been successfully tested on a quite large benchmark. The first version of Spen participated in the SL-COMP'14 contest [15] where it won one of its divisions and was second in another one. The later extensions now allow Spen to handle a richer fragment than those considered in the competition. Moreover, the improvements above lead to better execution times (e.g., by 10% within the SL-COMP'14 division won by the first version of Spen and by 30% on the division where Spen was the second).\n\nSpen is not the only solver for SL. The existing solvers differ in the fragment considered (Cyclist [2], Slide [9]) and\/or the techniques used (Asterix [12], Dryad [14], GRASShopper [13], Sleek [4]). A detailed comparison with these solvers is beyond the scope of this paper\u2014we refer the reader to the survey in [6, 8, 15].\n\n## 2 Logic Fragment\n\nSpen deals with decision problems in a fragment of SL, denoted as , that combines the symbolic heaps fragment of SL [1] with user-defined inductive predicates describing various kinds of lists (possibly nested, cyclic, or equipped with skip links) or trees, possibly extended with data constraints.\n\nSyntax: We write X, Y, Z to denote location variables, d to denote data variables, and x, y, z for both kinds of variables. We use the vector notation to abbreviate tuples. We denote by the tuples built from pairs of field labels and variables that specify structured values. We assume a finite set of predicate symbols, each with an associated arity, and a special location variable . A symbolic heap formula is a formula of the form where is a pure formula and is a spatial formula with the following syntax:\n\nHere, is a constraint over data variables. We let it unspecified, though Spen presently supports the first-order theory over multisets of integers with integer linear constraints. The spatial atoms (i.e., the empty heap, the heap cell allocated at X, resp. the heap region shaped by some predicate ) are composed by the separating conjunction \" \". An formula is a set of symbolic heaps interpreted as a disjunction .\n\nPredicates are defined by a set of inductive rules of the form where is a tuple of distinct variables including all free variables in the symbolic heap (the rule body). X is called the root node of the heap segment defined by P. A rule is called a base rule if its spatial part is , i.e., an empty heap; otherwise, it is an inductive rule.\n\nFragments: Spen considers a restricted class of inductive rules such that the defined predicates specify (possibly empty) heap segments connecting (by location fields) the root location X with all locations in the heap or . The restrictions have been defined formally in [6, 8]. They mainly require, for each inductive predicate P, the presence of a unique base rule and inductive rules where the root X points to a memory cell that contains at least one field from which another heap specified by P starts. The fragment defined in [6], called , can describe various kinds of lists that can be singly- or doubly-linked, cyclic, nested, and can have skip links. It does not permit data constraints and inductive tree structures. On the other hand, the fragment defined in [8] permits data constraints and can describe tree structures of bounded width, such as sorted list segments, AVL trees, binary search trees, but not nested cyclic lists.\n\nDecision Problems: For both fragments above, Spen considers the problems of checking satisfiability of a formula, i.e., checking whether holds, and the validity of an entailment where the symbolic heaps of can be quantified only over data variables. A simple example of an entailment problem in considered by Spen is:\n\nwhich, intuitively, checks whether a composition of two memory cells specified by the points-to atoms and and the predicate atom describes a set of heaps that are all also models of the predicate defining an acyclic singly-linked list segment between and .\n\nFig. 1.\n\nSpen workflow for satisfiability checking\n\n## 3 Satisfiability Checking\n\nGiven a set of inductive definitions and a symbolic heap , the procedures for checking satisfiability in Spen follow the workflow given in Fig. 1. The satisfiability checking of an formula makes a classic use of this basic procedure. The crux of the procedures for both fragments is the definition of a boolean formula , called boolean abstraction, such that the data-free part of is satisfiable iff is satisfiable [6, 7].\n\nOnce the boolean abstraction is computed, Spen queries a SAT solver (currently, minisat 2) for the satisfiability of . If is unsatisfiable, Spen can return an unsatisfiable core of , deduced from an unsatisfiable core of . If is satisfiable and , Spen has the option of returning a model of obtained from a model of by unfolding predicate atoms corresponding to non-empty heap segments. The unfolding of predicate atoms is done twice to emphasize the non-emptiness of the segment. For , the satisfiability checking continues by constructing a formula that conjuncts the data part of with the data parts obtained by unfolding the non-empty heap segments given by the model of . To check the satisfiability of , Spen queries an SMT solver for the theory of multisets with integer data (currently, Spen implements a wrapper for the UFLIA theory of z3 [5]).\n\nIf the boolean abstraction is satisfiable, it is then used to normalize the spatial part of , which is a step used by entailment checking too. This process saturates the pure part of with (dis-)equalities between locations variables and removes predicate atoms that correspond to empty heap segments, producing a normalized formula .\n\nFig. 2.\n\nSpen workflow for entailment in\n\n## 4 Entailment Checking\n\nTo check the validity of an entailment , Spen uses a sound procedure to deal with disjunctive formulas: it checks that for every disjunct in , there is a disjunct of such that . The procedure for deciding the validity of entailments between symbolic heaps follows the workflows given in Figs. 2 and 3 (the theoretical foundations were established in [6, 8]). The two formulas are first checked for satisfiability and normalized using the procedures from Sect. 3. If one of the two formulas is unsatisfiable, then the validity of the entailment can be already determined, e.g., if is unsatisfiable then the entailment is valid. When both formulas are satisfiable, Spen offers two different procedures tuned for each fragment of .\n\nFor the fragment , Spen reduces the entailment problem to a set of entailment queries of the form , called simple entailments, where is a sub-formula of and a is a (points-to or inductive) spatial atom of (there will be one such entailment for each spatial atom a in ). Intuitively, the sub-formula describes the region of a heap modelled by that should satisfy a. The procedures for computing and testing simple entailments use an intermediary graph representation of symbolic heap formulas, called an SL-graph and denoted . Basically, nodes of represent sets of aliased variables according to the pure part of , and edges represent dis-equalities and spatial atoms of , e.g., a spatial atom is represented by a directed edge from X to Y labeled by . Thus, when a is a predicate atom , is obtained from the SL-graph of by selecting the edges reachable from X and co-reachable from Y. The graph selected for is transformed into a tree , which is tested for membership in the language of a tree automaton built from the rules defining P for the atom .\n\nFig. 3.\n\nSpen workflow for entailment in\n\nFor the fragment , Spen implements a proof search strategy for the entailment problem . The strategy computes a sequence of formulas such that (1) and (2) is syntactically equivalent to . The entailments in point (1) are obtained by applying the inductive rules and lemmas obtained automatically thanks to restriction required on inductive definitions. The procedure requires to check entailments between data constraints, which is done using the previously mentioned wrapper to the SMT solver.\n\nFor both procedures, when the input entailment holds, Spen has the option of providing a proof witness that either indicates the fact that is unsatisfiable or it consists of the normalized forms of and and the mapping of sub-formulas in to atoms of . When the input entailment is not valid and the procedure terminates, Spen provides a diagnosis that explains why the entailment fails.\n\nTable 1.\n\nExperimental results on an Intel(R) Core(TM) i7-2600 CPU at 1.60 GHz\n\nFragments | Benchmark | Size | Time [s] | SL-COMP'14 results Time [s] StarExec\/solver\n\n---|---|---|---|---\n\n | | |\n\n | | sll0_sat | 110 | 11.20 | 11.28 | (I) 1.06\/Asterix, (II) 3.27\/Spen\n\n | | sll0_entl | 292 | 34.45 | 34.94 | (I) 2.98\/Asterix, (II) 7.58\/Spen\n\n | | FDB_entl | 43 | 1.08 | 1.00 | (I) 0.61\/Spen, (II) 43.65\/Sleek\n\n| |\n\nFDB_entl | 55 | 0.65 | \u2014 | \u2014\n\n## 5 Experimental Results\n\nSpen has been applied to a benchmark of 578 problems (available in the repository), 90% obtained from verification conditions of iterative programs on complex dynamic data structures. The remaining problems are crafted to test the capabilities of the solver. Tables 1 and 2 provide an overview of results obtained by Spen on this benchmark.\n\nThe benchmark of problems includes three divisions of SL-COMP'14: satisfiability and entailment problems for acyclic singly linked lists (sll0_sat resp. sll0_entl), and entailment checking for formulas describing more complicated types of linked lists, e.g., doubly-linked lists, skip lists, and nested lists (FDB_entl). Spen spends less than 0.05 s on 90% of the problems with the maximum time of 0.5 s; these times include calls to a SAT solver. The benchmark FDB_entl includes the problems not in the SL-COMP'14 benchmark (e.g., formulas describing lists of cyclic lists). The reported times in the last column have been obtained in 2014 on the StarExec3 platform.\n\nTable 2.\n\nResults for\n\nBenchmark | Size | Time [s]\n\n---|---|---\n\nsll0_sorted | 16 | 0.45\n\nBST | 45 | 1.67\n\nAVL | 22 | 1.21\n\nRBT | 21 | 3.61\n\nThe benchmark of problems (see Table 2) includes verification conditions for proving the correctness of iterative procedures (delete, insert, search) over recursive data structures storing integer data: sorted lists, binary search trees, AVL trees, and red-black trees. Spen spends less than 0.4 s on each problem, including calls to SAT and SMT solvers. The first three lines of Table 1 demonstrate that the two approaches implemented in Spen (based on tree automata\u2014column \" \"\u2014and on proof search\u2014column \" \") are not only complementary but also comparable on the common fragment. The improvements discussed in this paper reduce the execution times by 10% within the division sll0_entl and by 30% within FDB_entl w.r.t. the old version [6].\n\nAcknowledgement\n\nThis work was supported by the French ANR project Vecolib, the Czech Science Foundation (project 17-12465S), the BUT FIT project FIT-S-17-4014, the IT4IXS: IT4Innovations Excellence in Science project (LQ1602), and by the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement No. 678177).\n\nReferences\n\n1.\n\nBerdine, J., Calcagno, C., O'Hearn, P.W.: A decidable fragment of separation logic. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2004. LNCS, vol. 3328, pp. 97\u2013109. Springer, Heidelberg (2004). doi:10.\u200b1007\/\u200b978-3-540-30538-5_\u200b9 CrossRef\n\n2.\n\nBrotherston, J., Gorogiannis, N., Petersen, R.L.: A generic cyclic theorem prover. In: Jhala, R., Igarashi, A. (eds.) APLAS 2012. LNCS, vol. 7705, pp. 350\u2013367. Springer, Heidelberg (2012). doi:10.\u200b1007\/\u200b978-3-642-35182-2_\u200b25 CrossRef\n\n3.\n\nCalcagno, C., Yang, H., O'Hearn, P.W.: Computability and complexity results for a spatial assertion language for data structures. In: Hariharan, R., Vinay, V., Mukund, M. (eds.) FSTTCS 2001. LNCS, vol. 2245, pp. 108\u2013119. Springer, Heidelberg (2001). doi:10.\u200b1007\/\u200b3-540-45294-X_\u200b10 CrossRef\n\n4.\n\nChin, W.-N., David, C., Nguyen, H.H., Qin, S.: Automated verification of shape, size and bag properties via user-defined predicates in separation logic. Sci. Comput. Program. 77(9), 1006\u20131036 (2012). ElsevierCrossRefMATH\n\n5.\n\nDe Moura, L., Bj\u00f8rner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337\u2013340. Springer, Heidelberg (2008). doi:10.\u200b1007\/\u200b978-3-540-78800-3_\u200b24 CrossRef\n\n6.\n\nEnea, C., Leng\u00e1l, O., Sighireanu, M., Vojnar, T.: Compositional entailment checking for a fragment of separation logic. In: Garrigue, J. (ed.) APLAS 2014. LNCS, vol. 8858, pp. 314\u2013333. Springer, Cham (2014). doi:10.\u200b1007\/\u200b978-3-319-12736-1_\u200b17\n\n7.\n\nEnea, C., Saveluc, V., Sighireanu, M.: Compositional invariant checking for overlaid and nested linked lists. In: Felleisen, M., Gardner, P. (eds.) ESOP 2013. LNCS, vol. 7792, pp. 129\u2013148. Springer, Heidelberg (2013). doi:10.\u200b1007\/\u200b978-3-642-37036-6_\u200b9 CrossRef\n\n8.\n\nEnea, C., Sighireanu, M., Wu, Z.: On automated lemma generation for separation logic with inductive definitions. In: Finkbeiner, B., Pu, G., Zhang, L. (eds.) ATVA 2015. LNCS, vol. 9364, pp. 80\u201396. Springer, Cham (2015). doi:10.\u200b1007\/\u200b978-3-319-24953-7_\u200b7 CrossRef\n\n9.\n\nIosif, R., Rogalewicz, A., Vojnar, T.: Deciding entailments in inductive separation logic with tree automata. In: Cassez, F., Raskin, J.-F. (eds.) ATVA 2014. LNCS, vol. 8837, pp. 201\u2013218. Springer, Cham (2014). doi:10.\u200b1007\/\u200b978-3-319-11936-6_\u200b15\n\n10.\n\nIosif, R., Rogalewicz, A., Simacek, J.: The tree width of separation logic with recursive definitions. In: Bonacina, M.P. (ed.) CADE 2013. LNCS (LNAI), vol. 7898, pp. 21\u201338. Springer, Heidelberg (2013). doi:10.\u200b1007\/\u200b978-3-642-38574-2_\u200b2 CrossRef\n\n11.\n\nO'Hearn, P., Reynolds, J., Yang, H.: Local reasoning about programs that alter data structures. In: Fribourg, L. (ed.) CSL 2001. LNCS, vol. 2142, pp. 1\u201319. Springer, Heidelberg (2001). doi:10.\u200b1007\/\u200b3-540-44802-0_\u200b1 CrossRef\n\n12.\n\nP\u00e9rez, J.A.N., Rybalchenko, A.: Separation logic modulo theories. In: Shan, C. (ed.) APLAS 2013. LNCS, vol. 8301, pp. 90\u2013106. Springer, Cham (2013). doi:10.\u200b1007\/\u200b978-3-319-03542-0_\u200b7 CrossRef\n\n13.\n\nPiskac, R., Wies, T., Zufferey, D.: Automating separation logic using SMT. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 773\u2013789. Springer, Heidelberg (2013). doi:10.\u200b1007\/\u200b978-3-642-39799-8_\u200b54 CrossRef\n\n14.\n\nQiu, X., Garg, P., Stefanescu, A., Madhusudan, P.: Natural proofs for structure, data, and separation. In: Proceedings of PLDI 2013. ACM Press (2013)\n\n15.\n\nSighireanu, M., Cok, D.: Report on SL-COMP'14. JSAT 9, 173\u2013186 (2014)\n\nFootnotes\n\n1\n\nhttps:\/\/\u200bgithub.\u200bcom\/\u200bmihasighi\/\u200bspen.\n\n2\n\nAvailable at http:\/\/\u200bminisat.\u200bse.\n\n3\n\nwww.\u200bstarexec.\u200borg, an Intel(R) Xeon(R) CPU E5-2609 at 2.40 GHz of and 10 MB cache.\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_23\n\n# From Hazard Analysis to Hazard Mitigation Planning: The Automated Driving Case\n\nMario Gleirscher1 and Stefan Kugele1\n\n(1)\n\nTechnische Universit\u00e4t M\u00fcnchen, Munich, Germany\n\nMario Gleirscher (Corresponding author)\n\nEmail: mario.gleirscher@tum.de\n\nStefan Kugele\n\nEmail: stefan.kugele@tum.de\n\nAbstract\n\nVehicle safety depends on (a) the range of identified hazards and (b) the operational situations for which mitigations of these hazards are acceptably decreasing risk. Moreover, with an increasing degree of autonomy, risk ownership is likely to increase for vendors towards regulatory certification. Hence, highly automated vehicles have to be equipped with verified controllers capable of reliably identifying and mitigating hazards in all possible operational situations. To this end, available methods for the design and verification of automated vehicle controllers have to be supported by models for hazard analysis and mitigation.\n\nIn this paper, we describe (1) a framework for the analysis and design of planners (i.e., high-level controllers) capable of run-time hazard identification and mitigation, (2) an incremental algorithm for constructing planning models from hazard analysis, and (3) an exemplary application to the design of a fail-operational controller based on a given control system architecture. Our approach equips the safety engineer with concepts and steps to (2a) elaborate scenarios of endangerment and (2b) design operational strategies for mitigating such scenarios.\n\nKeywords\n\nRisk analysisHazard mitigationSafe stateController designAutonomous vehicleAutomotive systemModelingPlanning\n\n## 1 Challenges, Background, and Contribution\n\nAutomated and autonomous vehicles (AV) are responsible for avoiding mishaps and even for mitigating hazardous situations in as many operational situations as possible. Hence, AVs are examples of systems where the identification (2a) and mitigation (2b) of hazards have to be highly automated. This circumstance makes these systems even more complex and difficult to design. Thus, safety engineers require specific models and methods for risk analysis and mitigation.\n\nAs an example, we consider manned road vehicles in road traffic with an autopilot (AP) feature. Such vehicles are able to automatically conduct a ride only given some valid target and minimizing human intervention. The following AV-level (S)afety (G)oal specifies the problem we want to focus on in this paper:\n\n * SG: The AV can always reach a safest possible state wrt. the hazards identified and present in a specific operational situation .\n\nBackground. Adopted from [4, 9], we give a brief overview of terms used in this paper: We perceive a mishap as an event of harm, injury, damage, or loss. A hazard (or hazardous state) is an event that can lead to a mishap. We consider hazards to be factorable. Hence, a hazard can play the role of a causal factor of another hazard or a mishap. We denote causal factors, hazards, and mishaps\u2014i.e., the elements of a causal (event) chain\u2014by the term safety risk (risk state or risk for short). We perceive the part of a causal chain increasing risk as an endangerment scenario, and the part of a causal chain decreasing risk as a mitigation strategy. Table 1 exemplifies different endangerment scenarios and how these can be mitigated using corresponding strategies.\n\nMitigation strategies can be seen as specific system-level safety requirements implemented by a given control system architecture. We assume that a control system architecture consists of features deployed on sensors, actuators, and software components running on networked computing units (cf. Fig. 4a). By traditional driver assistance (TDA), we refer to driver assistance features already in the field, e.g. adaptive cruise control (ACC) and lane keeping assistance (LKA).\n\nWe distinguish between the domains vehicle, driver, and road environment. For highly and fully automated driving, not all domains have to be considered. For example, in full automation (e.g. level 5 in [12]), the vehicle has to operate under all road and environmental conditions manageable by a human driver and therefore a driver does not have to be taken into account.\n\nTable 1.\n\nExamples of endangerment scenarios and mitigation strategies.\n\nScenario of endangerment | Possible mitigation strategy\n\n---|---\n\nVehicle | Driver | RoadEnv\n\nVehicle | Subsystem fault | Dependability pattern | Controlled shutdown | car2x com., digital road signs\n\nDriver | Maloperation | Passive safety | Safe reaction (if controllable)\n\nRoadEnv | Unforeseen obstacle | Emergency braking assistant | Braking or circumvention | Digital road signs, x2car com.\n\nIT attack | Security pattern | Safe reaction (if controllable)\n\nContribution. Elaborating on previous work in [5, 6], we contribute\n\n 1. (1)\n\na framework for modeling, analysis, and design of planners (i.e., high-level controllers) capable of run-time hazard identification and mitigation, and\n\n 2. (2)\n\na procedure for constructing planning models from hazard analysis.\n\nFor this, we formalize the core engineering steps necessary for (2a) the identification and analysis of scenarios of endangerment and (2b) the design of operational mitigation strategies. Using an exemplary AV, we incrementally build up a risk structure involving three hazards in the vehicle domain, as well as several strategies to reach safe states in presence of these hazards. We discuss approaches to model reduction suited for run-time hazard analysis and mitigation planning where efficient identification of operational situations and acting therein play a crucial role.\n\nIn this paper, we discuss related work in Sect. 2, our abstraction in Sect. 3, and our modeling framework in Sect. 4. Section 5 shows a procedure for building a hazard mitigation planning model. We present an AV example in Sect. 6, discuss our approach in Sect. 7, and conclude in Sect. 8.\n\n## 2 Related Work\n\nAmong the related formal methods available in robotics planning, embedded systems, and automated vehicle control, we only discuss a few more recent ones and highlight how we can improve over them.\n\nG\u00fcdemann and Ortmeier [7] present a language for probabilistic system modeling for safety analysis. Formalized as Markov decision processes (MDP), they propose two ways of failure mode modeling (i.e., per-time and per-demand failure modes), and two ways of deductive cause consequence reasoning (i.e., quantitative and qualitative). Their model and reasoning can extend our approach. However, our work (i) adds stronger guidelines on how to build planning models and (ii) puts hazard analysis into the context of autonomous systems and mitigation planning.\n\nEastwood et al. [3] present an algorithm for finding permissive robot action plans optimal w.r.t. to safety and performance. They employ partially observable MDPs (helpful in regarding uncertainty and robot limitations) to model robot behavior, and two abstractions from this model to capture a system's modes and hazards. Our framework uses three layers of abstraction ( , , ), operational situations to capture control modes, and a structure to capture hazards. While they directly encode hazard severity for plan selection, our framework allows the planner to calculate the risk priority based on a causal event tree towards mishaps. As opposed to complete behavioral planning, our approach focuses the construction of mitigation planning models. For example, for system faults we can plan mitigations by using adaptation mechanisms of a given control system architecture.\n\nJha and Raman [8] discuss the synthesis of vehicle trajectories from probabilistic temporal logic assertions. Synthesized trajectories take into account perception uncertainty through approximation of sensed obstacles by combining Gaussian polytopes. In a similar context, Rizaldi and Althoff [10] formalize safe driving policies to derive safe control strategies implementing worst-case braking scenarios in autonomous driving. They apply a hybrid-trace-based formalization of physics required for model checking of recorded [10] and planned [11] strategies. [8, 10, 11] discuss low-level control for a specific class of driving scenarios, whereas our approach provides for (i) the investigation and combination of many related operational situations, thus, forming a more comprehensive perspective of driving safety, (ii) regarding various kinds of hazards that might play a role in high- and low-level control beyond safe and optimal trajectory planning and collision avoidance.\n\nWei et al. [14] describe an autonomous driving platform, capable of bringing vehicles to a safe state and stop, i.e., activating a fail-operational mode on critical failure, and a limp-home mode on less critical failure. These are mitigation strategies we can assess in our framework. Their work elaborates on designing a specific class of architectures. Additionally, we provide an approach to systematically evaluate risks and, consequently, derive an architecture design.\n\nBabin et al. [1] propose a system reconfiguration approach developed with the Event-B method in a correct-by-construction fashion using a behavior pattern similar to our approach (particularly, Fig. 2b). Reconfiguration as one way to mitigate faults is discussed in this work. Wardzi\u0144ski [13] discusses hazard identification and mitigation for autonomous vehicles by predetermined risk assessment (i.e., with safety barriers) and dynamic risk assessment. For both, he provides argumentation patterns for creating AV safety cases. In addition to his work, the abstraction and the method we propose covers both paradigms in one framework. We provide formal notions of all core concepts.\n\nFig. 1.\n\nAbstractions for state and predicate modeling, and for hazard analysis.\n\n## 3 Abstraction for Run-Time Hazard Mitigation\n\nFigure 1 depicts three abstractions\u2014 , , and \u2014for run-time hazard mitigation in AVs. The state space pertains to the quantization of continuous signals from the physical world encompassing the driver ( ), the vehicle ( ), and the road environment ( ). For instance, the quantity speed is represented by the discrete state variable , which in turn is used to formulate predicates to obtain the abstract state space . For example, a predicate over sensor values , , can encode , an invariant constraining the activity of leaving a tunnel. We describe this two-staged abstraction in more detail in [6].\n\nHere, we will work with the risk state space whose concepts\u2014actions, hazard phases, their composition and ordering\u2014are discussed below:\n\nActions. Let be a set of actions. We abstract from control loop behaviors within and across operational situations by distinguishing four classes of actions: endangerments , mitigations (see Fig. 2b), mishaps , and ordinary actions . Note that actions can take place in one or more out of the three domains, drv, veh, and renv, depending on the quantities they modify. We require .\n\nDefinition 1\n\n(Hazard Phases). Let be a set of hazards. Given , endangerment actions , and mitigation actions , we define the phases of a hazard h as the set whose elements denote the following:\n\n0\n\n: hazard h is (inact)ive,\n\n: hazard h has been (act)ivated by an action ,\n\n: (act)tivated hazard h has contributed to a mishap by an action , and\n\n: hazard h has been (mit)igated by an action .\n\nFor each hazard h, Fig. 2a depicts as a transition system where , the indices , the state mit subsumes phases, act subsumes phases and . For example, in the vehicle domain, can model degradation transitions and or can model repair transitions.\n\nFrom all the sets of hazard phases, we compose a tuple space as follows:\n\nDefinition 2\n\n(Risk State Space). Based on Definition 1, we define the risk state space as the set of -tuples\n\nFig. 2.\n\nCore concepts for building a risk state space .\n\nWe call any subset of a region. Let with and . To quantify risk in scenarios of endangerment and mitigation strategies (Table 1), we define a partial order over :\n\nDefinition 3\n\n(Mitigation Order). Let be a set of phases for hazard h (Definition 1) and . By the reflexive transitive closure1 , we define the mitigation order , for states , as follows:\n\nIntuitively, denotes \" is better or further in mitigation than .\"2\n\n## 4 Concepts for Run-Time Hazard Mitigation\n\nIn this section, we explain the core concepts of deriving a risk structure for a specific operational situation. Using the risk state space and actions , we define the notions of risk structure, risk region, and operational situation:\n\nDefinition 4\n\n(Risk Structure). A risk structure is a weighted labeled transition system with\n\n * a set called the risk state space (Definition 2),\n\n * a set of actions used as transition labels,\n\n * a relation called labeled transition relation, and\n\n * a set of partial functions called weights where the set can be, e.g. , or .3\n\nTo capture the notions of endangerment scenario and mitigation strategy (Table 1) based on , we consider paths and strategies:\n\nDefinition 5\n\n(Paths, Strategies, and Reachability). By convention, we write for . Then, for , a path is a sequence . By we denote the set of all paths of length l and by all paths over . Furthermore, we call a set a strategy. By with , we denote the set of states reachable in from a state .\n\nEndangerments. We consider an action as an endangerment, i.e., , if for a transition . The class models steps of endangerment scenarios. For example, a can stem from faults in drv, veh, and renv.\n\nMitigations. We consider an action as a mitigation, i.e., , if for a transition . The class models steps of mitigation strategies. One objective of a good mitigation strategy is to achieve a stable safe state.\n\nOperational Situations. States and regions in both correspond to subsets of (Sect. 3). To limit the scope of a risk analysis, we use an operational situation which combines an initial region with a (reasonably weak) invariant holding along the driving scenarios in a specific road environment.\n\nDefinition 6\n\n(Operational Situation). An operational situation is a tuple where and p is an invariant over including all representations of in . Let be the set of all operational situations.\n\nBelow, we will work with a risk structure and assume a fixed operational situation associated with . Hence, we use solely.\n\nRisk Regions. We consider specific subsets of called risk regions, particularly, the safe region , the hazardous region , and the mishap region (see Fig. 2b). Safety engineers aim at the design of mitigations which (i) avoid and (ii) react to endangerments as early and effectively as possible. Then, reduces to unavoidable actions from so-called near-mishaps still in towards . For example, we consider a successfully deployed airbag to be in such that is not reached in such an accident (more in Sect. 7).\n\nOur definitions of risk regions depend on : First, . We require mishaps to be final, i.e., . Second, and vary with a given operational situation. Moreover, they can be defined based on, e.g. weights and equivalences. However, and, for an , we start in the safe region iff .\n\nWeights. By associating weights with elements of , we quantify further details on the physical phenomena of the controlled process relevant for risk analysis.\n\nFor example, given with , the probability of endangerment yields the probability that hazard h gets activated in by performing in . Furthermore, given with ,\n\n * the probability of mitigation yields the probability that hazard h gets mitigated in by performing in .\n\n * the cost of mitigation yields the potential effort (i.e., time, energy, other resources) of performing the mitigation .\n\nFor any mishap , specifies its severity. Depending on the abstraction, we can use qualitative (as shown above) or quantitative scales for and . Anyway, we assume to have operators for and , e.g. see Fig. 3a.\n\nWeights are typically calculated from measurements of the controlled process. For example, the estimation of might be result of a controllability analysis of in (of an operational situation). Moreover, further quantities (e.g. risk priority) might be (i) calculated from weights, (ii) be propagated along , and (iii) lead to an update of weights.\n\nRisk Priority. Given , and a function , we can compute the minimum partial risk priority\n\n(1)\n\nwhere denotes the probability4 that from some mishap is eventually ( ) reached in . This definition implements a traditional measure of risk analysis (see, e.g. [4]), referring to the minimum negative outcome (i.e., damage, injury, harm, loss) possibly reachable from in a specific operational situation . Note that for , .\n\nEquivalences Over . For simplification of complex risk structures , we can construct equivalence classes over states. From the structure of states in , the dynamics in , and the elements of the control system architecture (Sect. 1), we give a brief informal overview of equivalences over to be considered:\n\nWe speak of feature equivalence, , iff both, and map to the same set of active features of the control system, i.e., in-the-loop no matter whether they are fully operational, faulty, or degraded. Note that out-of-the-loop features can be faulty, deactivated, or in standby mode. Next, we speak of degradation equivalence, , iff and both states share the same set of degraded features. Furthermore, we speak of hazard (or fault) equivalence, , iff , and, particularly, of mishap equivalence, , iff . Based on , we finally define:\n\nDefinition 7\n\n(Mitigation Equivalence). Based on Definition 3, two states are mitigation equivalent, written , iff\n\n## 5 Construction of Risk Structures\n\nIn this section, we describe an incremental and forward5 reasoning approach to building a risk structure .\n\nFig. 3.\n\nOperators and scheme\n\nIdentification of Hazards. Throughout the construction of , we assume to have a procedure for the identification of a set of hazards based on a fixed control loop design of a class of AVs and their environments, and a fixed set of operational situations (Definition 6). Failure mode effects and fault-tree analysis (see, e.g. [4]) incorporate widely practiced schemes for .\n\nBuilding the Risk Structure. Figure 3b shows the main steps of a procedure which, given a set and after termination, returns all elements of a complete risk structure . Here, completeness is relative to and means that can no more be extended by (i) states which are reachable by existing actions in , (ii) actions which allow reaching non-visited states in , (iii) transitions in which are technically possible and probable, and (iv) further knowledge by extending the domains of weights. Based on Fig. 3b, Algorithm 1 refines for a control loop and an operational situation .\n\nThe while-loop (cf. line 2) accounts for the alternation between adding endangerments and mitigations. By using the maps and (cf. lines 2, 3, 14, 17, 26), the algorithm keeps track of the endangerment- and mitigation-coverage of visited states, i.e., for which hazards has already been visited.\n\nWe assume to have (i) a function (cf. lines 9, 11, 22, 23) which acts as an oracle for weights (Sect. 4) depending on , and (ii) a function (cf. lines 6, 20) which acts as an oracle for determining the technical possibility of newly identified transitions.\n\nThe first for-loop checks for the addition of new transitions to (cf. line 7). The transition constructor returns a state with the given hazard or mishap activated (i.e., phases or ). Note that can generate reachable via .\n\nThe second for-loop checks for the addition of new transitions to (cf. line 21). The transition constructor returns a state with the given hazards mitigated to a new phase for each .\n\nNote that none of the constructors is idempotent, can construct several mitigation phases for each hazard (cf. lines 18, 26) and can construct two activation phases, and , both with the corresponding actions (cf. lines 4, 14).\n\nModel Reduction. To keep reasoning efficient, we have to apply reachability-preserving simplifications to (cf. lines 29f), e.g. equivalences such as in Definition 7. The mitigation order (Definition 3) helps in reducing the state space and in merging actions modifying phases of the same hazards (i.e., by hazard equivalence).\n\nAbstraction from Control System Architecture. In both stages of Algorithm 1, we need to analyze the given or envisaged architecture and to identify state variables, e.g. for software modules, at an appropriate level of granularity.\n\nIn the endangerment stage (lines 3ff), we can perform dependability analyses to identify events that can activate causal factors. Off-line, we then design specific measures to reach the safe region again, and, on-line, we design generic measures to be refined at run-time.\n\nMoreover, the mitigation stage (lines 17ff) helps to revise a control system architecture, e.g. by adding redundant execution units and degradation paths. Moreover, we can pursue off-line synthesis of respective parts of the control system architecture.\n\nHazard Mitigation Planning. First, is hybrid in the sense that it (i) performs the sensing of already known endangerment scenarios (e.g. near-collision detection, component fault diagnosis) on-line, and (ii) allows the addition of new scenarios from off-line hazard analysis.\n\nSecond, a simple planner would continuously perform shortest weighted path search in to keep a list of all available lowest-risk mitigation paths (Definition 5) and coordinate optimized lower-level controllers.\n\nBased on these two steps, we assume to be continuously updated according to the available information (i.e., adding or modifying endangerments and mitigations according to known scenarios). It is important to have powerful and precise update mechanisms, highly responsive actuation, and short control loop delays. Main issues of signal processing are briefly mentioned in Sect. 7.\n\nThe notion of safest possible state (SG, Sect. 1) is governed by the accuracy of (Sect. 3), the completeness of the results of , and the exhaustiveness of for a fixed setting . According to Definition 3, for a pair , we might say that is the safest possible state iff we have\n\n(2)\n\nwhere . Any controller for SG would have to find and completely conduct a shortest plan for to reach .\n\n## 6 Example: Fail-Operational Driver Assistance\n\nElaborating on an example in [6], we apply our framework and algorithm to hazard analysis and elaboration of mitigation strategies. We use the abbreviations introduced in Sect. 1.\n\nIdentifying an Operational Situation. We consider the situation : \"AV is taking an exit in a tunnel, at a speed between 30 and 90 km\/h, with the driver being properly seated, and the next road segments contain a crossing.\" Figure 4b depicts the corresponding street segment.\n\nFig. 4.\n\nTwo cutouts of the road vehicle domain.\n\nModeling the Road Vehicle Domain. Figure 4a shows a simplified control system architecture used for driver assistance systems. We model the relevant state information according to the abstractions described in Sect. 3. State variables commonly used for road vehicles are listed in Table 2. For , we assume to have the variables6 (prefixed with their domains, in parentheses their types): (coordinate), (vector of floats), (street map7), and (enumeration). veh denotes all variables of this domain. For , we identify the following predicates8:\n\nFurthermore, we use unspecified predicates:\n\nThe invariant for is . Note that the AP is active in the initial state associated with .\n\nNotation. In the following (Figs. 5a, b and 6), for each state, H denotes that the hazard H is active (phase ), that H contributed to a mishap (phase , only in Table 3), and that its ith mitigation phase is active (phase ). We do not indicate hazards which are in phase 0.\n\nTable 2.\n\nExemplary state variables of the different domains.\n\nDomain | State variables | Abbreviation\n\n---|---|---\n\nDriver | Physical presence, consciousness, vigilance, | drv\n\nVehicle | Speed, loc(ation), fault conditions, | veh\n\nRoadEnv | Daylight, weather, traffic, road, | renv\n\nIncremental Forward Construction of the Risk Structure. Refining the regions and (Fig. 2b), we construct from three hazards A, L, and R identified by (Sect. 5). Table 3 sketches the construction of the first and second increments towards , including the events \"AP sensor fault\" and \"TDA LKA software fault.\"\n\nTable 3.\n\nModel after two increments ( ). denotes true parallelism, ; concatenation.\n\nFigure 5a shows for . According to Algorithm 1, we try to add the fault condition L to and other states in (i.e., black states in Fig. 5a). Based on the action , this step yields the states , and AL. Then, a mitigation step yields the states and and, finally, another step of endangerment analysis based on the action yields .\n\nRisk Priority Estimation. From the state with , we can derive, e.g. according to Eq. (1). We can as well derive because reaching by driving assistance control is no more possible.\n\nEquivalences and Model Reduction. In Fig. 5a, for example,\n\n * because in both states A is mitigated and other hazards are inactive (0, cf. Definition 7),\n\n * because in the degraded variants of LKA and ACC, i.e., LKA and ACC , are in the loop,\n\n * because in both states LKA and ACC are in the loop,\n\n * because in both states, LKA and ACC are in the loop, and\n\n * because ACC (part of AP) is faulty and ACC (part of TDA) is fully operational.\n\nSimplifications can be derived from Fig. 5a, where we might (i) merge two states if , or (ii) merge two consecutive states on a \"safe\" mitigation path, e.g. from any to if actions such as limp-home, shutdown, and repair are feasible from .\n\nFig. 5.\n\nRisk structure and its simplification .\n\nTable 4.\n\nAdding endangerments for the third increment ( ).\n\n3 | Description | Model increment\n\n---|---|---\n\n | Driver reaction time increases |\n\n | States |\n\n | Action ...\"driver looks sidewards\" \"hands go off steering wheel\" |\n\n| |\n\nFig. 6.\n\nRisk structure after adding endangerments (in red) for the 3 increment (weights not shown, cf. Table 4). (Color figure online)\n\nFigure 5b shows a simplification of . We omit irrelevant transitions ( ) and collapse the mitigation-equivalent ( ) states and . Consequently, with the states and we get a refinement of . According to Eq. (2), is a safest possible state reachable from A.\n\nNext, Table 4 and Fig. 6 describe a cut-out of after the third increment where we added the event \"Driver reaction time increases.\"\n\n## 7 Discussion of Limitations, Applicability, and Strengths\n\nThe abstraction (Sect. 3) is subject to standard signal processing steps, i.e., sampling of continuous signals at discrete time points, quantization of dense domains to form finite domains, and clamping of domains. We assume all signals to be sampled faster then their respective Nyquist period, sufficiently small quantums, and sufficiently large ranges of data types. Furthermore, we expect a mitigation planner to be fast enough (sufficiently low latency) to provide outputs for effective and optimal control. Note that the risk structure abstracts from the low-level parameters necessary for actual control of mitigations which takes place at the level of .\n\nThe treatment of these issues will determine how accurate mitigations can take place at the right time and duration. In addition, we might consider higher-order mitigations to handle adverse impacts of first-order mitigations. However, such impacts have to be identified as hazards to get recognized in .\n\nElaborating on risk regions (Sect. 4), represents mitigation-less harmful states, however, includes all states where mitigations are feasible. Consequently, we allow \"bad things to happen\" as long as we have partial mitigations, e.g. an airbag would prevent from reaching at a certain probability.\n\n## 8 Conclusion and Future Work\n\nWe presented risk structures as a model to design high-level controllers capable of run-time hazard mitigation, i.e., of maintaining or reaching the safest states in a given operational situation. We sketched an incremental approach to develop mitigation strategies. Safety measures are a combination of reducing or eliminating endangerments with constructing or strengthening mitigations. Risk structures can help to derive safety requirements for a control system architecture. Moreover, they can lay a basis for the evaluation, choice, and combination of mitigation strategies. Our example highlights challenges to tackle in hazard mitigation of fail-operational automated driving. Finally, we indicate how several formalisms\u2014temporal specification, predicate abstraction, and transition systems\u2014can coherently aid in hazard mitigation planning.\n\nFuture Work. Based on risk structures, we aim to evaluate criteria such as (i) time, energy, and cost of mitigations, (ii) the role of human intervention, (iii) resilience to change of operational situations, (iv) control system simplicity.\n\nIn the next steps, we want to efficiently automate the derivation of acceptable mitigation strategies, and synthesize feasible and affordable mitigation strategies. Based on weights, we can define desirable properties of mitigation strategies implemented in , e.g. monotonicity.\n\nDefinition 8\n\n(Mitigation Monotonicity). Let be a strategy (Definition 5) and . We call S mitigation monotonous iff for each path .\n\nIntuitively, during planning we seek mitigation paths containing only endangerments, if any, which do not increase risk priority. This might, however, be a definition to be relaxed for practical use by, e.g. allowing -distances.\n\nGiven that we use our algorithm off-line, it is important to make the and steps in Algorithm 1 interactive for the safety engineer. Moreover, instead of elaborating -specific risk structures off-line, we aim at using our algorithm to generate such structures on-line given a specific operational situation, and combine this with a transition system switching between operational situations. Given that we use our algorithm on-line, it is important to develop simplification rules to be applied to based on the equivalences in Sect. 4.\n\nWe plan to evaluate our results in the automotive industry whose aims include checking whether fail-operational extensions of given in-vehicle network architectures for automated driving can be made acceptably safe.\n\nFinally, for a regulatory agency to apply our approach to AV, we have to show (i) our approach using a large example involving several operational situations, (ii) how our abstraction can be verified, and (iii) that the limits of controllers do not constrain our approach to achieve safe stable control loops.\n\nAcknowledgments\n\nWe are grateful to Maximilian Junker for a thorough review of this work. Moreover, we thank our project partners from the German automotive industry for inspiring discussions and providing a highly innovative practical context for our research. Furthermore, we thank our peer reviewers for suggestions on the use of risk structures, signal processing, and regulatory certification.\n\nReferences\n\n1.\n\nBabin, G., Ait-Ameur, Y., Pantel, M.: Correct instantiation of a system reconfiguration pattern: a proof and refinement-based approach. In: 17th International Symposium on High Assurance Systems Engineering (HASE), pp. 31\u201338, January 2016\n\n2.\n\nBaier, C., Katoen, J.P.: Principles of Model Checking. MIT Press, Cambridge (2008)MATH\n\n3.\n\nEastwood, R., Alexander, R., Kelly, T.: Safe multi-objective planning with a posteriori preferences. In: 17th International Symposium on High Assurance Systems Engineering (HASE), pp. 78\u201385, January 2016\n\n4.\n\nEricson, C.A.: Hazard Analysis Techniques for System Safety, 2nd edn. Wiley, Hoboken (2015)\n\n5.\n\nGleirscher, M., Kugele, S.: Reaching safe states in autonomous road vehicles. In: 35th Annual International Conference on Computer Safety, Reliability and Security (SAFECOMP). HAL, September 2016. https:\/\/\u200bhal.\u200blaas.\u200bfr\/\u200bhal-01370229. extended abstract\n\n6.\n\nGleirscher, M., Kugele, S.: Defining risk states in autonomous road vehicles. In: IEEE 18th International Symposium on High Assurance Systems Engineering (HASE), Singapore, January 2017\n\n7.\n\nG\u00fcdemann, M., Ortmeier, F.: A framework for qualitative and quantitative formal model-based safety analysis. In: IEEE 12th International Symposium on High Assurance Systems Engineering (HASE), pp. 132\u2013141, November 2010\n\n8.\n\nJha, S., Raman, V.: Automated synthesis of safe autonomous vehicle control under perception uncertainty. In: Rayadurgam, S., Tkachuk, O. (eds.) NFM 2016. LNCS, vol. 9690, pp. 117\u2013132. Springer, Cham (2016). doi:10.\u200b1007\/\u200b978-3-319-40648-0_\u200b10 CrossRef\n\n9.\n\nLeveson, N.G.: Engineering a Safer World: Systems Thinking Applied to Safety. Engineering Systems. MIT Press, Cambridge (2012)\n\n10.\n\nRizaldi, A., Althoff, M.: Formalising traffic rules for accountability of autonomous vehicles. In: IEEE 18th International Conference on Intelligent Transportation Systems, pp. 1658\u20131665, September 2015\n\n11.\n\nRizaldi, A., Immler, F., Althoff, M.: A formally verified checker of the safe distance traffic rules for autonomous vehicles. In: Rayadurgam, S., Tkachuk, O. (eds.) NFM 2016. LNCS, vol. 9690, pp. 175\u2013190. Springer, Cham (2016). doi:10.\u200b1007\/\u200b978-3-319-40648-0_\u200b14 CrossRef\n\n12.\n\nSAE International: J3016: Taxonomy and Definitions for Terms Related to On-Road Motor Vehicle Automated Driving Systems. Technical report, January 2014\n\n13.\n\nWardzi\u0144ski, A.: Safety assurance strategies for autonomous vehicles. In: Harrison, M.D., Sujan, M.-A. (eds.) SAFECOMP 2008. LNCS, vol. 5219, pp. 277\u2013290. Springer, Heidelberg (2008). doi:10.\u200b1007\/\u200b978-3-540-87698-4_\u200b24 CrossRef\n\n14.\n\nWei, J., Snider, J.M., Kim, J., Dolan, J.M., Rajkumar, R., Litkouhi, B.: Towards a viable autonomous driving research platform. In: Proceedings of the 2013 IEEE Intelligent Vehicles Symposium (IV), pp. 763\u2013770, June 2013\n\nFootnotes\n\n1\n\nHere, for a relation R, represents the composition of relations.\n\n2\n\nWe use the convention .\n\n3\n\n(m)arginal, (c)ritical, (f)atal; for other examples of severity scales, see [4].\n\n4\n\nSee, e.g. [2] for details about probabilistic temporal logic and reasoning.\n\n5\n\nFor generation of , backward reasoning is the alternative not shown here.\n\n6\n\nVariable types and usage depend on the AV sensors and car2X services through which they are measured. We assume individual error estimators for all variables.\n\n7\n\nWith, e.g. topological coordinate system, information about tunneled parts.\n\n8\n\nHere, refers to a pattern for the street map element class x which acts like a filter on the street map data type. For sake of brevity, we omit details of sensor fusion and street map calculations required for evaluating these predicates.\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_24\n\n# Event-B at Work: Some Lessons Learnt from an Application to a Robot Anti-collision Function\n\nArnaud Dieumegard1 , Ning Ge1, 2 and Eric Jenn1, 3\n\n(1)\n\nIRT Saint-Exup\u00e9ry, 118 Route de Narbonne, 31432 Toulouse, France\n\n(2)\n\nSysterel Toulouse, La Maison des Lois, 2 Impasse Michel Labrousse, 31036 Toulouse, France\n\n(3)\n\nThales Avionics, 105 Avenue du G\u00e9n\u00e9ral Eisenhower, BP 63647, 31036 Toulouse Cedex 1, France\n\nArnaud Dieumegard (Corresponding author)\n\nEmail: arnaud.dieumegard@irt-saintexupery.com\n\nNing Ge\n\nEmail: ning.ge@systerel.fr\n\nEric Jenn\n\nEmail: eric.jenn@irt-saintexupery.com\n\nAbstract\n\nThe technical and academic aspects of the Event-B method, and the abstract description of its application in industrial contexts are the subjects of numerous publications. In this paper, we describe the experience of development engineers non familiar with Event-B to getting to grips with this method. We describe in details how we used the formalism, the refinement method, and its supporting toolset to develop the simple anti-collision function embedded in a small rolling robot. We show how the model has been developed from a set of high-level requirements and refined down to the software specification. For each phase of the development, we explain how we used the method, expose the encountered difficulties, and draw some practical lessons from this experiment.\n\nKeywords\n\nFormal refinementSoftware verificationFormal verificationAnti-collisionEvent-B\n\n## 1 Introduction\n\nThe practical implementation details and the difficulties encountered during the application of the Event-B method by \"typical industrial engineers\" are usually not widely discussed. Therefore, in the current publication, we share the method we have used, the difficulties we have encountered, and some lessons we have learnt when applying this method to develop one particular function of our small rolling robot [1].\n\nIt is worth noting that even though this development was tightly driven by considerations about aeronautical certification, the question of compliance with ARPs [2] or DOs [3\u20135] objectives using Event-B is not directly addressed here.\n\nThe paper is organized as follows. Section 2 outlines our development process. Section 3 introduces our case study: the anti-collision function of a small rover. Section 4 details the elaboration of the software requirements using formal refinement. Section 5 covers related works. We conclude in Sect. 6.\n\n## 2 Formal Refinement in an Industrial Development Process\n\nOur experiment focuses on the following development activities: (i) formalization of the system specification, (ii) definition of a refinement strategy, (iii) application of the refinement strategy to elaborate a set of high-level software requirements compliant with the initial specification. Subsequent software production activities are not detailed and are the subject of an ongoing publication [6]. Other activities such as integration or testing are not addressed.\n\nThe development process starts with a set of informal requirements expressed in a natural language. In order to optimize the modelling and validation effort, the initial set of requirements is decomposed into disjoint subsets, the processing of which is realized sequentially. Processing a subset of the requirements involves several phases: formalization, where requirements are translated into Event-B constructs; validation, where these constructs are validated against the initial user specification; refinement, where these constructs are made more concrete; verification, where the correctness of these constructs is proved. This process stops when (i) all subsets have been processed and (ii) the set of modelling elements allocated to software is completely defined. The overall development process is depicted on Fig. 1.\n\nFig. 1.\n\nOverall development strategy\n\nWith respect to a typical development process in the aeronautical domain, this part of the overall process covers part of the system-level specification and design activity (as per ARP4754 [2]) and part of the software requirement activity (as per DO-178C [3]).\n\nIn our case, we consider the last refinement of the Event-B model to carry high-level requirements (HLR), i.e., \"software requirements developed from analysis of system requirements, safety-related requirements, and system architecture\" (DO-178C). The software code will be implemented from those HLR; this part of the process is described in [6].\n\n## 3 The Case Study\n\n### 3.1 The TwIRTee Rover and the ARP Function\n\nTwIRTee is the three-wheeled robot (or \"rover\") used as the demonstrator of the INGEQUIP project conducted at the Institut de Recherche Technologique of Toulouse (IRT Saint-Exup\u00e9ry). It is used to evaluate new methods and tools in the domain of hardware\/software co-design [1], virtual integration, and application of formal methods for the development of equipment [6\u20139]. TwIRTee's architecture, software, and hardware components are representative of aeronautical, spatial and automotive systems.\n\nA rover performs a sequence of missions (\u2776 on Fig. 2) defined by a start time and an ordered set of waypoints to be passed-by. Missions are planned off-line and transmitted to the rover by a supervision station (\u2777). To go from the first waypoint to the last, the rover moves on a track materialized by a dark line on the ground. In a more abstract way, a complete mission can be modelled by a path in a graph where nodes represent waypoints, and edges represent parts of the track joining two waypoints.\n\nFig. 2.\n\nSystem overview (Color figure online)\n\nA rover shares the tracks with several identical rovers. In order to prevent collisions, each of them embeds a protection function (or ARP) which purpose is to maintain some specified spatial (\u2778) and temporal separation (\u2779) between them. On Fig. 2, temporal separations are represented by light green and light red areas superimposed on the map: basically, rover 2 (resp. rover 1) shall never enter the light green (resp. light red).\n\nIn our implementation, the ARP essentially acts by reducing the rover speed and, in some specific cases, by performing a simple avoidance trajectory. To take the appropriate action, the ARP exploit the following information: the map, the position of all other rovers transmitted by a centralized supervision station (\u277a), and its own position.\n\nFor this paper, we rely on a simplified version of the ARP function where some specification elements such as the rovers positions, speeds, decelerations, etc. are represented as discrete values (no use of Real or Floating Point data). Interested readers can refer to another study [9] conducted on this same function but covering different formal modelling aspects.\n\n### 3.2 Rodin and Event-B\n\nEvent-B [10] is a method to develop systems according to a correct-by-construction approach. It is the system level modelling evolution of the B-method [11] successfully applied in real-size industrial applications [12]. The Event-B method constructs a correct model of a system via a series of refinements of its specification. The correction of a refinement is ensured by proving automatically or manually a set of proof obligations (PO) generated from the model.\n\nThe Rodin Platform1 is an Eclipse-based IDE for Event-B that provides effective support for refinement and mathematical proof. The platform is open source, based on the Eclipse framework. Its development started in 2004 during the RODIN project, and continued within the DEPLOY and ADVANCE projects. The community is still active regarding the development. The extensibility of the platform through the use of plugins is of great interest as it allows to rely among others on (i) analysis tools for verification (SMT solvers, model checkers) or validation (animators, simulators generators) of the models and the refinements, (ii) traceability facilities for link with requirement documents, (iii) code generation tooling, (iv) automated refinements methods easing the refinement work.\n\n## 4 From System-Level Requirements to High-Level Requirements\n\nIn our process, the latest refinement of the Event-B model represents software HLR. As already studied in [10, 13], the development of a refinement strategy is the entry point for the definition of Event-B models. It improves the understanding of the requirements by the designer and the robustness of the development process by providing an intermediate formalization phase between requirements and design. Refinement strategy application produces Event-B refinements.\n\n### 4.1 Building a Refinement Strategy\n\nOur refinement strategy is based on Abrial [10], Butler et al. [13] and Su et al. [14]. The work started with a thorough analysis of the requirements to identify the variables used in the system and classify them as either uncontrolled (environment), controlled (system), or commanded (operator). Requirements are classified according to the same three categories. The main role of the ARP function is to ensure the absence of collision between rovers by controlling the deceleration of the rover. The controlled variable deceleration of the control function is chosen as the first element of focus in the requirements document for the elaboration of the refinement strategy.\n\nRequirements Layering\n\nThe refinement strategy defines the order to process the requirements. This order is determined from the dependencies between variables and, consequently, between requirements. In our case study, we identified the deceleration feature as dependent of the occurrence of conflicts and emergency braking. As a first abstraction, conflicts might occur at any time and so might emergency braking. Our initial layer of refinement was thus only composed of these three variables.\n\nFrom this entry point, the next requirements layers are produced by gradually introducing new features such as: fleet of rovers, distances between rovers, emergency braking etc. Each feature is attached to a subset of the initial requirements. As some requirements are linked to multiple features, they are attached to multiple layers and their implementation is gradually completed along with the refinement of layers.\n\nComplementary to the previous horizontal refinements, vertical data refinements are also performed. For instance, the values of the deceleration variable, initially constrained by a simple range in the early refinement, become later constrained by axioms specifying the semantics of deceleration. Similarly, the calculus of the distance between rovers that was simply defined as a value in a range is refined as a shortest path function.\n\nLessons Learnt\n\nBuilding a consistent, adequate and applicable refinement strategy is the first step towards the correct understanding of the system and contributes to the correct modelling of the system. If requirement classification is a rather systematic activity, their layering (or sequencing) is more difficult. Layering starts with the identification of an entry point from which the activity starts. Layering may be driven by the identification of the minimal subset of features that ensures the capability to simulate and validate the model at each layer.\n\n### 4.2 Formalization of Requirements\n\nFormalization starts with the definition of Event-B contexts containing sets, constant variables and constant relations, the definition domain of which are specified as axioms. Then machines are detailed with variables and relations with their definition domain specified as invariants. Variables require the setting of their initial value in the special INITIALIZATION event. Variables shall be used in events specifying the condition under which their value changes (guards) and how their value changes (actions). Event execution modifies the state of the system. Properties expected to be verified by the system shall be added as invariants of the machine and shall hold in every event.\n\nProducing Event-B models from informal specification can be done using multiple approaches. A first approach relies on modelling the states of the system as sets. In that interpretation, state changes are represented by the \"movement\" of elements from one set to another. This approach has been used for instance in an alternative modelling of our use case in [9] where the study goal was on time and the data refinements relied on the use of real values.\n\nOur modelling approach, depicted in Fig. 3, is inspired from [10]. The function is first abstracted as a hierarchic cyclic state machine comprising two states: the first one updates the state of the environment of the system and the second updates the state of the system itself (i.e., performs the function under design). Transition from one state to the other is triggered by dedicated events ( arp_state_env_start and arp_state_fun_start ) updating a state variable arp_state . Sub state machines are triggered depending on activation variables ( [mm|fm|cm|em]_activated ). This approach provides a clear separation between the environment and the system under design, exposes the execution cycle, and so facilitates the production of the executable code from the model. Unfortunately, exposing the execution cycle of the function may also introduce implementation details too early in the refinement process.\n\nFig. 3.\n\nEvent-B model as a circuit\n\nLessons Learnt\n\nModelling the system using our approach does suffer from some serious limitations. We assume that all other rovers in the environment do implement the same ARP function as the one under design. For our implementation, this assumption was added as a new environment requirement. Such assumption was not necessary in the alternative modelling approach as every rover in the system was explicitly modelled and each of them implements the same ARP behaviour. Our modelling approach yields an advantage regarding the formal verification: as we do not model all the rovers, a level of universal quantification in the model is removed.\n\nVertical data refinements produce detailed specifications for variables and for functions. These specifications may be purely declarative or imperative. In the first case, implementation is provided outside of the Event-B world; in the second case, Event-B is used to \"code\" the function. In our use case, for instance, an imperative model of the simple \"deceleration function\" could be easily designed in Event-B. However, this would be much more tedious for the \"shortest path function\". Thus we have favoured a pure declarative approach in Event-B, leaving the implementation details to programming languages.\n\nThe choice of the \"set-oriented\" or \"finite-state-machine-oriented\" modelling approach has an impact on efficiency. The use of sets increases abstraction and reduces the modelling effort, but it increases the implementation work. Reciprocally, using the finite state machine approach is less abstract, less compact, more difficult to write, but simplifies the implementation. Additionally, this approach also facilitates the automatic discharging of POs but at the price of adding invariants to propagate the values of variables changed in sub states to the final state of the state machine. Note also that the nature of the variables and the system under design are likely to favor one or the other modelling approaches.\n\nFinally, it is worth noting that writing Event-B models does not require more knowledge than writing software. While using first order logic and set theory is a shift from classical software engineering methods, this belongs to the mathematical background of any engineer. However, writing Event-B model requires a strong capability of abstraction and a capability to describe without being able to execute...\n\n### 4.3 Verification of Refinements\n\nVerification of formal refinements in the Event-B method relies on the discharging of automatically generated POs. POs can be automatically discharged using predicate provers embedded in the Rodin toolset. Plugins have been developed to leverage the increasing capabilities of SMT solvers such as Alt-Ergo2, Z33, CV44, or others. Formal verification is conducted in parallel with formal refinement: as soon as any element is added in an Event-B model, PO are generated and potentially discharged automatically. In some way, this can be related to the automatic syntactic verifications performed by current IDEs.\n\nRefinement Verification in Practice\n\nThe number of generated POs increases with the size of the model. Even with automatic verification provided by embedded PP and SMT solvers, some POs remain to be proved \"manually\". Hopefully, the proof plug-ins in Rodin are easy to use and very intuitive for the users, and thus is of great help when manual proofs are required.\n\nUnfortunately, diagnosing why some PO fails to be discharged manually or automatically remains difficult. The reason may be that the property simply does not hold, or that either the automatic prover or the user is not able to carry out the proof. In the latter case, reasons may be the limited capabilities of the human or mechanical prover, or missing lemmas. Discriminating the various situations is very hard and may require a significant (but hard to estimate) effort.\n\nRodin embedded prover can be adapted through the definition\/modification (with a graphical interface) of profiles. Profiles customization finds its interest in case dependent models as it provides tactics adapted to specific goals to be proved. We relied on profiles customization in our use case in order to add tactics such as \"domain rewriting\" that were of great help for the automation of the proof work.\n\nPart of the proof work was additionally assisted by adding \"helper\" invariants. This was unfortunately not enough to fully automate the formal verification, as about 1% of the proofs remained to be done by hand (a total of 2442 POs including 15 proven by hand). Remaining proofs relate to the use of non-linear arithmetic for which automatic provers are not really efficient. We dealt with these proofs by adding theorems adapted to the proof goals and by performing their proof by hand. The necessary work was not complex but is time consuming due to the manual search for missing theorems.\n\nLessons Learnt\n\nFormal verification is the most time-consuming activity in the refinements process. This work is complex and requires experience and specific skills when automatic proof fails to discharge all POs. Worse, the effort to complete a proof is difficult to estimate. This problem is made even more critical due to the fact that no guidance can be provided to complete a proof. Avoiding manual proof work would thus be a way to avoid such limitation but would require modelling guidance on how to stay on the path of what is automatically provable.\n\nOn the other side, proofs performed fully automatically and immediately may cover other difficulties. Hence, our first proofs were performed in no time due to contradictory axioms\/invariants\/guards. Unfortunately, avoiding such inconsistencies is difficult and detection cannot be done automatically. So we relied on the voluntary insertion of inconsistent axioms\/invariants\/guards to check for the consistency of the other axioms\/invariants\/guards.\n\nAfter a relatively short training on the Event-B method, formalism and proof techniques, it appears to us that modelling systems and proving them using the Rodin toolset is a task that is accessible to engineers with some background in mathematical logics. However, the time needed for the modelling and verification of a system remains difficult to estimate. Worse, the effect of a simple model modification on the proof effort (especially, manual) is difficult to estimate. We really miss appropriate modeling guidance.\n\n### 4.4 Validation of Formal Requirements\n\nIdeally, the set of requirements is consistent and complete at each refinement level. In reality, it is very likely that some requirements have been ignored, misunderstood, or badly transcoded. As the rework of an Event-B model is fairly expensive, it shall be validated as early and often as possible.\n\nExecuting the model has been identified by Event-B experts as the only means to achieve validation [15, 16]. The production of simulators has been the subject of many works [17\u201319] and tools have been developed for this purpose.\n\nSimulator-Based Validation\n\nIn our experiment, we relied on ProB [20] complemented by B-Motion [21] and JeB [22] as validation tools. The last two additionally provide means to graphically represent the execution of the model: this greatly improves stakeholders' ability to validate the Event-B models.\n\nDuring the phase of requirement analysis, we developed a simulator including movement dynamics of the rovers on a map using ScicosLab5 as depicted in Fig. 4. The only purpose of the simulator was to validate our understanding of the specification. Such simulator also has the interesting effect of producing simulation scenarios that can be used as test vectors fed to the Event-B simulators [19]. Simulations relying on such values directly contribute to the validation of Event-B models as they rely on pre-validated sets of values. Integration of third party simulators and produced values can be technically done relying on FMI (Functional Model Interface) and the related plugin developed for integration in the Rodin platform [17].\n\nFig. 4.\n\nScicosLab simulator with graphical display (b) and underlying model (a)\n\nDeveloping Event-B simulators is easy, especially during the first steps of refinement. However, generating actual input vectors for the simulation can be quite tedious and complex when the variables or constants are specified using non-deterministic expressions.\n\nWe relied on JeB [18] for the generation of a web-based simulator and for the generation of values for constants. JeB provides an automatic translation of Event-B models to an executable JavaScript implementation. It is then possible to provide JavaScript functions computing the values for constants (resp. variables and parameters). Such functions produce values that are pretty-printed using Event-B notation. These values can then be used in the original Event-B model making JeB a very handy tool for the production of test vectors for complex data (relations pairs etc....). Computed values correction is formally verified using PP and SMT solvers when they are injected in the Event-B model. In our ARP function we produced values for the refined function for the calculus of the deceleration to be applied by the rover using JeB.\n\nIn control systems, liveness properties or correctness properties such as deadlock freeness shall be verified to ensure the responsiveness of the system. Simulation can be used to obtain a first level of confidence on the absence of deadlocks, before resorting to formal proof. Deadlock freeness theorems can be generated using dedicated Rodin plugins, but depending on the model size, their verification may become very challenging. Verifying these properties can also be done using model checking. But this approach suffers from the classical limitations of model checkers. In our experiment, we used a translation to another formalism and toolset (HLL and S3, see [6]) after introducing a scheduling sequence of events to the system under design to tackle more efficiently and automatically the verification of those properties.\n\nLessons Learnt\n\nValidating a formal model with respect to a set of informal requirements is a difficult task. Hopefully, the Event-B environment provides a set of very helpful animation tools. Animation allows stakeholders to see the behavior of the formal model and validate it. Furthermore, it allows to assess reachability and liveness properties that are difficult (and sometime impossible) to express directly on the Event-B model and to formally verify these properties using model checking. However, as for any test-based approach, confidence on the validation depends on the coverage of the validation scenarios.\n\n### 4.5 Model Review\n\nThe review activity in a classical development process aims at ensuring the correct implementation of requirements as code or the correct refinement of requirements, to detect inconsistencies and misinterpreted requirements, and enforce the use of development standard (e.g., code writing standards). Here, we consider three specific goals: ensure a correct encoding of the designer's intent, reduce the verification effort, and support traceability.\n\nEnsure Correct Encoding of Designer Intent\n\nThe correct encoding of the designer intent is ensured by the validity, correctness, consistency and completeness of the formal model with respect to the requirements. We provide here multiple elements supporting this goal.\n\nIntroduction of verification lemmas is a starting point advocated in many publications to assess the consistency of an Event-B model. As already stated, success in proving obviously false theorems\/invariants\/guards put in contexts\/machine\/events allows one to detect inconsistencies in contexts\/machine initialisation\/event guards and parameters definitions.\n\nAdditional automated tooling for checking expressions could also help in our verification process, as an example, checking if bounded logic variables are used in quantified constructs or writing implications in the body of existentially quantified expressions might raise a warning for the designer.\n\nA proofreading approach to model review could also be applied to Event-B models by having a reviewer to rewrite chosen guards and invariants using natural language. The reviewer would then check if the natural language expressions are indeed correct rewritings of the associated requirements. The opposite approach could also be done and would be safer (reviewer to write the natural language expression of the guard using FOL) but less straightforward for engineers. Proofreading should be focused on complex guards and invariants that are more likely to contain errors and on invariants stating key properties of the system under design.\n\nMinimize Verification Effort\n\nVerification is one of the most expensive activities in the development of embedded critical systems. Minimizing verification efforts is thus of primary interest.\n\nTo facilitate the (possibly automatic) verification process, we have to add additional lemmas to the model. Those lemmas were explicitly identified as \"helper\" lemmas, so as to ease the work of assessing the correction of the model. After several modifications of the model, some of those lemmas became unnecessary and were removed from the model to lighten the verification. It is worth noting that some tautologies were kept in the model even though they did not bring additional information as they appeared to be very helpful to support \"case splitting\" and simplify the automatic proof.\n\nThe verification effort obviously strongly depends on the ability for the verifier to understand the model. One way to achieve this goal relies on the compliance to a set of well-defined modelling rules compiled in a \"modelling standard\", in a way similar to what is usually done for software coding. Many rules for code writing such as MISRA-C [23] can be applied to the writing of logical expressions: avoid deep nesting, avoid too long lines of code, line breaks position according to operators, indentation consistency, parenthesizing consistency, avoid having two operator of different precedence at the same level of indentation. Verification effort can also be strongly reduced by an appropriate organization of the models. For instance, in our experiment, we applied the following rule about model elements ordering: \"the order of declaration of constants, variables or parameters should match the order of appearance of their respective definition (axioms, invariants, guards)\".\n\nIt is obvious but worth noting that adding comments in the model significantly contributes to a better understanding of the intent of the designer and of the structure and choices made during the design process. Comments shall be of help and not state obvious information.\n\nExisting tooling may also simplify the models and thus impact its understandability. For instance, the \"theory\" plugin provides the capability to factorize properties or expressions of the model and thus simplifies the writing (and, later, the understanding) of complex Event-B models.\n\nWe have provided here a few examples of good practices for the writing of an Event-B model to produce more readable, reviewable and thus understandable models. There exists many works and standards used in the industry to ensure such properties for code but to our knowledge there is a minimal work done on applying this to logical specification. We plan on tackling these with more details on a dedicated publication.\n\nTraceability\n\nAeronautics certifications require to trace each design elements to some requirement. The corresponding certification objective is \"High-level requirements are traceable to system requirements\" (DO178 Annex A, table A-3, objective 6). In our experiment, ensuring traceability during the refinement process first relied on making explicit the mapping between the elements in the informal specification and Event-B constructs. At high level, naming conventions allowed us to link each refinement layer defined by the refinement strategy to its corresponding Event-B machine and context. Newly introduced model element (constant, axiom, variable, invariant, event, guard and action) were commented with the name of the requirement to which it was linked. If an element could not be linked to a requirement, it was marked as \"derived\" and the corresponding derived requirement was added to the specification.\n\nWe decided to use this approach to keep the traceability artefacts visible at all time. An alternative solution would be to rely on the traceability plugin integrated in the Rodin platform (RMF). This solution would simplify the traceability review process and avoid cluttering of the models. Unfortunately, it was not available for the version of Rodin we used in our experiment (such integration is planned to be provided at the time of writing).\n\nLessons Learnt\n\nWe advocate that code review can be applied to Event-B models and may help in (i) demonstrating the correct encoding of the intent of the designer in the formal model; and (ii) minimizing the verification effort by adopting appropriate modelling patterns.\n\nModel review against a well-defined modelling standard is a simple and efficient means to enhance the quality of the model and reduce the number of errors. The benefits of such activity strongly overcome its cost. Hence, it shall be an integral part of the Event-B models development process. We believe that the complexity of such a review activity is affordable for software engineers with basic mathematical knowledge.\n\nAdditionally, generating appropriate documentation from Event-B models would also greatly simplify the review work. Indeed, the way of displaying models in the Rodin environment is not really adapted to a proper review activity. For instance, a categorization of model elements and comments according to their purpose\/role (traceability, design choices, model element meaning, general information...) with associated documentation generation would greatly help the review process.\n\nOur approach to deal with traceability was applicable to our use case because of the granularity of our requirements. Tracing more abstract requirements to specific model elements would be difficult to manage and verify that way. Relying on an intermediate level of (semi-)formal requirements as advocated in the use of the \"extended problem frame\" approach [24] would be more generalizable.\n\n## 5 Related Works\n\nResearch projects have produced a large literature on the methodology and tools around the use of Event-B for system modelling. Project such as DEPLOY, for instance, [24] have provided some very valuable results on the application of Event-B on industrial use cases. In this work, they rely on the \"extended problem frames\" approach as an intermediate formalism between informal requirements and Event-B models to further formalize relations between requirements elements and thus simplify the formalization work. Model validation is tackled in their approach using traceability and animation through the use of ProB. To assess deadlock freeness, they rely exclusively on ProB.\n\nA complete approach for the design and conception of a pacemaker system [25] and an adaptive cruise control has been developed by Singh [19]. Formalization of requirements is done through the extraction of modes and variables and introduction of refinement charts [25]. Event-B models are then produced, verified and validated [26]. The whole process is also confronted to a potential use in a software certification environment [27].\n\nOur work on the analysis and formalization of requirements does not provide additional elements compared to previously presented state of the art applications. We advocate on relying on animation technologies to improve the understanding of simulation results by stakeholders by providing graphical simulators generated using B-Motion and\/or JeB. Simulation input data may be produced through the use of simulators generators like JeB. We propose to additionally rely on a transformation of Event-B models to HLL for verification and validation. A similar approach is advocated in the FORMOSE6 project relying on UPPAAL [28]. We propose an additional review process to complement validation relying on software review techniques ensuring a better detection of conception errors and misunderstanding of the specification during Event-B models design.\n\n## 6 Conclusion\n\nThis work focuses on the application of the Event-B method on part of the process followed during an industrial development. We give some lessons and proposed some of the simple practices that we applied during this experiment. Relying on the Event-B method for the development of systems provides a framework for the formalization of textual requirements. This is strengthening the traditional error prone formalization step of a software development process. Formal modelling, verification and validation of Event-B models at an early stage provide a very valuable and fast feedback on the correction of requirements.\n\nOne important conclusion of our experiment resides in the very fact that we \u2013 \"standard\" software engineers \u2013 were able to apply the method on a non-trivial problem in a very reasonable time. This is in particular due to the great maturity of the toolset and the efficiency of the underlying provers. However, this positive conclusion is certainly largely due to the natural adequacy of our problem to the method. An additional conclusion of our experiment is that classical verification and validation activities shall be complemented by review activities. They strongly contribute to reduce the number of errors and more generally to enhance the quality of the model.\n\nBefore moving to a large scale industrial application, some very important questions remain to be answered: what is the actual usage domain of the method, considering the constraints imposed by the capability of the automatic verification means? How robust is the method to a change in the requirements? What are the good modeling practices to enhance this robustness and to reduce the verification effort? Definitely, it is necessary to evaluate the method on different types of systems to detect weak and strong points for its application.\n\nThis work will be pursued to answer these questions, and more specifically to address the applicability of the Event-B method in a DO-178C compliant development process. Additional tooling may be necessary in order to assess requirements coverage and improve review activities. Purpose\/role focused documentation generation could serve these activities that needs to be conducted in a certification environment.\n\nReferences\n\n1.\n\nCuenot, P., Jenn, E., Faure, E., Broueilh, N., Rouland, E.: An experiment on exploiting virtual platforms for the development of embedded equipments. In: 8th European Congress on Embedded Real Time Software and Systems (ERTS 2016) (2016)\n\n2.\n\nSAE: SAE ARP4754 Certification Considerations for Highly-Integrated Or Complex Aircraft Systems. Society of Automotive Engineers (SAE), Warrendale, USA (1996)\n\n3.\n\nRTCA: DO-178C, Software Considerations in Airborne Systems and Equipment Certification. Special Committee 205 of RTCA (2011)\n\n4.\n\nRTCA: DO-333 Formal Methods Supplement to DO-178C and DO-278A. RTCA & EUROCAE, December 2011\n\n5.\n\nRTCA: DO-331 Model-Based Development and Verification Supplement to DO-178C and DO-278A. RTCA & EUROCAE, December 2011\n\n6.\n\nGe, N., Dieumegard, A., Jenn, E., Voisin, L.: From Event-B to verified C via HLL, October 2016\n\n7.\n\nClabaut, M., Ge, N., Breton, N., Jenn, E., Delmas, R., Fonteneau, Y.: Industrial grade model checking use cases, constraints, tools and applications. In: 8th European Congress on Embedded Real Time Software and Systems (ERTS 2016), Toulouse, France (2016)\n\n8.\n\nGe, N., Jenn, E., Breton, N., Fonteneau, Y.: Formal verification of a rover anti-collision system. In: Beek, Maurice H., Gnesi, S., Knapp, A. (eds.) FMICS\/AVoCS -2016. LNCS, vol. 9933, pp. 171\u2013188. Springer, Cham (2016). doi:10.\u200b1007\/\u200b978-3-319-45943-1_\u200b12 CrossRef\n\n9.\n\nSingh, N.K., Ait-Ameur, Y., Pantel, M., Dieumegard, A., Jenn, E.: Stepwise formal modeling and verification of self-adaptive systems with Event-B. The automatic rover protection case study. Presented at the ICECCS 2016 (2016)\n\n10.\n\nAbrial, J.-R.: Modeling in Event-B - System and Software Engineering. Cambridge University Press, Cambridge (2010)CrossRefMATH\n\n11.\n\nAbrial, J.-R.: The B-book: Assigning Programs to Meanings. Cambridge University Press, New York (1996)CrossRefMATH\n\n12.\n\nBoulanger, J.-L.: Formal Methods Applied to Complex Systems: Implementation of the B Method. Wiley, Hoboken (2014)CrossRef\n\n13.\n\nButler, M.: Towards a cookbook for modelling and refinement of control problems (2009)\n\n14.\n\nSu, W., Abrial, J.-R., Huang, R., Zhu, H.: From requirements to development: methodology and example. In: Qin, S., Qiu, Z. (eds.) ICFEM 2011. LNCS, vol. 6991, pp. 437\u2013455. Springer, Heidelberg (2011). doi:10.\u200b1007\/\u200b978-3-642-24559-6_\u200b30 CrossRef\n\n15.\n\nMashkoor, A., Jacquot, J.-P., Souqui\u00e8res, J.: Transformation heuristics for formal requirements validation by animation. In: 2nd International Workshop on the Certification of Safety-Critical Software Controlled Systems-SafeCert 2009 (2009)\n\n16.\n\nHallerstede, S., Leuschel, M., Plagge, D.: Refinement-animation for Event-B \u2014 towards a method of validation. In: Frappier, M., Gl\u00e4sser, U., Khurshid, S., Laleau, R., Reeves, S. (eds.) ABZ 2010. LNCS, vol. 5977, pp. 287\u2013301. Springer, Heidelberg (2010). doi:10.\u200b1007\/\u200b978-3-642-11811-1_\u200b22 CrossRef\n\n17.\n\nSavicks, V., Butler, M., Colley, J., Bendisposto, J.: Rodin multi-simulation plug-in. Presented at the 5th Rodin User and Developer Workshop, Toulouse, France (2014)\n\n18.\n\nYang, F.: A simulation framework for the validation of Event-B specifications. Universit\u00e9 de Lorraine (2013)\n\n19.\n\nSingh, N.K.: Reliability and safety of critical device software systems. Ecole Centrale de Nantes (2011)\n\n20.\n\nLeuschel, M., Butler, M.: ProB: a model checker for B. In: Araki, K., Gnesi, S., Mandrioli, D. (eds.) FME 2003. LNCS, vol. 2805, pp. 855\u2013874. Springer, Heidelberg (2003). doi:10.\u200b1007\/\u200b978-3-540-45236-2_\u200b46 CrossRef\n\n21.\n\nLadenberger, L., Bendisposto, J., Leuschel, M.: Visualising Event-B models with B-motion studio. In: Alpuente, M., Cook, B., Joubert, C. (eds.) FMICS 2009. LNCS, vol. 5825, pp. 202\u2013204. Springer, Heidelberg (2009). doi:10.\u200b1007\/\u200b978-3-642-04570-7_\u200b17 CrossRef\n\n22.\n\nYang, F., Jacquot, J.-P., Souqui\u00e8res, J.: JeB: safe simulation of Event-B models in Javascript. In: 2013 20th Asia-Pacific Software Engineering Conference (APSEC), vol. 1, pp. 571\u2013576 (2013)\n\n23.\n\nMIRA Ltd: MISRA-C:2004 guidelines for the use of the C language in critical systems (2004)\n\n24.\n\nPetre, L., Sere, K., Tsiopoulos, L.: Deploy methods: final report. D44, April 2012\n\n25.\n\nM\u00e9ry, D., Singh, N.K.: Formal specification of medical systems by proof-based refinement. ACM Trans. Embed. Comput. Syst. 12(1), 15:1\u201315:25 (2013)CrossRef\n\n26.\n\nM\u00e9ry, D., Singh, N.K.: Real-time animation for formal specification. In: M\u00e9ry, D., Singh, N.K. (eds.) Complex Systems Design & Management 2010, pp. 49\u201360. Springer, Heidelberg (2010)\n\n27.\n\nM\u00e9ry, D., Singh, N.K.: Trustable formal specification for software certification. In: Margaria, T., Steffen, B. (eds.) ISoLA 2010. LNCS, vol. 6416, pp. 312\u2013326. Springer, Heidelberg (2010). doi:10.\u200b1007\/\u200b978-3-642-16561-0_\u200b31 CrossRef\n\n28.\n\nBehrmann, G., et al.: UPPAAL 4.0. In: Third International Conference on the Quantitative Evaluation of Systems - (QEST 2006), pp. 125\u2013126 (2006)\n\nFootnotes\n\n1\n\nhttp:\/\/\u200bwww.\u200bevent-b.\u200borg\/\u200b.\n\n2\n\nhttp:\/\/\u200balt-ergo.\u200blri.\u200bfr\/\u200b.\n\n3\n\nhttps:\/\/\u200bgithub.\u200bcom\/\u200bZ3Prover\/\u200bz3.\n\n4\n\nhttp:\/\/\u200bcvc4.\u200bcs.\u200bnyu.\u200bedu\/\u200bweb\/\u200b.\n\n5\n\nhttp:\/\/\u200bwww.\u200bscicoslab.\u200borg\/\u200b.\n\n6\n\nhttp:\/\/\u200bformose.\u200blacl.\u200bfr\/\u200b.\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_25\n\n# Reasoning About Safety-Critical Information Flow Between Pilot and Computer\n\nSeth Ahrenbach1\n\n(1)\n\nUniversity of Missouri, Columbia, Missouri 65201, USA\n\nSeth Ahrenbach\n\nEmail: SJK7v7@mail.missouri.edu\n\nAbstract\n\nThis paper presents research results that develop a dynamic logic for reasoning about safety-critical information flow among humans and computers. The logic advances previous efforts to develop logics of agent knowledge, which make assumptions that are too strong for realistic human agents. We introduce Dynamic Agent Safety Logic (DASL), based on Dynamic Epistemic Logic (DEL), with extensions to account for safe actions, belief, and the logical relationships among knowledge, belief, and safe action. With this logic we can infer which safety-critical information a pilot is missing when executing an unsafe action. We apply the logic to the Air France 447 incident as a case study and provide a mechanization of the case study in the Coq proof assistant.\n\n## 1 Introduction\n\nA common theme for aviation mishaps attributed to human error is for a pilot to become overwhelmed by data, lose situational awareness, and provide unsafe inputs to the flight controls. As yet, little work has been done to leverage the power of formal methods to address this problem. This paper remedies that by defining a dynamic logic of belief, knowledge, and safe action. We use the logic to create an axiomatic model of agency suitable for reasoning about safety-critical information flow among pilots and the flight computer. We mechanize this model in the Coq Proof Assistant and apply it to the Air France 447 incident as a case study.1\n\nThe research contributions of this paper include the development of a dynamic logic that is suitable for reasoning about safety-critical information flow. The dynamic logic is extended beyond most dynamic logics' treatment of action in that it treats both mere action and safe action, and captures the relationship between the two. The subsequent application and mechanization in Coq explore novel uses of formal methods in aviation safety, beyond mere verification of system component correctness. They introduce the idea of formally analyzing the human component of the safety-critical systems.\n\nDynamic Logic is a type of modal logic used for reasoning about state transition diagrams of programs [3, 8]. A diagram consists of nodes and edges, representing states of the system and labeled transitions between them, respectively. It is distinguished from other logics by the fact that truth is dynamic, rather than static, in its semantics. Thus, it is capable of representing the way actions change the truth of propositions. It serves as a foundation for a variety of logics similarly concerned with changes in some aspect of the truth as a result of actions. This family of logics has been described as logical dynamics, and includes Public Announcement Logic (PAL) and Dynamic Epistemic Logic (DEL) [5].\n\nLogical dynamics allows researchers to model information flow, rationality, and action in multi-agent systems [5]. In Ahrenbach and Goodloe [1], the authors develop a static modal logic for knowledge, belief, and safety to analyze a family of aviation mishaps involving a type of reasoning error suffered by a single pilot. This paper extends that work by employing dynamic methodologies from logical dynamics to the analysis of mishaps. The use of a dynamic logic rather than a static logic connects safety-critical information and actions in a more natural way, and allows for easier inference from action to information. The application of these methods advances the discipline of logical dynamics by employing them in the real world, beyond toy examples and logic puzzles, and likewise improves the discipline of aviation safety by introducing a formal method suitable for analyzing safety-critical information flow between pilots and machine.\n\nRecent work at the intersection of game theory and logical dynamics focuses on information flow during games. Van Ditmarsch identifies a class of games called knowledge games, in which players have diverging information [6]. This slightly relaxes the assumption of classical game theory that players have common knowledge about each other's perfect information. This invites logicians to study the information conveyed by the fact that an action is executed. For example, if agent 1 asks agent 2 the question, \"p?\", the information conveyed is that 1 does not know whether p, believes that 2 knows whether p, and after the action occurs, this information becomes publicly known. Many actions convey such information, beyond mere speech acts. For example, when a pilot provides flight control inputs, her action conveys information about what she believes about the aircraft's state, namely that it is in a state that safely permits those inputs. Anyone observing her inputs, like the first officer or the flight computer, can make such inferences about her mental picture based on her actions.\n\nThis paper proceeds as follows. In Sect. 2 we define the formal model, which consists of a set of axioms in a dynamic modal logic for reasoning about pilot knowledge, belief, and safety. Section 3 mechanizes the model in the Coq Proof Assistant and applies it to case studies, illustrating the logic's use as a formal method for aviation safety. We offer a brief discussion of future work in Sect. 4 and conclude in Sect. 5.\n\n## 2 Dynamic Agent Safety Logic\n\nThe logic for reasoning about information flow in knowledge games is called Dynamic Epistemic Logic (DEL). As its name suggests, it combines elements of epistemic logic and dynamic logic. Epistemic logic is the static logic for reasoning about knowledge, and dynamic logic is used to reason about actions. In dynamic logic semantics, nodes are states of the system or the world, and relations on nodes are transitions via programs or actions from node to node. If we think of each node in dynamic logic as being a model of epistemic logic, then actions become relations on models, representing transitions from one multi-agent epistemic model to another. For example, if we have a static epistemic model M1 representing the knowledge states of agents 1 and 2 at a moment, then the action \"p?\" is a relation between M1 and M2, a new static epistemic model of 1's and 2's knowledge after the question is asked. All of this is captured by DEL.\n\nWe are concerned with an additional element: the safety status of an action, and an agent's knowledge and belief about that. To capture this, we extend DEL and call the new logic Dynamic Agent Safety Logic (DASL). The remainder of this section presents DASL's syntax, semantics, and proves its soundness.\n\n### 2.1 Syntax and Semantics\n\nThe Dynamic Agent Safety Logic (DASL) used in this paper has the following syntax.\n\nwhere is an atomic proposition, refers to , is the name of an action, called an action token, belong to a set of such tokens, Actions, and refers to an action structure. The knowledge operator indicates that \"agent i knows that ...\" Similarly, the operator for belief, can be read, \"agent i believes that...\" The notion of action tokens and structures will be defined in the semantics. The operators and are the dynamic operators for agent i executing action token from action structure A in the former case, and doing so safely in the latter case. Note that the in stands for 'safety', and is not a variable, whereas the are variables for agents, action structures, and action tokens, respectively. One can read the action operators as \"after i executes from A, holds.\" We define the dual modal operators , , , and in the usual way.\n\nThe semantics of DASL involve two structures that are defined simultaneously, one for epistemic models, and one for action structures capturing the transition relation among epistemic models. Additionally, we define numerous helper functions that straddle the division between metalanguage and object language.\n\nKripke Model. A Kripke model is a tuple . It is a set of worlds, sets of epistemic and doxastic relations on worlds for agents, a world denoting the actual world, and a valuation function V mapping atomic propositions to the set of worlds satisfying them. Most readers will be somewhat familiar with epistemic logic, the logic for reasoning about knowledge. Doxastic logic is a similar logic for reasoning about belief [9].\n\nAction Structure. An action structure is a tuple . It is a set of action tokens, sets of epistemic and doxastic relations on action tokens for agents, and an action token, , denoting an actual action token executed.\n\nAn action structure captures the associated subjective events of an action occurring, including how it is observed by various agents, incorporating their uncertainty. The action tokens are the actual objective events that might occur. For example, if I am handed a piece of paper telling me who won the Oscar for Best Actress, and I read it, and you see me read it, then the action structure will include possible tokens in which I read that each nominee has won, and you will consider each of these tokens to be possible. When I read the paper, I consider only one action token to be the one executed. This action structure represents that transition from one epistemic model, in which both of us considers all nominees the potential winner, to an epistemic model in which I know the winner and you still do not know the winner. We can think of the action structure A as the general action \"Agent 1 reads the piece of paper\" and the tokens as the specific actions \"Agent 1 reads that nominee n has won the award.\"\n\nModel Relation. Just as denotes a relation on worlds, denotes a relation on Kripke model-world pairs. It represents the relation that holds between M, w and when agent i executes action at M, w and causes the world to transition to .\n\nPrecondition Function. The Precondition function, , maps an action to the formula capturing the conditions under which the action can occur. For example, if we assume agents tell the truth, then an announcement action has as a precondition that the announced proposition is true, as with regular Public Announcement Logic.\n\nPostcondition Function. The Postcondition function, , takes an action structure and an atomic proposition, and maps to the corresponding atomic proposition after the action occurs.\n\nUpdate Function. The Update function, , takes a Kripke model M, an action structure A, a world from the Kripke model, an action token from the Action structure, and an agent executing the action, and returns a new Kripke model-world pair. It represents the effect actions have on models, and is more complicated than other DEL semantics in that actions can change the facts on the ground in addition to the knowledge and belief relations. It is a partial function that is defined iff a model-world pair satisfies the action's preconditions.\n\n :\n\n 1. 1.\n\n 2. 2.\n\n 3. 3.\n\n 4. 4.\n\n 5. 5.\n\n 6. 6.\n\n 7. 7.\n\n 8. 8.\n\nSafety Precondition Function. The Safety Precondition Function, , is a more restrictive function than pre. Where pre returns the conditions that dictate whether the action is possible, returns the conditions that dictate whether the action is safely permissible. This function is the key reason the dynamic approach allows for easy inference from action to safety-critical information.\n\nThe logic DASL has the following Kripke semantics.\n\nThe definitions of the dynamic modalities make use of a relation between two model-world pairs, which we now define.\n\n### 2.2 Hilbert System\n\nDASL is axiomatized by the following Hilbert system.\n\nAll propositional tautologies are axioms.\n\nplus the inference rules Modus Ponens and Necessitation for and .\n\nAbove are the axioms characterizing the logic. Knowledge is weaker here than in most epistemic logics, and belief is standard [7]. They are related logically by EP(1\u20133), which hold that knowledge entails belief, belief entails that one believes that one knows, and belief entails than one knows that one believes. Finally, actions and safe actions are logically related by SP and PR, which hold that necessary consequences of mere action are also necessary consequences of safe actions, and that a pilot can execute an action only if he believes that he is executing a safe action.\n\n### 2.3 Soundness\n\nProof\n\n correspond to the axioms that is a T modality and is a KD45 modality in the usual way. (3) corresponds to EP1, EP2, and EP3. Axioms AP through SB are reduction axioms. This leaves (4), corresponding to SP, and (5) which corresponds to PR. Here we will prove (5). Let M be a Kripke structure satisfying the five conditions above. Let A be an Action structure with and i as its actual action token and agent.\n\nWe prove (5) via the contrapositive of PR: . Assume . By the semantics of , there exists a v, such that and . From the semantics, it follows that forall , if then . By slightly abusing the notation, and letting be equivalent to , we can create the composed relation . It then holds, by condition (5), that implies . So, for all , if , then . So, .\n\n## 3 Case Study and Mechanization\n\nWe apply the logic just developed to the formal analysis of the Air France 447 aviation incident. We also mechanize the formalization in the Coq Proof Assistant. Our mechanization follows similar work by Malikovi\u0107 and \u010cubrilo [12, 13], in which they mechanize an analysis of the game of Cluedo using Dynamic Epistemic Logic, based on van Ditmarsch's formalization of the game [6]. It is commonly assumed that games must be adversarial, but this is not the case. Games need only involve situations in which players' payoffs depend on the actions of other players. Similarly, knowledge games need not be adversarial, and must only involve diverging information. Thus, it is appropriate to model aviation incidents as knowledge games of sorts, where players' payoffs depend on what others do, specifically the way the players communicate information with each other. The goal is to achieve an accurate situational awareness and provide flight control inputs appropriate for the situation. Failures to achieve this goal result in disaster, and often result from imperfect information flow. A formal model of information flow in these situations provides insight and allows for the application of formal methods to improve information flow during emergency situations.\n\n### 3.1 Air France 447\n\nThis case study is based on the authoritative investigative report into Air France 447 performed and released by France's Bureau d'Enqu\u00eates et d'Analyses pour la S\u00e9curit\u00e9 de l'Aviation Civile (BEA), responsible for investigating civil aviation incidents and issuing factual findings [4]. The case is mechanized by instantiating, in Coq, the above logic to reflect the facts of the case. One challenge associated with this is that the readings about inputs present in aviation are often real values on a continuum, whereas for our purposes we require discrete values. We accomplish this by dividing the continuum associated with inputs and readings into discrete chunks, similar to how fuzzy logic maps defines predicates with real values [10].\n\nThis paper will formalize an excerpted instance from the beginning of the case, involving an initial inconsistency among airspeed indicators, and the subsequent dangerous input provided by the pilot. Formalized in the logic, the facts of the case allow us to infer that the pilot lacked negative introspection about the safety-critical data required for his action. This demonstrates that the logic allows information about the pilot's situational awareness to flow to the computer, via the pilot's actions. It likewise establishes a safety property to be enforced by the computer, namely that a pilot should maintain negative introspection about safety-critical data, and if he fails to do so, it should be re-established as quickly as possible.\n\nAccording to the official report, at 2 h and 10 min into the flight, a Pitot probe likely became clogged by ice, resulting in an inconsistency between airspeed indicators, and the autopilot disconnecting. This resulted in a change of mode from Normal Law to Alternate Law 2, in which certain stall and control protections ceased to exist. The pilot then made inappropriate control inputs, namely aggressive nose up commands, the only explanation for which is that he mistakenly believed that the aircraft was in Normal Law mode with protections in place to prevent a stall. This situation, and the inference regarding the pilot's mistaken belief, is modeled in the following application and mechanization of the logic.\n\n### 3.2 Mechanization in Coq\n\nThe following mechanization demonstrates progress from the artificially simply toy examples normally analyzed in the literature to richer real-world examples. However, it does not represent the full richness of the approach. The actions and instrument readings mechanized in this paper are constrained to those most relevant to the case study. The approach is capable of capturing the full richness of all instrument reading configurations and actions available to a pilot. To do so, one needs to consult a flight safety manual and formally represent each action available to a pilot, and each potential instrument reading, according to the following scheme.\n\nBefore beginning, we note that our use of sets in the following Coq code requires the following argument passed to coqtop before executing: -impredicative-set. In CoqIDE, this can be done by selecting the 'Tools' dropdown, then 'Coqtop arguments'. Type in -impredicative-set.\n\nWe first formalize the set of agents.\n\nNext we formalize the set of available inputs. These themselves are not actions, but represent atomic propositions true or false of a configuration.\n\nWe represent readings by indicating which side of the panel they are on. Typically, an instrument has a left-side version, a right-side version, and sometimes a middle version serving as backup. When one of these instruments conflicts with its siblings, the autopilot will disconnect and give control to the pilot.\n\nWe divide the main instruments into chunks of values they can take, in order to provide them with a discrete representation in the logic. For example, the reading VertUp1 may represent a nose up reading between 0 and 10 , while VertUp2 represents a reading between 11 and 20 .\n\nWe define a set of potential modes the aircraft can be in.\n\nWe define a set of global instrument readings representing the mode and all of the instrument readings, left, right, and middle, combined together. This represents the configuration of the instrumentation.\n\nThe set of atomic propositions we are concerned with are those representing facts about the instrumentation.\n\nNext we follow Malikovi\u0107 and \u010cubrilo [12, 13] in defining a set prop of propositions in predicate calculus, distinct from Coq's built in type Prop. The definition provides constructors for atomic propositions consisting of particular instrument reading predicate statements, implications, propositions beginning with a knowledge modality, and those beginning with a belief modality. Interestingly, modal logic cannot be directly represented in Coq's framework [11]. We first define propositions in first-order logic, which we then use to define DASL. This appears to be the standard technique for mechanizing modal logics in Coq.\n\nWe use the following notation for implication and universal quantification.\n\nWe likewise follow Malikovi\u0107 and \u010cubrilo [12, 13] by defining an inductive type theorem representing a theorem of DASL. The constructors correspond to the Hilbert system, either as characteristic axioms, or inference rules. The first three represent axioms for propositional logic, then the rule Modus Ponens, then the axioms for the epistemic operator plus its Necessitation rule, then the doxastic operator and its Necessitation rule. Do not confuse the Necessitation rules with material implication in the object language. The final constructors capture the axioms relating belief and knowledge. The axioms for dynamic modal operators are defined separately, and are not included here.\n\nWe use the following notation for theorem:\n\nWe encode actions as records in Coq, recording the acting pilot, the observability of the action (whether it is observed by other agents or not), the input provided by the pilot, and the preconditions for the action and the safety preconditions for the action, both represented as global atoms.\n\nThe variable c holds the configuration representing the precondition for the action, while the variable c_s holds the configuration for the safety precondition.\n\nWe encode the precondition and safety precondition functions as follows.\n\nIn the object language, the dynamic modalities of action and safe action are encoded as follows.\n\nMany standard properties of logic, like the simplification of conjunctions, hypothetical syllogism, and contraposition, are encoded as Coq axioms. As an example, here is how we encode simplifying a conjunction into just its left conjunct.\n\nWe formalize the configuration of the instruments at 2 h 10 min into the flight as follows.\n\nThe mode is Alternate Law 2, and the left and central backup instruments falsely indicate that the airspeed is very slow, while the right side was not recorded, but because there was a conflict, we assume it remained correctly indicating a cruising airspeed.\n\nThe pilot's dangerous input, a hard nose up command, is encoded as follows.\n\nThe action is represented in the object language by taking the dual of the dynamic modality, , equivalently , indicating that the precondition is satisfied and the action token is executed.\n\nThe actual configuration satisfies the precondition for the action, but it is inconsistent with the safety precondition. The safety precondition for the action indicates that the mode should be Normal and the readings should consistently indicate cruising airspeed. However, in Config_1, the conditions do not hold. Thus, the action is unsafe. From the configuration and the action, DASL allows us to deduce that the pilot lacks negative introspection of the action's safety preconditions.\n\nNegative introspection is an agent's awareness of the current unknowns. To lack it is to be unaware of one's unknown variables, so lacking negative introspection about one's safety preconditions is to be unaware that they are unknown.\n\nIn fact, in general it holds that if the safety preconditions for an action are false, and the pilot executes that action, then the pilot lacks negative introspection of those conditions. We have proven both the above theorem, and the more general theorem, in Coq.\n\nThis indicates that negative introspection about safety preconditions is a desirable safety property to maintain, consistent with the official report's criticism that the Airbus cockpit system did not clearly display the safety critical information. The logic described in this research accurately models the report's findings that the pilot's lack of awareness about safety-critical information played a key role in his decision to provide unsafe inputs. Furthermore, the logic supports efforts to automatically infer which safety-critical information the pilot is unaware of and effectively display it to him.\n\n## 4 Future Work\n\nThe case study presented in this paper is overly simplified due to space constraints. Future work will undertake the task of extending the approach to other actions in the Air France 447 incident, and the safety-critical information expressed by them. For example, when both pilots provided conflicting inputs to the aircraft, the computer could have inferred that neither was aware of the other's actions. This will illustrate the use of the approach in a multi-agent context. Similarly, as recommended by an anonymous reviewer, we shall apply the approach to other aviation mishaps involving complicated safety-critical information flow, specifically Asiana Airlines Flight 214 [14].\n\nAn important extension of the foundational work provided by this paper is the construction of a system that takes advantage of the logic as a runtime safety monitor. It will monitor the pilot's control inputs and current flight configurations, and in the event that an action's safety preconditions do not hold, infer which instrument readings the pilot is unaware of and act to correct this. In order to avoid further information overload, the corrective action taken by the computer should be to temporarily remove or dim the non-safety-critical information from competition for the pilot's attention, until the pilot's unsafe control inputs are corrected, indicating awareness of the safety-critical information. Construction of a prototype of this system is underway.\n\n## 5 Conclusion\n\nThis paper has described Dynamic Agent Safety Logic (DASL), a logic for reasoning about safety-critical information flow. It formalized actions and knowledge in the way common to Dynamic Epistemic Logic, but also formalized the notion of safe actions and beliefs. Additionally, it formalized a more realistic model of human reasoning, capturing a weaker notion of knowledge than most epistemic logics, and modeled the logical relationship between knowledge and belief. It formalized a realistic notion of rationality. The logic was mechanized in the Coq proof assistant and applied to the case of Air France 447 to validate its usefulness as a formal method for aviation safety.\n\nAcknowledgements\n\nSeth Ahrenbach was partially supported by NSF CNS 1553548. The author is grateful for the criticism and suggestions provided by anonymous reviewers, and for the very generous assistance from Alwyn Goodloe, Rohit Chadha, and Chris Hathhorn.\n\nReferences\n\n1.\n\nAhrenbach, S., Goodloe, A.: Formal analysis of pilot error using agent safety logic. In: Innovations in Systems and Software Engineering (submitted)\n\n2.\n\nBarras, B., Boutin, S., Cornes, C., Courant, J., Filliatre, J.C., Gimenez, E., Herbelin, H., Huet, G., Munoz, C., Murthy, C., Parent, C.: The Coq proof assistant reference manual: version 6.1 (Doctoral dissertation, Inria) (1997)\n\n3.\n\nBlackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, New York (2001)CrossRefMATH\n\n4.\n\nBureau d'Enqu\u00eates et d'Analyses: Final report on the accident on 1st June 2009 to the Airbus A330-203 registered F-GZCP operated by Air France flight AF 447 Rio de Janeiro-Paris. BEA, Paris (2012)\n\n5.\n\nvan Benthem, J.: Logical Dynamics of Information and Interaction. Cambridge University Press, New York (2011)CrossRefMATH\n\n6.\n\nVan Ditmarsch, H.: Knowledge games. Bull. Econ. Res. 53(4), 249\u2013273 (2001)MathSciNetCrossRef\n\n7.\n\nFagin, R., Halpern, J., Moses, Y., Vardi, M.: Reasoning About Knowledge. The MIT Press, Cambridge (2003)MATH\n\n8.\n\nHarel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press, Cambridge (2000)MATH\n\n9.\n\nHintikka, J.: Knowledge and Belief. Cornell University Press, Ithaca (1962)MATH\n\n10.\n\nKlir, G., Yuan, B.: Fuzzy Sets and Fuzzy Logic, vol. 4. Prentice Hall, New Jersey (1995)MATH\n\n11.\n\nLescanne, P.: Mechanizing common knowledge logic using COQ. Ann. Math. Artif. Intell. 48(1\u20132), 15\u201343 (2006). APAMathSciNetMATH\n\n12.\n\nMalikovi\u0107, M., \u010cubrilo, M.: Modeling epistemic actions in dynamic epistemic logic using Coq. In: CECIIS 2010 (2010)\n\n13.\n\nMalikovi\u0107, M., \u010cubrilo, M.: Reasoning about epistemic actions and knowledge in multi-agent systems using Coq. Comput. Technol. Appl. 2(8), 616\u2013627 (2011)\n\n14.\n\nNational Transportation Safety Board: Descent below visual glidepath and impact with Seawall Asiana Flight 214, Boeing 777-200ER, HL 7742, San Francisco, California, 6 July 2013 (Aircraft Accident Report NTSB\/AAR-14\/01). NTSB, Washington, DC (2014)\n\nFootnotes\n\n1\n\nCode: https:\/\/\u200bgithub.\u200bcom\/\u200bsethkurtenbach\/\u200bDASL\/\u200bblob\/\u200bmaster\/\u200bDASL.\u200bv.\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_26\n\n# Compositional Falsification of Cyber-Physical Systems with Machine Learning Components\n\nTommaso Dreossi1 , Alexandre Donz\u00e92 and Sanjit A. Seshia1\n\n(1)\n\nUniversity of California, Berkeley, USA\n\n(2)\n\nDecyphir, Inc., San Francisco, USA\n\nTommaso Dreossi (Corresponding author)\n\nEmail: dreossi@berkeley.edu\n\nAlexandre Donz\u00e9\n\nEmail: alex.r.donze@gmail.com\n\nSanjit A. Seshia\n\nEmail: sseshia@berkeley.edu\n\nAbstract\n\nCyber-physical systems (CPS), such as automotive systems, are starting to include sophisticated machine learning (ML) components. Their correctness, therefore, depends on properties of the inner ML modules. While learning algorithms aim to generalize from examples, they are only as good as the examples provided, and recent efforts have shown that they can produce inconsistent output under small adversarial perturbations. This raises the question: can the output from learning components can lead to a failure of the entire CPS? In this work, we address this question by formulating it as a problem of falsifying signal temporal logic (STL) specifications for CPS with ML components. We propose a compositional falsification framework where a temporal logic falsifier and a machine learning analyzer cooperate with the aim of finding falsifying executions of the considered model. The efficacy of the proposed technique is shown on an automatic emergency braking system model with a perception component based on deep neural networks.\n\nKeywords\n\nCyber-physical systemsMachine learningFalsificationTemporal logic\n\nThis work is funded in part by the DARPA BRASS program under agreement number FA8750-16-C-0043, NSF grants CNS-1646208 and CCF-1139138, and by TerraSwarm, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA. The second author did much of the work while affiliated with UC Berkeley.\n\n## 1 Introduction\n\nOver the last decade, machine learning (ML) algorithms have achieved impressive results providing solutions to practical large-scale problems (see, e.g., [2, 8, 10, 14]). Not surprisingly, ML is being used in cyber-physical systems (CPS) \u2014 systems that are integrations of computation with physical processes. For example, semi-autonomous vehicles employ Adaptive Cruise Controllers (ACC) or Lane Keeping Assist Systems (LKAS) that rely heavily on image classifiers providing input to the software controlling electric and mechanical subsystems (see, e.g., [3]). The safety-critical nature of such systems involving ML raises the need for formal methods [18]. In particular, how do we systematically find bugs in such systems?\n\nWe formulate this question as the falsification problem for CPS models with ML components (CPSML): given a formal specification in signal temporal logic (STL) [12], and a CPSML model M, find an input for which M does not satisfy . A falsifying input generates a counterexample trace that reveals a bug. To solve this problem, multiple challenges must be tackled. First, the input space to be searched can be intractable. For instance, a simple model of a semi-autonomous car already involves several control signals (e.g., the angle of the acceleration pedal, steering angle) and other sensor input (e.g., images captured by a camera). Second, CPSML are often designed using languages (such as C, C++, or Simulink), for which clear semantics are not given, and involve third-party components that are opaque or poorly-specified. This obstructs the development of formal methods for the analysis of CPSML models and may force one to treat them as gray\/black-boxes. Third, the formal verification of ML components is a difficult, and somewhat ill-posed problem due to the complexity of the underlying ML algorithms, large feature spaces, and the lack of consensus on a formal definition of correctness [18]. Hence, we need a technique to systematically analyze ML components within the context of a CPS.\n\nIn this paper, we propose a framework for the falsification of CPSML addressing the issues described above. Our technique is compositional in that it divides the search space for falsification into that of the ML component and of the remainder of the system, while establishing a connection between the two. The obtained subspaces are respectively analyzed by a temporal logic falsifier and an ML analyzer that cooperate. This cooperation mainly comprises a series of input space projections, leads to small subsets in which counterexamples are easier to find. Further, our technique can handle any machine learning technique, including the methods based on deep neural networks [8] that have proved effective in many recent applications. The proposed ML analyzer identifies sets of misclassifying features, i.e., inputs that \"fool\" the ML algorithm. The analysis is performed by considering subsets of parameterized features spaces that are used to approximate the ML components by simpler functions. The information gathered by the temporal logic falsifier and the ML analyzer together reduce the search space, providing an efficient approach to falsification for CPSML models.\n\nFig. 1.\n\nAutomatic Emergency Braking System. An image classifier is used to perceive vehicles in the frame of view.\n\nExample 1\n\nAs an illustrative example, let us consider a simple model of an Automatic Emergency Braking System (AEBS) as a closed-loop control system composed of a controller (automatic brake), a plant (car transmission), and a sensor (obstacle detector) (see Fig. 1). The controller regulates the acceleration and braking of the plant using the velocity of the subject (ego) vehicle and the distance between it and an obstacle. The sensor used to detect the obstacle includes a camera along with an image classifier. In general, this sensor can provide noisy measurements due to incorrect image classifications which in turn can affect the correctness of the overall system.\n\nSuppose we want to verify whether the distance between the subject vehicle and a preceding obstacle is always larger than 5 m. Such a verification requires the exploration of an intractable input space comprising the control inputs (e.g., acceleration and braking pedal angles) and the ML component's feature space (e.g., all the possible pictures observable by the camera). Note that feature space of RGB px pictures for an image classifier contains elements.\n\nAt first, the input space of the model described in Example 1 appears intractable. However, we can observe some interesting aspects of the relationship between the \"pure CPS\" input space and its ML feature space:\n\n 1. 1.\n\nUnder the assumption of \"perfect ML components\" (i.e., all feature vectors are correctly classified), we can study the CPSML model on a lower-dimensional input space (the \"pure CPS\" one) and identify regions of values that satisfy the specification but might be affected by the malfunctioning of some ML modules;\n\n 2. 2.\n\nInstead of verifying the ML components on their whole feature spaces, we can focus only on those features related to the non-robust input values identified in the previous step, and\n\n 3. 3.\n\nIf we are able to determine misclassifications on the restricted feature space, then we can relate them back to CPSML input space, thus focusing the falsification on a smaller input space.\n\nThese three observations constitute the core idea of the compositional falsification method proposed in this paper. Specifically, we use a temporal logic falsifier, Breach [4], in Steps (1) and (3) to partition a given input set into values that do and do not satisfy a given specification, and an ML analyzer in Step (2) to determine subsets of feature vectors that are misclassified by the ML components.\n\nThe proposed method, however, presents certain challenges that need to be addressed. First, we need to construct a validity domain of a specification against a CPSML model with (assumed) correct ML components. Second, we need a method to relate the non-robust input areas to the feature space of the ML modules. Third, we need to systematically analyze the ML components with the goal of finding feature vectors leading to misclassifications. We describe in detail in Sects. 3 and 4 how we tackle these challenges.\n\nIn summary, the main contributions of this paper are:\n\n * A compositional framework for the falsification of temporal logic properties of CPSML models that works for any machine learning classifier.\n\n * A machine learning analyzer that identifies misclassifications leading to system-level property violations, based on two main ideas:\n\n * An input space parameterization used to abstract the feature space and relate it to the CPSML input space, and\n\n * A classifier approximation method used to identify misclassifications that can lead to unsafe executions of the CPSML.\n\nIn Sect. 5, we demonstrate the effectiveness of our approach on an Automatic Emergency Braking System (AEBS) involving an image classifier for obstacle detection based on deep neural networks using leading software packages Caffe [10] and TensorFlow [13].\n\nRelated Work\n\nThe verification of both CPS and ML algorithms have attracted several research efforts, and we focus here on the most closely related work. Techniques for the falsification of temporal logic specifications against CPS models have been implemented based on nonlinear optimization methods and stochastic search strategies (e.g., Breach [4], S-TaLiRo [1], RRT-REX [5], C2E2 [6]). While the verification of ML programs is less well-defined [18], recent efforts [19] show how even well trained neural networks can be sensitive to small adversarial perturbations, i.e., small intentional modifications that lead the network to misclassify the altered input with large confidence. Other efforts have tried to characterize the correctness of neural networks in terms of risk [21] (i.e., probability of misclassifying a given input) or robustness [7] (i.e., the minimal perturbation leading to a misclassification), while others proposed methods to generate pictures [16] or perturbations [9, 15] in such a way to \"fool\" neural networks. To the best of our knowledge, our work is the first to address the verification of temporal logic properties of CPSML\u2014the combination of CPS and ML systems.\n\n## 2 Background\n\n### 2.1 CPSML Models\n\nIn this work, we consider models of cyber-physical systems with machine learning components (CPSML). We assume that a system model is given as a gray-box simulator defined as a tuple , where is a set of system states, is a set of input values, and is a simulator that maps a state and input value at time to a new state , where for a time-step .\n\nGiven an initial time , an initial state , a sequence of time-steps , and a sequence of input values , a simulation trace of the model is a sequence:\n\nwhere and for .\n\nThe gray-box aspect of the CPSML model is that we assume some knowledge of the internal ML components. Specifically, these components, termed classifiers, are functions that assign to their input feature vector a label , where and are a feature and label space, respectively. Without loss of generality, we focus on binary classifiers whose label space is . A ML algorithm selects a classifier using a training set where the are labeled examples with and , for . The quality of a classifier can be estimated on a test set of examples comparing the classifier predictions against the labels of the examples. Precisely, for a given test set , the number of false positives and false negatives of a classifier f on T are defined as:\n\n(1)\n\nThe error rate of f on T is given by:\n\n(2)\n\nA low error rate implies good predictions of the classifier f on the test set T.\n\n### 2.2 Signal Temporal Logic\n\nWe consider Signal Temporal Logic [12] (STL) as the language to specify properties to be verified against a CPSML model. STL is an extension of linear temporal logic (LTL) suitable for the specification of properties of CPS.\n\nA signal is a function , with an interval and either or , where and is the set of reals. Signals defined on are called booleans, while those on are said real-valued. A trace is a finite set of real-valued signals defined over the same interval D.\n\nLet be a finite set of predicates , with , , and a function in the variables .\n\nAn STL formula is defined by the following grammar:\n\n(3)\n\nwhere is a predicate and is a closed non-singular interval. Other common temporal operators can be defined as syntactic abbreviations in the usual way, like for instance , , or . Given a , a shifted interval I is defined as .\n\nDefinition 1\n\n(Qualitative semantics). Let w be a trace, , and be an STL formula. The qualitative semantics of is inductively defined as follows:\n\n(4)\n\nA trace w satisfies a formula if and only if , in short . For given signal w, time instant , and STL formula , the satisfaction signal is if , otherwise.\n\nDefinition 2\n\n(Quantitative semantics). Let w be a trace, , and be an STL formula. The quantitative semantics of is defined as follows:\n\n(5)\n\nThe robustness of a formula with respect to a trace w is the signal .\n\n## 3 Compositional Falsification Framework\n\nIn this section, we formalize the falsification problem for STL specifications against CPSML models, define our compositional falsification framework, and show its functionality on the AEBS system of Example 1.\n\nDefinition 3\n\n(Falsification of CPSML). Given a model and an STL specification , find an initial state and a sequence of input values such that the trace of states generated by the simulation of M from under does not satisfy , i.e., . We refer to such as counterexamples for . The problem of finding a counterexample is often called falsification problem.\n\nWe now present the compositional framework for the falsification of STL formulas against CPSML models. Intuitively, the proposed method decomposes a given model into two abstractions: a version of the CPSML model under the assumption of perfectly correct ML modules and its actual ML components. The two abstractions are separately analyzed, the first by a temporal logic falsifier that builds the validity domain with respect to the given specification, the second by an ML analyzer that identifies sets of feature vectors that are misclassified by the ML components. Finally, the results of the two analysis are composed and projected back to a targeted input subspace of the original CPSML model where counterexamples can be found by invoking a temporal logic falsifier. Let us formalize this procedure.\n\nLet be a CPSML model and be an STL specification. Let be a version of M with perfectly behaving ML components, that is, every feature vector of the ML feature spaces is correctly classified. Let us denote by ml the isolated ML components of the model M.\n\nUnder the assumption of correct ML components, the lower-dimensional input space of can be analyzed by constructing the validity domain of , that is the partition of the input space into the sets and that do and do not satisfy , respectively. Note that considering the original model M, a possible misclassification of the ML components ml might affect the elements of and . In particular, we are interested in the elements of that, due to misclassifications of ml, do not satisfy anymore. This corresponds to analyze the behavior of the ML components ml on the input set . We refer to this step as the ML analysis, that can be seen as the procedure of finding a subset of input values that are misclassified by the ML components ml. It is important to note that the input space of the CPS model and the feature spaces of the ML modules ml are different, thus the ML analyzer must adapt and relate the two different spaces. This important step will be clarified in Sect. 4.\n\nFinally, the intersection of the subsets identified by the decomposed analysis of the CPS model and its ML components targets a small set of input values that are misclassified by the ML modules and are likely to falsify . Thus, counterexamples in can be determined by invoking a temporal logic falsifier on against M.\n\nThe compositional falsification procedure is formalized in Algorithm 1. CompFalsfy receives as input a CPSML model M and an STL specification , and returns a set of falsifying counterexamples. At first, the algorithm decomposes M into and ml, where is an abstract version of M with perfectly working ML modules, and ml are the ML components of M (Line 2). Then, the validity domain of with respect to the abstraction is computed by ValidityDomain (Line 3) and subsets of input that are misclassified by ml are identified by MLAnalysis (Line 4). Finally, the targeted input set , consisting in the intersection of the sets identified by the decomposed analysis, is searched by a temporal logic falsifier on the original model M (Line 5) and a collection of counterexamples is returned.\n\nFig. 2.\n\nCompositional falsification scheme on AEBS model.\n\nExample 2\n\nLet us consider the model described in Example 1 and let us assume that the input space U of the model M consists of the initial velocity of the subject vehicle vel(0), the initial distance between the vehicle and the proceeding obstacle dist(0), and the set of pictures that can be captured by the camera. Let be a specification that requires the vehicle to be always farther than from the preceding obstacle. Instead of analyzing the whole input space U (including a vast number of pictures), we can adopt our compositional framework to target a specific subset of U. Let be the AEBS model with a perfectly working image classifier and ml be the actual classifier. We begin by computing the validity subsets and of against , considering only vel(0) and dist(0) and assuming exact distance measurements during the simulation. Next, we analyze only the image classifier ml on pictures of obstacles whose distances fall in , say in (see Fig. 2). Our ML analyzer generates only pictures of obstacles whose distances are in , finds possible sets of images that are misclassified, and returns the corresponding distances that, when projected back to U, yield the subset . Finally, a temporal logic falsifier can be invoked over and a set of counterexamples is returned.\n\nThis example illustrates how the compositional approach relies on tools, such as Breach [4], that compute validity domains and falsify STL specifications, as well as a ML analyzer. In the next section, we introduce our ML analyzer that identifies misclassifications of the ML component relevant to the overall CPSML input space.\n\n## 4 Machine Learning Analyzer\n\nIn this section, we define an ML analyzer that adapts the input of a model to its classifiers feature spaces and identifies subsets of feature vectors for which wrong labels are predicted. The analysis involves the construction of an approximation function used to study the original classifiers. In particular, given a classifier , the ML analyzer determines a simpler function that approximates on the abstract domain . The abstract domain of the function is analyzed and clusters of misclassifying abstract elements are identified. The concretizations of such elements are subsets of features that are misclassified by the original classifier .\n\n### 4.1 Feature Space Abstraction\n\nLet be a subset of the feature space of . Let be a total order on a set called the abstract set. An abstraction function is an injective function that maps every feature vector to an abstract element . Conversely, the concretization function maps every abstraction to a feature .\n\nThe abstraction and concretization functions play a fundamental role in our falsification framework. First, they allow us to map the input space of the CPS model to the feature space of its classifiers. Second, the abstract space can be used to analyze the classifiers on a compact domain as opposite to intractable feature spaces. These concepts are clarified in the following example, where a feature space of pictures is abstracted into a three-dimensional unit hyper-box.\n\nExample 3\n\nLet be the set of RGB pictures of size , i.e., . Suppose we are interested in analyzing an image classifier in the automotive context, i.e., on pictures of road scenarios rather than on the whole . Suppose that we focus on the constrained feature space composed by the set of pictures of cars overlapped in different positions over a desert road background. We also consider the brightness level of the picture. The x and z positions of the car and the brightness level of the picture can be seen as the dimensions of an abstract set . In this setting, we can define the abstraction and concretization functions and that relate the abstract set and . For instance, the picture sees the car on the left, close to the observer, and low brightness; the picture places the car shifted to the right; on the other extreme, has the car on the right, far away from the observer, and with a high brightness level. Figure 3 depicts some car pictures of disposed accordingly to their position in the abstract domain (the surrounding box).\n\nFig. 3.\n\nExample of feature space abstraction (the surrounding box) and some concretized element of the feature space (road pictures).\n\n### 4.2 Approximation of Learning Components\n\nWe now describe how the feature space abstraction can be used to construct an approximation that helps the identification of misclassified feature vectors.\n\nGiven a classifier and a constrained feature space , we want to determine an approximated classifier , such that , for some and test set , with , for .\n\nIntuitively, the proposed approximation scheme samples elements from the abstract set, computes the labels of the concretized elements using the analyzed learning algorithm, and finally, interpolates the abstract elements and the corresponding labels in order to obtain an approximation function. The obtained approximation can be used to reason on the considered feature space and identify clusters of potentially misclassified feature vectors.\n\nThe Approximation algorithm (Algorithm 2) formalizes the proposed approximation construction technique. It receives in input an abstract domain for the concretization function , with , the error threshold , and returns a function that approximates on the constrained feature space . The algorithm consists in a loop that iteratively improves the approximation . At every iteration, the algorithm populates the interpolation test set by sampling abstract features from and computing the concretized labels accordingly to (Line 4), i.e., , where is a finite subset of samples determined with some sampling method. Next, the algorithm interpolates the points of (Line 5). The result is a function that simplifies the original classifier on the concretized constrained feature space . The approximation is evaluated on the test set . Note that at each iteration, changes while incrementally grows. The algorithm iterates until the error rate is smaller than the desired threshold (Line 7).\n\nThe technique with which the samples in and are selected strongly influences the accuracy of the approximation. In order to have a good coverage of the abstract set , we propose the usage of low-discrepancy sampling methods that, differently from uniform random sampling, cover sets quickly and evenly. In this work, we use the Halton and lattice sequences, that are two common and easy to implement sampling methods. For details see, e.g., [17].\n\nExample 4\n\nWe now analyze two image classifiers: the Caffe [10] version of AlexNet [11] and the Inception-v3 model of Tensorflow [13], both trained on the ImageNet database.1 We sample 1000 points from the abstract domain defined in Example 3 using the lattice sampling techniques. These points encode the x and z displacements of a car in a picture and its brightness level (see Fig. 3). Figure 4(a) depicts the sampled points with their concretized labels. The green circles indicate correct classifications, i.e., the classifier identified a car, the red circles denote misclassifications, i.e., no car detected. The linear interpolation of the obtained points leads to an approximation function. The error rates of the obtained approximations (i.e., the discrepancies between the predictions of the original image classifiers and their approximations) computed on 300 randomly picked test cases are 0.0867 and 0.1733 for Caffe and Tensorflow, respectively. Figure 4(b) shows the projections of the approximation functions for the brightness value 0.2. The more red a region, the larger the sets of pictures for which the neural networks do not detect a car. For illustrative purposes, we superimpose the projections of Fig. 4(b) over the background used for the picture generation. These illustrations show the regions of the concrete feature vectors in which a vehicle is misclassified.\n\nFig. 4.\n\nML analysis of Caffe (top) and Tensorflow (bottom) on a road scenario. (Color figure online)\n\nThe analysis of Example 4 on Caffe and Tensorflow provides useful insights. First, we observe that Tensorflow outperforms Caffe on the considered road pictures since it correctly classifies more pictures that Caffe. Second, we notice that Caffe tends to correctly classify pictures in which the x abstract component is either close to 0 or 1, i.e., pictures in which the car is not in the middle of the street, but on one of the two lanes. This suggests that the model might not have been trained enough with pictures of cars in the center of the road. Third, using the lattice method on Tensorflow, we were able to identify a corner case misclassification in a cluster of correct predictions (note the isolated red circle with coordinates (0.1933, 0.0244, 0.4589)). All this information provides insights on the classifiers that can be useful in the hunt for counterexamples.\n\n## 5 Experimental Results\n\n### 5.1 Implementation Details\n\nThe presented falsification framework has been implemented in a Matlab toolbox publicly available at https:\/\/\u200bgithub.\u200bcom\/\u200btommasodreossi\/\u200bFalsifCPSML. The tool deals with Simulink models of CPSML and STL specifications. It consists of a temporal logic falsifier and an ML analyzer that interact to falsify the given STL specification against the decomposed Simulink model. As an STL falsifier, we chose the existing tool Breach [4], while the ML analyzer has been implemented from scratch. The ML analyzer implementation includes the feature space abstractor and the ML approximation algorithm (see Sect. 4). The feature space abstractor implements a picture generator that concretizes the abstracted feature vectors. The approximation algorithm, that computes an approximation of the analyzed ML component, gives to the user the possibility of selecting the sampling sequence method, interpolation technique, and setting the desired error rate. Our tool is interfaced with the deep learning frameworks Caffe [10] and Tensorflow [13]. Our tool has been tested on a desktop computer Dell XPS 8900, Intel (R) Core(TM) i7-6700 CPU 3.40 GHz, DIMM RAM 16 GB 2132 MHz, GPU NVIDIA GeForce GTX TITAN X, with Ubuntu 14.04.5 LTS and Matlab R2016b.\n\n### 5.2 Case Studies\n\nFor the experimental evaluations, we consider a closed-loop Simulink model of a semi-autonomous vehicle with an Advanced Emergency Braking System (AEBS) [20] connected to an image classifier. The model mainly consists of a four-speed automatic transmission controller linked to an AEBS that automatically prevents collisions with preceding obstacles and alleviate the harshness of a crash when a collision is likely to happen (see Fig. 5). The AEBS determines a braking mode depending on the speed of the vehicle , the possible presence of a preceding obstacle, its velocity , and the longitudinal distance dist between the two. The distance dist is provided by radars having 30 m of range. For obstacles farther than 30 m, the camera, connected to an image classifier, alerts the AEBS that, in the case of detected obstacle, goes into warning mode.\n\nFig. 5.\n\nSimulink model of a semi-autonomous vehicle with AEBS.\n\nDepending on , and the presence of obstacles detected by the image classifier, the AEBS computes the time to collision and longitudinal safety indices, whose values determine a controlled mode among safe, warning, braking, and collision mitigation. In safe mode, the car does not need to brake. In warning mode, the driver should brake to avoid a collision. If this does not happen, the system goes into braking mode, where the automatic brake slows down the vehicle. Finally, in collision mitigation mode, the system, determining that a crash is unavoidable, triggers a full braking action aimed to minimize the damage.\n\nTo establish the correctness of the system and in particular of its AEBS controller, we formalize the STL specification , that requires dist(t) to always be positive, i.e., no collision happens. The input space is (mph), (m), and the set of all RGB pictures of size . The preceding vehicle is not moving, i.e., (mph).\n\nFig. 6.\n\nValidity domain for . Proved (red crosses) and disproved (green circles) candidate counterexamples. Dotted (horizontal) line: image classifier activation threshold. Dashed (vertical) line: validity boundary of for worst-case misclassifications. (Color figure online)\n\nAt first, we compute the validity domain of assuming that the radars are able to provide exact measurements for any distance dist(t) and the image classifier correctly detects the presence of a preceding vehicle. The computed validity domain is depicted in Fig. 6: green for and red for . Next, we identify candidate counterexamples that belong to the satisfactory set (i.e., the inputs that satisfy the specification) but might be influenced by a misclassification of the image classifier. Since the AEBS relies on the classifier only for distances larger than 30 m, we can focus on the subset of the input space with . Specifically, we identify potential counterexamples by analyzing a pessimistic version of the model where the ML component always misclassifies the input pictures (see Fig. 6, area with dashed boundary). From this sub-input space, we can identify candidate counterexamples, such as, for instance, (25, 40) (i.e., and ).\n\nNext, let us consider the Caffe image classifier and the ML analyzer presented in Sect. 4 that generates pictures from the abstract feature space , where the dimensions of determine the x and z displacements of a car and the brightness of a generated picture, respectively. The goal now is to determine an abstract feature related to the candidate counterexample (25, 40), that generates a picture that is misclassified by the ML component and might lead to a violation of the specification . The dist(0) component of determines a precise z displacement in the abstract picture. Now, we need to determine the values of the abstract x displacement and brightness. Looking at the interpolation projection of Fig. 4(b), we notice that the approximation function misclassifies pictures with abstract component and . Thus, it is reasonable to try to falsify the original model on the input element , and concretized picture . For this targeted input, the temporal logic falsifier computed a robustness value for of , meaning that a falsifying counterexample has been found. Other counterexamples found with the same technique are, e.g., (27, 45) or (31, 56) that, associated with the correspondent concretized pictures with and , lead to the robustness values and , respectively (see Fig. 6, red crosses). Conversely, we also disproved some candidate counterexamples, such as (28, 50), (24, 35), or (25, 45), whose robustness values are 9.93, 7.40, and 7.67 (see Fig. 6, green circles).\n\nFor experimental purposes, we try to falsify a counterexample in which we change the x position of the abstract feature so that the approximation function correctly classifies the picture. For instance, by altering the counterexample (27, 45) with to (27, 45) with , we obtain a robusteness value of 9.09, that means that the AEBS is able to avoid the car for the same combination of velocity and distance of the counterexample, but different x position of the preceding vehicle. Another example, is the robustness value of the falsifying input (31, 56) with , that altered to , changes to 12.41.\n\nFinally, we test Tensorflow on the corner case misclassification identified in Sect. 4.2 (i.e., the picture ). The distance related to this abstract feature is below the activation threshold of the image classifier. Thus, the falsification points are exactly the same as those of the computed validity domain (i.e., and ). This study shows how a misclassification of the ML component might not affect the correctness of the CPSML model.\n\n## 6 Conclusion\n\nWe presented a compositional falsification framework for STL specifications against CPSML models based on the separate analysis of a CPS system and its ML components. We introduced an ML analyzer able to abstract feature spaces, approximate ML classifiers, and provide sets of misclassified feature vectors that can be used to drive the falsification process. We implemented our framework and showed its effectiveness for an autonomous driving controller using perception based on deep neural networks.\n\nThis work lays the basis for future advancements. We intend to improve our ML analyzer exploring the automatic generation of feature space abstractions from given training sets. Another direction is to integrate other techniques for generating misclassifications of ML components (e.g. [9, 15]) into our approach. One could also apply our ML analyzer outside the falsification context, such as for controller synthesis. Finally, our compositional methodology could be extended to other, non-cyber-physical, systems that contain ML components.\n\nReferences\n\n1.\n\nAnnpureddy, Y., Liu, C., Fainekos, G., Sankaranarayanan, S.: S-TaLiRo: a tool for temporal logic falsification for hybrid systems. In: Abdulla, P.A., Leino, K.R.M. (eds.) TACAS 2011. LNCS, vol. 6605, pp. 254\u2013257. Springer, Heidelberg (2011). doi:10.\u200b1007\/\u200b978-3-642-19835-9_\u200b21 CrossRef\n\n2.\n\nBlum, A.L., Langley, P.: Selection of relevant features and examples in machine learning. Artif. Intell. 97(1), 245\u2013271 (1997)MathSciNetCrossRef00063-5)MATH\n\n3.\n\nBojarski, M., et al.: End to end learning for self-driving cars. arXiv:\u200b1604.\u200b07316 (2016)\n\n4.\n\nDonz\u00e9, A.: Breach, a toolbox for verification and parameter synthesis of hybrid systems. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 167\u2013170. Springer, Heidelberg (2010). doi:10.\u200b1007\/\u200b978-3-642-14295-6_\u200b17 CrossRef\n\n5.\n\nDreossi, T., Dang, T., Donz\u00e9, A., Kapinski, J., Jin, X., Deshmukh, J.V.: Efficient guiding strategies for testing of temporal properties of hybrid systems. In: Havelund, K., Holzmann, G., Joshi, R. (eds.) NFM 2015. LNCS, vol. 9058, pp. 127\u2013142. Springer, Cham (2015). doi:10.\u200b1007\/\u200b978-3-319-17524-9_\u200b10\n\n6.\n\nDuggirala, P.S., Mitra, S., Viswanathan, M., Potok, M.: C2E2: a verification tool for stateflow models. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 68\u201382. Springer, Heidelberg (2015). doi:10.\u200b1007\/\u200b978-3-662-46681-0_\u200b5\n\n7.\n\nFawzi, A., Fawzi, O., Frossard, P.: Analysis of classifiers' robustness to adversarial perturbations. arXiv preprint arXiv:\u200b1502.\u200b02590 (2015)\n\n8.\n\nHinton, G., et al.: Deep neural networks for acoustic modeling in speech recognition: the shared views of four research groups. IEEE Signal Process. Mag. 29(6), 82\u201397 (2012)CrossRef\n\n9.\n\nHuang, X., Kwiatkowska, M., Wang, S., Wu, M.: Safety verification of deep neural networks. CoRR, abs\/1610.06940 (2016)\n\n10.\n\nJia, Y., Shelhamer, E., Donahue, J., Karayev, S., Long, J., Girshick, R., Guadarrama, S., Darrell, T.: Caffe: convolutional architecture for fast feature embedding. In: ACM Multimedia Conference, ACMMM, pp. 675\u2013678 (2014)\n\n11.\n\nKrizhevsky, A., Sutskever, I., Hinton, G.E.: Imagenet classification with deep convolutional neural networks. In: Advances in Neural Information Processing Systems, pp. 1097\u20131105 (2012)\n\n12.\n\nMaler, O., Nickovic, D.: Monitoring temporal properties of continuous signals. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS\/FTRTFT-2004. LNCS, vol. 3253, pp. 152\u2013166. Springer, Heidelberg (2004). doi:10.\u200b1007\/\u200b978-3-540-30206-3_\u200b12 CrossRef\n\n13.\n\nTensorFlow, M.A., et al.: Large-scale machine learning on heterogeneous systems (2015). Software available from tensorflow.\u200borg\n\n14.\n\nMichalski, R.S., Carbonell, J.G., Mitchell, T.M.: Machine Learning: An Artificial Intelligence Approach. Springer Science & Business Media, Heidelberg (2013)MATH\n\n15.\n\nMoosavi-Dezfooli, S.-M., Fawzi, A., Frossard, P.: Deepfool: a simple and accurate method to fool deep neural networks. In: IEEE Computer Vision and Pattern Recognition, pp. 2574\u20132582 (2016)\n\n16.\n\nNguyen, A., Yosinski, J., Clune, J.: Deep neural networks are easily fooled: high confidence predictions for unrecognizable images. In: Computer Vision and Pattern Recognition, CVPR, pp. 427\u2013436. IEEE (2015)\n\n17.\n\nNiederreiter, H.: Low-discrepancy and low-dispersion sequences. J. Number Theory 30(1), 51\u201370 (1988)MathSciNetCrossRef90025-X)MATH\n\n18.\n\nSeshia, S.A., Sadigh, D., Sastry, S.S.: Towards verified artificial intelligence. CoRR, abs\/1606.08514 (2016)\n\n19.\n\nSzegedy, C., Zaremba, W., Sutskever, I., Bruna, J., Erhan, D., Goodfellow, I., Fergus, R.: Intriguing properties of neural networks. arXiv:\u200b1312.\u200b6199 (2013)\n\n20.\n\nTaeyoung, L., Kyongsu, Y., Jangseop, K., Jaewan, L.: Development and evaluations of advanced emergency braking system algorithm for the commercial vehicle. In: Enhanced Safety of Vehicles Conference, ESV, pp. 11\u20130290 (2011)\n\n21.\n\nVapnik, V.: Principles of risk minimization for learning theory. In: NIPS, pp. 831\u2013838 (1991)\n\nFootnotes\n\n1\n\nhttp:\/\/\u200bimage-net.\u200borg\/\u200b.\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_27\n\n# Verifying a Class of Certifying Distributed Programs\n\nKim V\u00f6llinger1 and Samira Akili1\n\n(1)\n\nHumboldt University of Berlin, Berlin, Germany\n\nKim V\u00f6llinger\n\nEmail: voellinger@hu-berlin.de\n\nAbstract\n\nA certifying program produces in addition to each output a witness that certifies the output's correctness. An accompanying checker program checks whether the computed witness is correct. Such a checker is usually simpler than the original program, and its verification is often feasible while the verification of the original program is too costly. By verifying the checker and by giving a machine-checked proof that the witness certifies the output's correctness, we get formal instance correctness, i.e. a machine-checked proof that a particular input-output pair is correct. This verification method was demonstrated on sequential programs. In contrast, we are concerned with the correctness of distributed programs which behave fundamentally differently. In this paper, we present a verification method to obtain formal instance correctness for one class of certifying distributed programs. Moreover, we demonstrate our method on the leader election problem using the theorem prover Coq.\n\nKeywords\n\nCertifying distributed programFormal instance correctnessCoq\n\n## 1 Introduction\n\nA major problem in software engineering is assuring the quality of software. Well-known methods are testing and formal verification. While testing does not cover all inputs, formal verification is often too costly. We suggest certifying programs \u2013 a formal method that is, on the one hand, more rigorous than testing, and on the other hand, less costly than formal verification.\n\nA certifying program verifies the correctness of its output at runtime. The idea is to adapt the underlying algorithm of a program at design time to protect its user not only against a faulty implementation but also against a faulty algorithm and a faulty execution (e.g. caused by a hardware failure). To this end, a certifying program produces a witness in addition to each output that certifies the output's correctness. Since the witness is computed by the untrusted program itself, a simple checker program checks whether the witness is correct. Furthermore, there is a verification method for certifying programs to achieve formal instance correctness for an output \u2013 a machine-checked proof that a particular input-output pair is correct.\n\nIn contrast, we are concerned with the correctness of distributed programs. Certifying distributed programs behave differently to certifying sequential programs; for instance, the witness is distributed over a system and checked by many checkers. In this paper, we present a verification method to achieve formal instance correctness for one class of certifying distributed programs. As a case study, we demonstrate our method on the leader election problem in networks using the theorem prover Coq for program verification and theorem proving. The whole formalization is available on GitHub1.\n\n### 1.1 Structure of this Paper\n\nWe give the preliminaries in Sect. 2. In Sect. 3, we discuss how to apply the concept of certifying sequential programs to distributed programs. We define a class of certifying distributed algorithms. Our class is particularly interesting since the witness is computed and checked in a distributed manner (Sect. 3.3). Hence, the certification itself is distributed. For this class, we introduce a verification method to obtain formal instance correctness (Sect. 3.4). In Sect. 4, we give a certifying variant of solving the leader election problem in networks and demonstrate our verification method on certifying leader election using the theorem prover Coq. We present related work in Sect. 5, draw our conclusions in Sect. 6 and discuss future work in Sect. 7.\n\n## 2 Preliminaries\n\nIn this section, we recap certifying sequential programs (Sect. 2.1), and a verification method to obtain formal instance correctness for certifying sequential programs (Sect. 2.2).\n\n### 2.1 Certifying Sequential Programs\n\nThe idea of a certifying program is to adapt the underlying algorithm of a program such that it verifies the correctness of its output at runtime [7]. We assume a program that takes an input x from a set X and produces an output y from a set Y. The specification of the program is given by a precondition and a postcondition . Let W be a set of potential witnesses. A witness predicate for the specification is a predicate with the witness property:\n\n(1)\n\nIf the witness property holds for x, y, w, then the input-output pair (x, y) satisfies the specification, and we call w a witness for .\n\nA (correct) certifying program produces in addition to each output a witness such that the witness property is satisfied. However, the idea is that a user of a certifying program does not have to trust the program but a (simpler) checker program that decides the witness predicate . Figure 1 sums up the concept of a certifying program.\n\nFig. 1.\n\nA certifying program accompanied by its checker.\n\nAs an example, we consider the problem of deciding if a graph is bipartite, i.e. if its vertices can be divided in two partitions so that each edge has a vertex in each of both partitions. A certifying variant of a program deciding that a particular graph G is not bipartite additionally produces an odd cycle in G as a witness. The witness predicate holds if the witness is a cycle of odd length contained in G; it can easily be decided by a checker program. The witness certifies the output: an odd cycle contained in G proves that G is not bipartite since an odd cycle itself is not bipartite. Thus, the witness predicate has the witness property. For a bipartite graph, the witness could be a bipartition.\n\nThere is always a certifying variant of a program, for instance, with a witness that is the computation itself. In general, this is not a good witness, since proving the witness property becomes program verification then. The challenge is to find \"good\" witnesses.\n\n### 2.2 Verification of Certifying Sequential Programs\n\nThe user of a certifying program has to trust its witness property, and its accompanying checker. A checker is usually much simpler than the original program, and its verification is often feasible while the verification of the original program is too costly. Rizkallah's method is to use the theorem Prover Isabelle to give a machine-checked proof for the witness property, and to verify the checker (e.g. with VCC) [11]. By this combination of certifying programs with theorem proving and program verification, we achieve formal instance correctness for instances for which the checker accepts.\n\n## 3 Verification Method for a Class of Certifying Distributed Programs\n\nIn this section, we give a verification method to obtain formal instance correctness for one class of certifying distributed programs. We begin with what we consider to be a distributed program and with discussing the challenges of applying the concept of certifying sequential programs to distributed programs. Subsequently, we define a class of certifying distributed programs. Finally, for this class, we give a verification method to obtain formal instance correctness.\n\n### 3.1 Distributed Programs\n\nA distributed system consists of computing components that can communicate with each other by shared memory or message-passing channels. A distributed algorithm describes for each component an algorithm such that all components together solve one problem. For instance, there are distributed algorithms to solve problems associated with distributing a computation over a system such as coordination, communication or synchronization of the components. To give some examples, there are distributed algorithms to elect a leader, find a consensus or identify a substructure of the system such as a tree [10]. An implementation of a distributed algorithm is a distributed program.\n\n### 3.2 Challenges of Certifying Distributed Programs\n\nThe distributed setting has all the challenges of the sequential setting, and additionally, its own specific challenges [9, Sect. 1.3]. That is why distributed programs are known to be especially hard to verify. While non-termination is considered a fault in sequential programs, some distributed programs should run continuously, e.g. communication protocols. Certification of non-terminating programs poses questions such as when should a non-terminating program compute a witness. For a terminating distributed program, each component holds its output after termination. Hence, the output of the distributed program is distributed over the system. The output's distribution leads to questions such as should there be a witness for each component or one witness for the whole system, and should we verify the correctness of a component's output or of the network's output. Hence, there is not only one way of applying the concept of a certifying sequential program to distributed programs.\n\n### 3.3 A Class of Certifying Distributed Programs\n\nFor defining a class of certifying distributed programs, we focus on networks (i.e. distributed systems with message-passing channels) that are static (i.e. components and channels do not leave the system) and asynchronous (i.e. no global clock exists), and on distributed programs that terminate. After termination, each component holds its local output and the global output of the distributed program is the collective of the local outputs. Our approach is to make such a distributed program certifying by making it compute many local witnesses that together prove the global output's correctness. The local witnesses are computed and checked in a distributed manner at runtime. Hence, we present certifying distributed programs where the certification itself is distributed.\n\nWe represent a network by a graph G that is a finite directed connected graph with a vertex set and an edge set E that is symmetric. Each vertex presents a component and two directed edges (i, j) and (j, i) present a bidirectional channel between the components i and j. We call such a graph G a network graph.\n\nLet G be a network graph. Let X, Y and W be sets containing potential local inputs, local outputs and local witnesses, respectively. A certifying distributed program p of class C computes for a global input a global output , and in addition, a global witness . Hence, each component computes for a local input a local output and additionally a local witness . The specification of p is given by a (global) precondition and a (global) postcondition .\n\nA global witness predicate is a predicate with the (global) witness property:\n\n(2)\n\nIf the witness property holds for , , , then the global input-output pair ( , ) satisfies the specification, and we call a global witness for .\n\nWe want that the global witness predicate is decided in a distributed manner. That is why we define a local witness predicate. A local witness predicate is a predicate with the composition property:\n\n(3)\n\nFor a triple , we call a local witness of component i. For the class C, the global witness predicate is checked after termination of p in the way that each component i has a local checker that decides the local witness predicate for i. Since the checking occurs after termination, we do not have to care about asynchrony.\n\n### 3.4 Verification Method for Class C\n\nWe give a verification method to obtain formal instance correctness, i.e. a proof that a particular input-output pair is correct. Let p be a certifying distributed program of class C. In order to obtain formal instance correctness for p, we have to solve the following proof obligations:\n\n * Witness Property: We have to give a machine-checked proof for the implication (2).\n\n * Composition Property: We have to give a machine-checked proof of the implication (3).\n\n * Correctness of the Local Checkers: We have to prove that the local checker of each component i checks the local witness predicate , assuming the precondition holds, i.e.\n\n 1. 1.\n\nIf and , then halts and accepts.\n\n 2. 2.\n\nIf and , then halts and rejects.\n\nIf we solve these proof obligations, we obtain formal instance correctness for each instance on which all local checkers accept:\n\nTheorem 1\n\nLet be a network graph with . Let X, Y and W be sets. Let be a precondition and a postcondition. Let be a global witness predicate for and , and let be a local witness predicate for , , and G. Let . Let c be a local checker deciding . Assuming , if c accepts on for all , then .\n\nProof\n\n for all since c decides . Since is a local witness predicate and , it follows from the composition property that . From being a global witness predicate and , it follows by the witness property that .\n\nNotice that the program p itself is not mentioned in the theorem. The machine-checked proofs and the verified local checkers can indeed be combined with any program producing an input, output and witness. Moreover, the reader may wonder why we do not prove: if , then there exists a global witness such that . In fact, with such a proof, we would reason about the correctness of p. However, we do not want to establish the correctness of p but to achieve formal instance correctness for p. Verifying formal instance correctness is a different problem than verifying programs.\n\nVerification Within Coq. We use the theorem prover Coq for theorem proving and program verification. Coq [4] is an interactive theorem prover that provides its user with a specification language, a higher-order logic, a richly-typed functional programming language, and some proof automations. Moreover, Coq implements a mechanism to extract programs written in Coq to languages like Haskell and Objective Caml. Coq's programming language is not turing-complete since it allows only structural recursion enforcing that every program halts.\n\nWe use Coq for theorem proving in order to solve the proof obligations witness property and composition property, and for program verification in order to solve the proof obligation correctness of the local checkers. Moreover, we extract a verified local checker from Coq to Haskell.\n\nTo model a network in Coq, we build upon the graph library Graph Basics [3] that defines basic concepts of graph theory such as undirected graphs, trees or connectivity. The purpose of this library is to express mathematical and computational aspects of graph theory in the same formalism. To the best of our knowledge, there is no other graph library for Coq.\n\n### 3.5 Further Classes of Certifying Distributed Programs\n\nWe give a brief outlook of further classes of certifying distributed programs. One modification is to define a different composition property:\n\n(4)\n\nHence, if at least one component satisfies the local witness predicate, then the global witness predicate holds. We used such a composition property for a certifying variant of distributed bipartite testing. Other logical combinations of local witness predicates could be of interest as well.\n\nA different modification is to certify local outputs instead of the global output. Assume all components compute their distance to one component as often done in routing protocols. If one component is buggy, then the local witness predicate cannot hold for all components. However, many components probably hold their actual distance. In this scenario, it would be interesting to verify local outputs. To this end, we need a local witness property. For instance in the form: if the component's local witness predicate holds, then its local input-output pair is correct. Since for many examples such a local witness property is too ambitious, it could also have the form: if for all the components in a subnetwork the local witness predicate hold, then the components of the subnetwork hold their correct local output. Additionally, we need a local specification and more reasoning in general. In that case, we would have to adapt our verification method.\n\nAnother modification is to consider non-terminating distributed programs. In this case, the witness and composition property would look significantly different and the checking would become more difficult since it would be done on-line by an reactive checker. Thus, non-termination would also lead to an adapted verification method.\n\nConsidering unreliable communication channels or dynamic networks would remarkably complicate the certification and verification. There are many more modifications to take into account but they are outside the scope of this paper.\n\n## 4 Case Study: Leader Election\n\nAs a case study, we consider the leader election problem: all components of a network have to elect exactly one of them as a leader. Usually, a leader is elected for coordination purposes. There are various distributed algorithms that solve leader election. For instance, Lynch gives an asynchronous leader election algorithm for a network of arbitrary topology and components that have unique identifiers [6].\n\nIn this section, we first give a certification for leader election that belongs to class C (see Sect. 3.3) and then we give a formalization in Coq.\n\n### 4.1 Certifying Leader Election\n\nThe specification of the leader election problem states that the problem is solved if all components of a network agree on exactly one of them as a leader. Thus, in order to verify the global output's correctness, we have to certify that all components agree on the leader and that the elected leader exists. To certify the agreement on the leader, the global witness consists in each component holding the elected leader of its neighbors. From agreement in all neighborhoods, it follows agreement in the network since neighborhoods overlap. To certify that the elected leader exists, the global witness consists of a spanning tree in the network that is rooted at the leader. In order to check the spanning tree in a distributed manner, we use a characterization of the spanning tree using the distance and the parent function. Note that a component cannot simply check that the elected leader is a component of the network, since it doesn't know all components.\n\nLet be a network graph with . The local input of a component i is i's neighborhood, i.e. i's neighboring components and i's channels. The local output of a component i is (i's elected leader). The postcondition states that there exists with for all .\n\nThe local witness of a component i consists of:\n\n * (i's distance from its elected leader),\n\n * (i's parent in the spanning tree),\n\n * (the distance that i's parent has from its elected leader) and\n\n * for all neighbors j of i (the elected leaders of i's neighbors).\n\nThe global witness predicate holds if there exists (\"the elected leader and root of the spanning tree\") with such that , and for all neighbors j of l, and if for all with it holds that , is a neighbor of i, and for all neighbors j of i. By the global witness predicate, we can tell that the global witness is a spanning tree in G rooted at the elected leader.\n\nThe witness property states that if all components agree with their neighbors on the leader then all components agree on exactly one leader, and if this elected leader is the root of a spanning tree then the leader exists in the network.\n\nThe local witness predicate states the properties required by the global witness predicate for the neighborhood of a component. There is one clause for the elected leader and another clause for all the other components. Each component i has a local checker deciding whether . The composition property states that if the local witness predicate holds for all components then the global witness predicate holds.\n\nFig. 2.\n\nA network graph with six components. A spanning tree is highlighted by dashed lines. For the components 2 and 3, the properties required to satisfy local witness predicates are listed. Component 2 is the elected leader.\n\nAs an example, Fig. 2 shows a specific network graph and a spanning tree as the global witness in this network. Moreover, for two components the properties required to satisfy their local witness predicates are listed.\n\nFor the purpose of this paper, it is not important how a component computes its local witness. However, there are distributed algorithms to compute a spanning tree and Lynch even gives a leader election algorithm that is based on a spanning tree [6].\n\n### 4.2 Verification in Coq\n\nAs a proof-of-concept, we demonstrate our verification method to obtain formal instance correctness (see Sect. 3.4) on certifying leader election using Coq. We begin with the formalization of the network graph and continue with solving the proof obligations composition property, witness property and correctness of the local checkers.\n\nNetwork Formalization. We formalize the network as an undirected, connected graph provided by the GraphBasics library. We define a vertex of the graph as a Component with an unique identifier.\n\nWe construct the local input of a component i in such a way that the global input satisfies the precondition. Hence, for the following formalization of the composition property and the witness property, we assume that the precondition holds.\n\nComposition Property. The composition property states that if the local witness predicate holds for each component, then the global witness predicate is satisfied. For certifying leader election, the local witness predicate is a disjunction in which one clause applies for the elected leader and the other clause for all other components (see Sect. 4.1). In Coq, we formalize each clause of the local witness predicate as a single predicate: gamma_root is the local witness predicate of the elected leader and gamma_i is the local witness predicate of all other components.\n\nEach component i holds its values , and . From a global perspective on the network, we can canonically define the functions leader, parent and distance that each maps a component i to its corresponding value. To instantiate the functions, we added additional properties to the local witness predicate; for instance, we require the mapping between the component i and its function value parent_i by stating the equation parent i = parent_i. In the following Coq formalization of the local witness predicate, we commented on such additional properties with (*x*):\n\nIf the local witness predicate holds for all components, then only in the way that there is one component (root \u2013 the elected leader) that satisfies the clause gamma_root and all other components satisfy the clause gamma_i. Suppose there is more than one component fulfilling the gamma_root clause. Then there is more than one component that has elected itself as a leader. Since the graph is connected, there is a path between every component. Hence, there must be a path between two components that have a different leader. If we follow the path, there must be a pair of components that contradicts the property that neighbors agree on their leader.\n\nSuppose otherwise that all components fulfill the clause gamma_i, then every component has a parent that is not itself. As there is always an edge between a component and its parent, there are as many edges as components in the subgraph. Hence, this subgraph contains a cycle. Within a cycle the distance property is violated leading to a contradiction.\n\nAs a consequence, we fix one component as root and formalize the composition property in Coq as follows:\n\nThe proof of the composition property in Coq is straightforward and only uses syntactic rewriting.\n\nWitness Property. The witness property states that if the global witness predicate holds, then the leader election problem is solved: the spanning tree witnesses the existence of a leader, and by the agreement between neighbors, there can only be one leader.\n\nAs an assumption in Coq, we state that the global witness predicate holds. As a consequence, we can formalize the witness property as follows:\n\nIn order to prove the witness property, we formalize and prove additional properties. We define an inductive type Connection: a Connection is an undirected path between two vertices, consisting of edges that are induced by the parent function. A Connection is constructed from a parent to its child, and has a length.\n\nMoreover, we define the function parent_iteration which takes a component c and a natural number n as input and recursively applies the parent function n-times on c. An ancestor of a component is a component that can be obtained by the application of the parent_iteration function on c.\n\nThe proof of the witness property rests upon three central lemmata. The first lemma states that there is a Connection between every component and root:\n\nWe conduct a proof by induction on the distance of a component - the length of the Connection. The base case follows from the assumptions. For the induction step, we assume a Connection co between root and the parent of a component x with length n. By definition of Connection, co can be extended by the edge between parent and x to a Connection . By definition, the length of is which equals the distance of x.\n\nThe second lemma states that a component x agrees with all its ancestors on the leader:\n\nWe conduct a proof by induction on the argument n of the parent_iteration function. The proof is similar to the one presented above.\n\nThe third lemma states that if there is a Connection between a component and root, then root is ancestor of the component:\n\nBy induction, we can establish that if a Connection exists from component x to component y with length n, then x is the result of applying the parent_iteration function n-times on y. Since we already proved that there is a Connection between every component and root, we conclude that root is an ancestor of each component.\n\nWe prove the witness property by case analysis. For the first case, we have to prove that root is the leader of root which follows from the assumptions. For the second case, we have to prove that all other components have root as their leader. We first use the lemma parent_is_leader such that we are left with proving that the leader of each ancestor of each component is root. Using the lemma parent_transitive_is_root, we establish that each component has root as its ancestor. As root has itself as leader and all other components have the leader of their ancestors as leader, we conclude that root is leader of each component.\n\nCorrectness of the Local Checkers. As the certifying leader election belongs to class C, every component has a local checker. The local checker of a component i decides its local witness predicate . Hence, the checker needs i's local input , i's local output and i's local witness .\n\nThe local input of a component i is the neighborhood of i in accordance to the network Graph G. For modeling purposes, we define a function that takes the network graph as input and generates a checker for each component i that is initialized with i's local input. Furthermore, we bundle i's local output and local witness in the variable checker_input. We implement the local checker in Coq as follows:\n\nNote that a local checker accepts if the disjunction of the clauses gamma_root and gamma_i holds.\n\nTo verify correctness of a local checker , we have to prove that only accepts if the local witness predicate holds for i. We formalize the checker correctness as follows:\n\nThe proof of the checker_correctness is straightforward and uses syntactic rewriting. Note that we added the helper predicates leaderconsistency, distanceconsistency, neighborsconsistency and componentconsistency to ensure consistency between two neighbouring components, i.e. to make sure their witnesses match on corresponding values. For example, if a component i chooses a component j as its parent ( ), the value of equals . In a real network, the consistency check requires additional communication between the checkers. We can realize communication in Coq by making the checker's code reactive. As shown in [2], Coq suits to implement interactive software. To model the communication, we can define an inductive type that models the state transitions of the checker caused by incoming or outgoing messages. A similar approach was used to formalize the Border Gateway Protocol (BGP) in Coq [13]. In order to extract checkers from Coq to e.g. Haskell that can run on a real network, we have to integrate communication in our formalization.\n\nFormal Instance Correctness. We solved the proof obligations composition property, witness property and correctness of the local checkers for certifying leader election using Coq. Thus, we achieved formal instance correctness for certifying leader election.\n\n## 5 Related Work\n\nLiterature offers more than 100 certifying sequential algorithms. A theory of certifying sequential algorithms along with several examples and further reading is given in [7]. Some of these certifying sequential algorithms are implemented in the industrial-level library LEDA (Library for Efficient Data Structures and Algorithms) [8] \u2013 a library for combinatorial and geometric computing. In addition, Rizkallah developed a verification method to achieve formal instance correctness for certifying sequential programs and demonstrated her verification method on some programs from the LEDA libraries. Her dissertation [11] points to her further publications on this field. However, all this work was done for sequential and not for distributed programs. V\u00f6llinger and Reisig gave a certification for the shortest path problem in networks as an first example [12]. To the best of our knowledge, there is no other research on certifying distributed programs and no verification method to obtain formal instance correctness for certifying distributed programs.\n\nHowever, some techniques for making a distributed program self-stabilizing share similarities to our approach of making a distributed program certifying. The idea of self-stabilization is that a system in a faulty state stabilizes itself to a correct state. To this end, the components of a system have to detect that the system's state is faulty whereby local detection is desired. As a consequence, there are some similarities to proof labeling schemes [5] as well, since if there exists a (silent) self-stabilizing program, then there exists a proof labeling scheme for that program and vice versa [1]. In contrast, we separate the checking from the computation, rely on witnesses, and integrate proofs for the witness property and the composition property.\n\n## 6 Conclusion\n\nSince verification of a distributed program is often too costly, we investigated a verification method to obtain formal instance correctness, i.e. a proof that a particular input-output pair is correct. For this purpose, we considered certifying programs. A checker of a certifying program is usually simpler than the original program, and its verification is often feasible while the verification of the original program is too costly. By verifying the checker and by giving a machine-checked proof that the witness certifies the output's correctness, we get formal instance correctness. Rizkallah demonstrated this verification method on certifying sequential programs.\n\nIn contrast, we are concerned with the correctness of distributed programs. In this paper, we defined a class of certifying distributed programs that is particularly interesting since the global witness is computed and checked in a distributed manner (Sect. 3.3). Moreover, we presented a verification method to obtain formal instance correctness for the defined class of certifying distributed programs (Sect. 3.4). Furthermore, we gave a certifying variant of the leader election problem in networks (Sect. 4.1). As a case study, we demonstrated our verification method on certifying leader election using the interactive theorem prover Coq (Sect. 4.2).\n\n## 7 Future Work\n\nIn order to evaluate our verification method, more case studies are of interest. We expect that the library Graph Basics would be also helpful for the verification of other certifying distributed programs. However, the library does not offer graphs with weighted edges. Since weighted edges are necessary for the formalization of computing shortest paths in a network, it could be an interesting extension. A first step in this direction is the definition of the inductive type Connection that adds the concept of the length of a path.\n\nMoreover, we expect that the formalization of the spanning tree as a global witness can be reused for further case studies, since a lot of our certifying distributed programs rely on a spanning tree.\n\nAnother interesting direction would be to investigate further classes of certifying distributed programs and to find a verification method to obtain formal instance correctness for these classes.\n\nReferences\n\n1.\n\nBlin, L., Fraigniaud, P., Patt-Shamir, B.: On proof-labeling schemes versus silent self-stabilizing algorithms. In: Felber, P., Garg, V. (eds.) SSS 2014. LNCS, vol. 8756, pp. 18\u201332. Springer, Cham (2014). doi:10.\u200b1007\/\u200b978-3-319-11764-5_\u200b2\n\n2.\n\nClaret, G.: Pluto: a first concurrent web server in Gallina. http:\/\/\u200bcoq-blog.\u200bclarus.\u200bme\/\u200bpluto-a-first-concurrent-web-server-in-gallina.\u200bhtml\n\n3.\n\nDuprat, J.: A coq toolkit for graph theory (2011). rapport de recherche. Ecole Normale Superieur de Lyon\n\n4.\n\nINRIA: The coq proof assistant. http:\/\/\u200bcoq.\u200binria.\u200bfr\/\u200b\n\n5.\n\nKorman, A., Kutten, S., Peleg, D.: Proof labeling schemes. Distrib. Comput. 22(4), 215\u2013233 (2010)CrossRefMATH\n\n6.\n\nLynch, N.A.: Distributed Algorithms. Morgan Kaufmann Publishers Inc., San Francisco (1996)MATH\n\n7.\n\nMcConnell, R.M., Mehlhorn, K., N\u00e4her, S., Schweitzer, P.: Certifying algorithms. Comput. Sci. Rev. 5, 119\u2013161 (2011)CrossRefMATH\n\n8.\n\nMehlhorn, K., N\u00e4her, S.: LEDA: A Platform for Combinatorial and Geometric Computing. Cambridge University Press, Cambridge (1999)MATH\n\n9.\n\nPeleg, D.: Distributed Computing: A Locality-Sensitive Approach. Society for Industrial and Applied Mathematics, Philadelphia (2000)CrossRefMATH\n\n10.\n\nRaynal, M.: Distributed Algorithms for Message-Passing Systems. Springer, Heidelberg (2013)CrossRefMATH\n\n11.\n\nRizkallah, C.: Verification of program computations. Ph.D. thesis (2015)\n\n12.\n\nV\u00f6llinger, K., Reisig, W.: Certification of distributed algorithms solving problems with optimal substructure. In: Calinescu, R., Rumpe, B. (eds.) SEFM 2015. LNCS, vol. 9276, pp. 190\u2013195. Springer, Cham (2015). doi:10.\u200b1007\/\u200b978-3-319-22969-0_\u200b14 CrossRef\n\n13.\n\nWeitz, K., Woos, D., Torlak, E., Ernst, M.D., Krishnamurthy, A., Tatlock, Z.: Formal semantics and automated verification for the border gateway protocol. In: ACM SIGCOMM Workshop on Networking and Programming Languages (NetPL 2016), Florianopolis, Brazil (2016)\n\nFootnotes\n\n1\n\nhttps:\/\/\u200bgithub.\u200bcom\/\u200bvoellinger\/\u200bverified-certifying-distributed-algorithms\/\u200btree\/\u200bmaster\/\u200bleader-election.\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_28\n\n# Compact Proof Witnesses\n\nMarie-Christine Jakobs1 and Heike Wehrheim1\n\n(1)\n\nPaderborn University, Paderborn, Germany\n\nMarie-Christine Jakobs (Corresponding author)\n\nEmail: marie.christine.jakobs@upb.de\n\nHeike Wehrheim\n\nEmail: wehrheim@upb.de\n\nAbstract\n\nProof witnesses are proof artifacts showing correctness of programs wrt. safety properties. The recent past has seen a rising interest in witnesses as (a) proofs in a proof-carrying-code context, (b) certificates for the correct functioning of verification tools, or simply (c) exchange formats for (partial) verification results. As witnesses in all theses scenarios need to be stored and processed, witnesses are required to be as small as possible. However, software verification tools \u2013 the prime suppliers of witnesses \u2013 do not necessarily construct small witnesses.\n\nIn this paper, we present a formal account of proof witnesses. We introduce the concept of weakenings, reducing the complexity of proof witnesses while preserving the ability of witnessing safety. We develop a weakening technique for a specific class of program analyses, and prove it to be sound. Finally, we experimentally demonstrate our weakening technique to indeed achieve a size reduction of proof witnesses.\n\nKeywords\n\nSoftware verificationProof witnessProof re-use\n\n## 1 Introduction\n\nIn the past years, automatic verification of programs with respect to safety properties has reached a level of maturity that makes it applicable to industrial-size programs. The annual software verification competition SV-COMP [4] demonstrates the advances of program verification, in particular its scalability. Software verification tools prove program correctness, most often for safety properties written into the program in the form of assertions. When the verification tool terminates, the result is typically a yes\/no answer optionally accompanied by a counterexample. While this is the obvious result a verification tool should deliver, it became clear in recent years that all the information computed about a program during verification is too valuable to just be discarded at the end. Such information should better be stored in some form of proof.\n\nProofs are interesting for several reasons: (A) Proofs can be used in a proof-carrying code (PCC) context [25] where a program is accompanied by its proof of safety. Verifying this proof allows to more easily recheck the safety of the program, e.g., when its provider is untrusted. (B) A proof can testify that the verification tool worked correctly, and checking the proof gives confidence in its soundness [5]. (C) Verification tools are sometimes unable to complete proving (e.g., due to timeouts). A proof can then summarize the work done until the tool stopped (see e.g. [6]) so that other tools can continue the work. All these scenarios use proofs as witnesses of the (partial) correctness of the program.\n\nFor these purposes, witnesses need to be small. If the witness is very large, the gain of having a witness and thus not needing to start proving from scratch is lost by the time and memory required to read and process the witness. Our interest is thus in compact proof witnesses. However, the proof artifacts that software verification tools produce are often even larger than the program itself.\n\nLarge proofs are a well-known problem in PCC approaches (e.g. [1, 2, 22, 24, 26, 29]). To deal with the problem, Necula and Lee [24] (who employ other types of proofs than automatic verification tools produce) use succinct representations of proofs. A different practice is to store only parts of a proof and recompute the remaining parts during proof validation like done by Rose [28] or Jakobs [22]. An alternative approach employs techniques like lazy abstraction [9, 20] to directly construct small proofs. Further techniques as presented by Besson et al. [2] and Seo et al. [29] try to remove irrelevant information from proofs that are fixpoints. The latter two approaches have, however, only looked at proofs produced by path-insensitive program analyses.\n\nIn this paper, we first of all present a formal account of proof witnesses. We do so for verification tools generating for the safety analysis some form of abstract state space of the program, either by means of a path insensitive or a path sensitive analysis. We call this abstract reachability graph in the sequel, following the terminology for the software verification tool CPAchecker [8]. We formally state under what circumstances proof witnesses can actually soundly testify program safety. Based on this, we study weakenings of proof witnesses, presenting more compact forms of proofs while preserving being a proof witness. Next, we show how to compute weakenings for a specific category of program analyses. Finally, we experimentally show our weakening technique to be able to achieve size reduction of proof witnesses. To this end, we evaluated our weakening technique on 395 verification tasks taken from the SV-COMP [3] using explicit-state software model checking as analysis method for verification. Next to proof size reduction, we also evaluate the combination of our approach with lazy refinement [9] plus examine its performance in a PCC setting [22].\n\n## 2 Background\n\nWitnesses are used to certify safety of programs. In this section, we start with explaining programs and their semantics. For this presentation, we assume to have programs with assignments and assume statements (representing if and while constructs) and with integer variables only1. We distinguish between boolean expressions used in assume statements, and abbreviate assume bexpr simply by bexpr, and arithmetic expressions aexpr used in assignments. The set contains all these statements, and the set is the set of variables occuring in a program. Following Configurable Software Verification [7] \u2013 the technique the tool CPAchecker, in which we integrated our approach, is based on \u2013, we model a program by a control-flow automaton (CFA) . The set represents program locations, is the initial program location, and models the control-flow edges. The set of error locations defines which locations are unsafe to reach. In the program, these safety properties are written as assert statements. Note that all safety properties can be encoded this way [23], and that we assume that all properties of interest are encoded at once.\n\nFig. 1.\n\nProgram (i input variable) and its control-flow automaton\n\nFigure 1 gives a small (completely artificial) program called (which we use later for explanation) and its control-flow automaton. Here, location is the only error location. The program is called since it tests whether the input is zero (which is recorded as value 1 in r). The assertion checks whether the number of assignments to r or checks on r is 3 when r is 1. This number is accumulated in the variable c.\n\nThe semantics of a program is defined by a labeled transition system made up of a set of concrete states plus locations L, the labels (the control-flow edges of the program) and a transition relation . We write for . A concrete state in C is a mapping . A transition is contained in the transition relation if either , 2 and , or , , and . We call a path of P if , , is a transition in . The set of all paths, i.e. (partial) program executions, of program is denoted by . Finally, a program is safe if no program execution reaches an error location, i.e., .\n\nWe build our technique for witness compaction on top of the configurable program analysis (CPA) framework of Beyer et al. [7] which allows to specify customized, abstract interpretation based program analyses. The advantage of using CPAs is that our results are not just valid for one analysis, but for a whole range of various analyses (namely those specifiable as CPAs). A CPA for a program is a four-tuple containing\n\n 1. 1.\n\nan abstract domain consisting of a set of concrete states, a complete lattice on a set of abstract states and a concretization function , with\n\n 2. 2.\n\na transfer function defining the abstract semantics: s.t.\n\n 3. 3.\n\na merge operator and a termination check operator steering the construction of the abstract state space, and satisfying (a) and (b) . Both of these operators will play no role in the following, and are thus not further discussed here.\n\nBased on a given analysis , an abstract state space of a given program is then constructed in the form of an abstract reachability graph (ARG). To this end, the initial abstract state is fixed to be , and the root of the ARG becomes . The ARG is then further constructed by examining the edges of the CFA and computing successors of nodes under the transfer function of the analysis . The stop operator fixes when to end such an exploration. An ARG for a program is thus a graph with nodes being pairs of locations and abstract values, i.e., and edges . We say that two nodes and are location equivalent, , if . We lift the ordering on elements in A to elements in by saying that if and . We write , , if , and if , , and .\n\n## 3 Proof Witnesses and Weakenings\n\nAbstract reachability graphs represent overapproximations of the state space of the program. They are used by verification tools for inspecting safety of the program: if no error location is reachable in the ARG, it is also unreachable in the program, and the tool can then testify safety. Thus, ARGs are excellent candidates for proof witnesses. However, our definition of an ARG only fixes the syntactical appearance and allows ARGs that are not necessarily proper proof witnesses (and real overapproximations), e.g., our definition allows that an ARG could simply have ignored the exploration of certain edges in the CFA.\n\nDefinition 1\n\nAn ARG G constructed by an analysis is a proof witness for program P if the following properties hold:\n\n * Rootedness. The root node root ,\n\n * Soundness. All successor nodes are covered:\n\n * Safety. No error nodes are present: .\n\n(Sound) verification tools construct ARGs which are indeed proof witnesses (unless the program is not safe). When such an ARG is used as a proof witness, safety of the program can then be checked by validating the above three properties for the ARG. Such checks are often less costly than building a new ARG from scratch. This makes proof witnesses excellent candidates for proofs in a proof-carrying code setting.\n\nProposition 1\n\nIf an ARG G is a proof witness for program P, then P is safe.\n\nHowever, ARGs are often unnecessarily complex witnesses. They often store information about program variables that is either too detailed or even not needed at all. Our interest is thus in finding smaller witnesses. In terms of the analysis, too much detail means that the information stored for program locations is unnecessarily low in the lattice ordering . We build our compaction technique on the following assumption about the size of witnesses.\n\n> Assumption. The weaker (i.e., the higher in the lattice ordering) the abstract values stored for program locations, the more compact the witness.\n\nAs an example justifying this assumption take the weakest element : as it represents the whole set of concrete states, it brings us no specific information at all and can thus also be elided from a witness. This assumption is also taken in the work of Besson et al. [2]. We base the following approach on the assumption \u2013 which our experiments also confirm \u2013 and define weakenings for proof witnesses.\n\nDefinition 2\n\nA function is a weakening function for a domain and program if it satisfies the following two properties:\n\n * (weakening),\n\n * (location preserving).\n\nA weakening function for D and P is consistent with the transfer function if the following holds:\n\n * for all , : implies ,\n\n * for all : if and , then for : .\n\nWhile formally being similar to widenings [13] used in program analysis during fixpoint computation, weakenings serve a different purpose. And indeed, widening functions are too limited for being weakenings as they do not take the program under consideration into account.\n\nWeakening functions are applied to ARGs just by applying them to all nodes and edges: for an ARG G, , where . Note that since the root already uses the top element in the lattice.\n\nTheorem 1\n\nIf an ARG G is a proof witness for program P and w is a weakening function for D and P consistent with the transfer function, then w(G) is a proof witness for program P as well.\n\nProof\n\nWe use the following notation: is the ARG, its weakening. We need to show the three properties of proof witnesses to be valid in w(G).\n\n * Soundness. The most interesting property is soundness. We need to show that , there is an .\n\nLet be the node with .\n\nThus, choose .\n\n * Rootedness, Safety. Both follow by w being a weakening function, and w(G) being constructed by applying w on all nodes of the ARG.\n\n## 4 Variable-Separate Analyses\n\nThe last section introduced proof witnesses, and showed that we get a smaller, yet proper proof witness when using a weakening consistent with the transfer function. Next, we show how to define such weakening functions for a specific sort of program analyses . In the following, we study analyses that use mappings of program variables to abstract values as its abstract domain D. We call such analyses variable-separate because they separately assign values to variables. Examples of variable-separating analyses are constant propagation and explicit-state model checking (both assigning concrete values to variables), interval analysis (assigning intervals to variables), sign analysis (assigning signs to variables), or arithmetical congruence (assigning a congruence class to variables, i.e., variable value is congruent to c modulo m).\n\nDefinition 3\n\nA variable-separate analysis consists of a base domain , that is a complete lattice equipped with an evaluation function on variable-free expressions such that\n\n * and\n\n * ,\n\nfor .\n\nB is lifted to the variable-separate analysis with domain where\n\n * is obtained by pointwise lifting of :\n\n ,\n\n * expression evaluation is obtained by replacing variables with their values: ,\n\n * if and\n\n * if for and .\n\nNote that the execution of an assume statement (bexpr) further constrains the successor state to those satisfying bexpr. The analysis uses the meet operator for this. As an example analysis in our experiments, we use explicit-state model checking [15]. It tracks precise values of variables, however, if combined with lazy refinement [9] it does not track all but just some variables, and therefore does not plainly build the complete state space of a program.\n\nExample 1\n\nExplicit-state model checking uses the flat lattice with and for all , all other elements are incomparable. The operators and are the least upper bound and greatest lower bounds operators, respectively. Assigning to a variable amounts to not tracking the value of that variable or the analysis failed to determine a precise, concrete value. The evaluation function computes the usual arithmetic semantics (denoted ), except on elements (which can appear in expressions when variables are instantiated according to an abstract value).\n\nHere, we write for replacing all occurrences in expr by (possibly different) elements from .\n\nFigure 2 shows the ARG computed for program when using explicit-state model checking without lazy refinement. We directly elide variables which are mapped to as these will not be stored in a proof witness.\n\nFig. 2.\n\nARG of program using explicit-state model checking\n\nFig. 3.\n\nWeakened witness of program\n\nFor variable-separate analyses, we obtain weakenings by computing the set of variables relevant at an ARG node. This is similar to the computation of live variables [27], where, however, the variables to be tracked are tailored towards not introducing new paths in the weakening that were not present in the ARG. The computation of relevant variables has similiarities with program slicing [30] as we compute backward dependencies of variables. For , we define\n\n * ,\n\n *\n\nThe definition of init aims at keeping those variables for which the ARG has already determined that a syntactically possible outgoing edge is semantically impossible; the definition of trans propagates these sets backwards via dependencies. Together, this gives rise to a family of equations for the nodes in the ARG:\n\nNote that we remove all variables from this set that are assigned in a, since no knowledge from previous nodes is required to compute this information. We use to stand for the smallest solution to this equation system that can be computed by a fixpoint computation starting with the emptyset of relevant variables for all nodes3.\n\nDefinition 4\n\nLet be the family of relevant variables. We define the weakening wrt. Rel for nodes as\n\nFor all , we set .\n\nFigure 3 shows the weakened ARG for program . We see that in several abstract states fewer variables have to be tracked. Due to init, the weakened ARG tracks variables and at locations and . Furthermore, it tracks those values required to determine the values of these variables at those locations.\n\nThe key result of this section states that this construction indeed defines a weakening function consistent with the transfer function.\n\nTheorem 2\n\nLet G be an ARG of program P constructed by a variable-separate analysis, the family of relevant variables. Then is a weakening function for G consistent with .\n\nThis theorem follows from the following observations and lemmas: (a) follows from being the top element in the lattice B, and (b) by definition of .\n\nLemma 1\n\nLet be an ARG node, an edge. Then implies .\n\nProof\n\nLet , , (otherwise the CFA would already forbid an edge), . Proof by contraposition.\n\nLemma 2\n\nLet be a node of the ARG. If and , then such that we get .\n\nProof\n\nLet , . Let furthermore and .\n\n * Case 1. .\n\n * : Then by definition of Rel, . We have to show . We first look at x.\n\nNext , .\n\nNext . Note that by definition of Rel, , hence .\n\n * : We have since by definition of weaken. The case for is the same as for .\n\n * Case 2. . Similar to case 1, using the fact that if then\n\n## 5 Experiments\n\nThe last section has introduced a technique for computation of weakenings. Next, we experimentally evaluate this weakening technique for the explicit-state model checking analysis. In our experiments, we wanted to study three questions:\n\n * Q1. Does weakening reduce the size of proof witnesses?\n\n * Q2. Does explicit-state model checking with lazy refinement [9] benefit from weakening?\n\n * Q3. Do PCC approaches benefit from ARG weakenings?\n\nTo explain question 2: Lazy refinement already aims at \"lazily\" including new variables to be tracked, i.e., as few as possible. The interesting question is thus whether our weakenings can further reduce the variables. For question 3, we employed an existing ARG-based PCC technique [22]. To answer these questions, we integrated our ARG weakening within the tool CPAchecker [8] and evaluated it on category Control Flow and Integer Variables of the SV-COMP [3]. We excluded all programs that were not correct w.r.t. the specified property, or for which the verification timed out after 15 min, resulting in 395 programs (verification tasks) in total. For explicit-state model checking with and without lazy refinement we used the respective standard value analyses provided by CPAchecker. Both analyses generate ARGs.\n\nWe run our experiments within BenchExec [10] on an Intel Xeon E3-1230 v5 @ 3.40 GHz and OpenJDK 64-Bit Server VM 1.8.0_121 restricting each task to 5 of 33 GB. To re-execute our experiments, start the extension of BenchExec bundled with CPAchecker 4 with pcc-slicing-valueAnalysis.xml.\n\nQ1. We measure the size reduction of the proof witness for explicit-state model checking by the number of variable assignments stored in the weakened ARG divided by the number of these assignments in the original ARG (1 thus means \"same number of variables\", <1 = \"fewer variables\", >1 = \"more variables\"). In the left of Fig. 4, we see the results where the x-axis lists the verification tasks and the y-axis the size reduction. For the original ARG, the number of variable assignments was between 10 and several millions. Our experiments show that we always profit from ARG weakening. On average the proof size is reduced by about 60%.\n\nFig. 4.\n\nComparison of number of variable assignments in original and weakened ARG for explicit-state model checking without (left) and with lazy refinement (right)\n\nQ2. The right part of Fig. 4 shows the same comparison as the diagram in the left, but for ARGs constructed by lazy refinement. Lazy refinement already tries to track as few variables as possible, just those necessary for proving the desired property. Still, our approach always reduces the proof size, however, not as much as before (which was actually expected).\n\nFig. 5.\n\nComparison of validation times for certificates from original and weakened ARG constructed by explicit-value state model checking with and without lazy refinement\n\nQ3. Last, we used the weakenings within the PCC framework of [22]. This uses ARGs to construct certificates of program correctness. Although the certificate stores only a subset of the ARG's nodes, the comparison of the number of variable assignments still looks similar to the graphics in Fig. 4. Thus, we in addition focused on the effect of our approach on certificate validation. Figure 5 shows the speed-up, i.e., the validation time for the certificate from the original ARG divided by the same time for the certificate from the weakened ARG, both for analyses with and without lazy refinement. In over 70% (50% for lazy refinement) of the cases, the speed-up is greater than 1, i.e., checking the certificate from the weakened ARG is faster. On average, checking the certificate constructed from the weakened ARG is 27% (21% for lazy refinement) faster.\n\nAll in all, the experiments show that weakenings can achieve more compact proof witnesses, and more compact witnesses help to speed up their processing.\n\n## 6 Conclusion\n\nIn this paper, we presented an approach for computing weakenings of proof witnesses produced by software verification tools. We proved that our weakenings preserve the properties required for proof witnesses. We experimentally evaluated the technique using explicit-state model checking. The experiments show that the weakenings can significantly reduce the size of witnesses. Weakenings can thus successfully be applied in all areas in which proof witnesses are employed. In the future, we plan for more experiments with other program analyses.\n\nRelated Work. Our computation of relevant variables is similar to the computation of variables in slicing [30] or cone-of-influence reduction. Our \"slicing criterion\" and the dependencies are tailored towards the purpose of preserving properties of proof witnesses.\n\nA number of other approaches exist that try to reduce the size of a proof. First, succinct representations [24, 26] were used in PCC approaches. Later, approaches have been introduced, e.g. in [1, 22, 28], that store only a part of the original proof. Our approach is orthogonal to these approaches. In the experiments we combined our technique with one such approach (namely [22]) and showed that a combination of proof reduction and weakenings is beneficial.\n\nA large number of techniques in verification already try to keep the generated state space small by the analysis itself (e.g. symbolic model checking [12] or predicate abstraction [19]). Giacobazzi et al. [17, 18] describe how to compute the coarsest abstract domain, a so called correctness kernel, which maintains the behavior of the current abstraction. Further techniques like lazy refinement [9, 20] and abstraction slicing [11] (used in the certifying model checker SLAB [14]) try to reduce the size of the explored state space during verification, and thus reduce the proof size. In our experiments, we combined our technique with lazy refinement for explicit-state model checking [9] and showed that our technique complements lazy refinement.\n\nTwo recent approaches aim at reducing the size of inductive invariants computed during hardware verification [16, 21]. While in principle our ARGs can be transformed into inductive invariants and thus these approaches would theoretically be applicable to software verification techniques constructing ARGs, it is not directly straightforward how to encode arbitrary abstract domains of static analyses as SAT formulae. We see thus our technique as a practically useful reduction technique for proof witnesses of software verifiers constructing ARGs.\n\nWe are aware of only two techniques [2, 29] which also replace abstract states in a proof by more abstract ones. Both weaken abstract interpretation results, while we look at ARGs. Besson et al. [2] introduce the idea of a weakest fixpoint, explain fixpoint pruning for abstract domains in which abstract states are given by a set of constraints and demonstrate it with a polyhedra analysis. Fixpoint pruning repeatedly replaces a set of constraints \u2013 an abstract state \u2013 by a subset of constraints s.t. the property can still be shown. In contrast, we directly compute how to \"prune\" our abstract reachability graph. Seo et al. [29] introduce the general concept of an abstract value slicer. An abstract value slicer consists of an extractor domain and a backtracer. An extractor from the extractor domain is similar to our operator and the task of the backtracer is related to the task of . In contrast to us, they do not need something similar to init since their abstract semantics never forbids successor nodes (and they just consider path-insensitive analyses).\n\nSumming up, none of the existing approaches can be used for proofs in the form of abstract reachability graphs.\n\nAcknowledgements\n\nThis work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Centre \"On-The-Fly Computing\" (SFB 901). The experiments were run in the VerifierCloud hosted by Dirk Beyer and his group.\n\nReferences\n\n1.\n\nAlbert, E., Arenas, P., Puebla, G., Hermenegildo, M.: Reduced certificates for abstraction-carrying code. In: Etalle, S., Truszczy\u0144ski, M. (eds.) Logic Programming. LNCS, vol. 4079, pp. 163\u2013178. Springer, Heidelberg (2006)CrossRef\n\n2.\n\nBesson, F., Jensen, T., Turpin, T.: Small witnesses for abstract interpretation-based proofs. In: Nicola, R. (ed.) ESOP 2007. LNCS, vol. 4421, pp. 268\u2013283. Springer, Heidelberg (2007). doi:10.\u200b1007\/\u200b978-3-540-71316-6_\u200b19 CrossRef\n\n3.\n\nBeyer, D.: Status report on software verification. In: \u00c1brah\u00e1m, E., Havelund, K. (eds.) TACAS 2014. LNCS, vol. 8413, pp. 373\u2013388. Springer, Heidelberg (2014). doi:10.\u200b1007\/\u200b978-3-642-54862-8_\u200b25 CrossRef\n\n4.\n\nBeyer, D.: Reliable and reproducible competition results with benchexec and witnesses (report on SV-COMP 2016). In: Chechik, M., Raskin, J.-F. (eds.) TACAS 2016. LNCS, vol. 9636, pp. 887\u2013904. Springer, Heidelberg (2016). doi:10.\u200b1007\/\u200b978-3-662-49674-9_\u200b55 CrossRef\n\n5.\n\nBeyer, D., Dangl, M., Dietsch, D., Heizmann, M.: Correctness witnesses: exchanging verification results between verifiers. In: Zimmermann et al. [31], pp. 326\u2013337\n\n6.\n\nBeyer, D., Henzinger, T.A., Keremoglu, M.E., Wendler, P.: Conditional model checking: a technique to pass information between verifiers. In: FSE, pp. 57:1\u201357:11. ACM, New York (2012)\n\n7.\n\nBeyer, D., Henzinger, T.A., Th\u00e9oduloz, G.: Configurable software verification: concretizing the convergence of model checking and program analysis. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 504\u2013518. Springer, Heidelberg (2007). doi:10.\u200b1007\/\u200b978-3-540-73368-3_\u200b51 CrossRef\n\n8.\n\nBeyer, D., Keremoglu, M.E.: CPAchecker: a tool for configurable software verification. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 184\u2013190. Springer, Heidelberg (2011). doi:10.\u200b1007\/\u200b978-3-642-22110-1_\u200b16 CrossRef\n\n9.\n\nBeyer, D., L\u00f6we, S.: Explicit-state software model checking based on CEGAR and interpolation. In: Cortellessa, V., Varr\u00f3, D. (eds.) FASE 2013. LNCS, vol. 7793, pp. 146\u2013162. Springer, Heidelberg (2013). doi:10.\u200b1007\/\u200b978-3-642-37057-1_\u200b11 CrossRef\n\n10.\n\nBeyer, D., L\u00f6we, S., Wendler, P.: Benchmarking and resource measurement. In: Fischer, B., Geldenhuys, J. (eds.) SPIN 2015. LNCS, vol. 9232, pp. 160\u2013178. Springer, Cham (2015). doi:10.\u200b1007\/\u200b978-3-319-23404-5_\u200b12 CrossRef\n\n11.\n\nBr\u00fcckner, I., Dr\u00e4ger, K., Finkbeiner, B., Wehrheim, H.: Slicing abstractions. In: Arbab, F., Sirjani, M. (eds.) FSEN 2007. LNCS, vol. 4767, pp. 17\u201332. Springer, Heidelberg (2007). doi:10.\u200b1007\/\u200b978-3-540-75698-9_\u200b2 CrossRef\n\n12.\n\nBurch, J., Clarke, E., McMillan, K., Dill, D., Hwang, L.: Symbolic model checking: 1020 states and beyond. Inf. Comput. 98(2), 142\u2013170 (1992)CrossRef90017-A)MATH\n\n13.\n\nCousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: POPL, pp. 238\u2013252. ACM, New York (1977)\n\n14.\n\nDr\u00e4ger, K., Kupriyanov, A., Finkbeiner, B., Wehrheim, H.: SLAB: a certifying model checker for infinite-state concurrent systems. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 271\u2013274. Springer, Heidelberg (2010). doi:10.\u200b1007\/\u200b978-3-642-12002-2_\u200b22 CrossRef\n\n15.\n\nD'Silva, V., Kroening, D., Weissenbacher, G.: A survey of automated techniques for formal software verification. TCAD 27(7), 1165\u20131178 (2008)\n\n16.\n\nGhassabani, E., Gacek, A., Whalen, M.W.: Efficient generation of inductive validity cores for safety properties. In: Zimmermann et al. [31], pp. 314\u2013325\n\n17.\n\nGiacobazzi, R., Ranzato, F.: Example-guided abstraction simplification. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 211\u2013222. Springer, Heidelberg (2010). doi:10.\u200b1007\/\u200b978-3-642-14162-1_\u200b18 CrossRef\n\n18.\n\nGiacobazzi, R., Ranzato, F.: Correctness kernels of abstract interpretations. Inf. Comput. 237, 187\u2013203 (2014)MathSciNetCrossRefMATH\n\n19.\n\nGraf, S., Saidi, H.: Construction of abstract state graphs with PVS. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 72\u201383. Springer, Heidelberg (1997). doi:10.\u200b1007\/\u200b3-540-63166-6_\u200b10 CrossRef\n\n20.\n\nHenzinger, T.A., Jhala, R., Majumdar, R., Sutre, G.: Lazy abstraction. In: POPL, pp. 58\u201370. ACM, New York (2002)\n\n21.\n\nIvrii, A., Gurfinkel, A., Belov, A.: Small inductive safe invariants. In: Formal Methods in Computer-Aided Design, FMCAD 2014, Lausanne, Switzerland, 21\u201324 October 2014, pp. 115\u2013122. IEEE (2014)\n\n22.\n\nJakobs, M.-C.: Speed up configurable certificate validation by certificate reduction and partitioning. In: Calinescu, R., Rumpe, B. (eds.) SEFM 2015. LNCS, vol. 9276, pp. 159\u2013174. Springer, Cham (2015). doi:10.\u200b1007\/\u200b978-3-319-22969-0_\u200b12 CrossRef\n\n23.\n\nJhala, R., Majumdar, R.: Software model checking. ACM Comput. Surv. 41(4), 21:1\u201321:54 (2009)CrossRef\n\n24.\n\nNecula, G., Lee, P.: Efficient representation and validation of proofs. In: LICS, pp. 93\u2013104. IEEE (1998).\n\n25.\n\nNecula, G.C.: Proof-carrying code. In: POPL, pp. 106\u2013119. ACM, New York (1997)\n\n26.\n\nNecula, G.C., Rahul, S.P.: Oracle-based checking of untrusted software. In: POPL, pp. 142\u2013154. ACM, New York (2001)\n\n27.\n\nNielson, F., Nielson, H.R., Hankin, C.: Principles of program analysis, 1st edn. Springer, Berlin (2005). (corr. 2. print. edn.)MATH\n\n28.\n\nRose, E.: Lightweight bytecode verification. J. Autom. Reason. 31(3\u20134), 303\u2013334 (2003)CrossRefMATH\n\n29.\n\nSeo, S., Yang, H., Yi, K., Han, T.: Goal-directed weakening of abstract interpretation results. In: TOPLAS, October 2007, vol. 29(6) (2007)\n\n30.\n\nWeiser, M.: Program slicing. In: ICSE, pp. 439\u2013449. IEEE Press, Piscataway (1981)\n\n31.\n\nZimmermann, T., Cleland-Huang, J., Su, Z. (eds.): Proceedings of the 24th ACM SIGSOFT International Symposium on Foundations of Software Engineering, FSE 2016, Seattle, WA, USA, 13\u201318 November 2016. ACM, New York (2016)\n\nFootnotes\n\n1\n\nOur implementation in CPAchecker [8] supports programs written in C.\n\n2\n\nTo get c(bexpr) substitute the variables v occurring in bexpr by c(v) and apply standard integer arithmetic.\n\n3\n\nThe fixpoint exists as we have a finite number of variables .\n\n4\n\nhttps:\/\/\u200bsvn.\u200bsosy-lab.\u200borg\/\u200bsoftware\/\u200bcpachecker\/\u200btrunk\/\u200b rv 24405.\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_29\n\n# Qualification of a Model Checker for Avionics Software Verification\n\nLucas Wagner1 , Alain Mebsout2 , Cesare Tinelli2 , Darren Cofer1 and Konrad Slind1\n\n(1)\n\nAdvanced Technology Center, Rockwell Collins, Cedar Rapids, USA\n\n(2)\n\nThe University of Iowa, Iowa City, USA\n\nLucas Wagner (Corresponding author)\n\nEmail: lucas.wagner@rockwellcollins.com\n\nAlain Mebsout\n\nEmail: alain-mebsout@uiowa.edu\n\nCesare Tinelli\n\nEmail: cesare-tinelli@uiowa.edu\n\nDarren Cofer\n\nEmail: darren.cofer@rockwellcollins.com\n\nKonrad Slind\n\nEmail: konrad.slind@rockwellcollins.com\n\nAbstract\n\nFormal methods tools have been shown to be effective at finding defects in safety-critical systems, including avionics systems in commercial aircraft. The publication of DO-178C and the accompanying formal methods supplement DO-333 provide guidance for aircraft manufacturers and equipment suppliers who wish to obtain certification credit for the use of formal methods for software development and verification.\n\nHowever, there are still a number of issues that must be addressed before formal methods tools can be injected into the design process for avionics systems. DO-178C requires that a tool used to meet certification objectives be qualified to demonstrate that its output can be trusted. The qualification of formal methods tools is a relatively new concept presenting unique challenges for both formal methods researchers and software developers in the aerospace industry.\n\nThis paper presents the results of a recent project studying the qualification of formal methods tools. We have identified potential obstacles to their qualification and proposed mitigation strategies. We have conducted two case studies based on different qualification approaches for an open source formal verification tool, the Kind 2 model checker. The first case study produced a qualification package for Kind 2. The second demonstrates the feasibility of independently verifying the output of Kind 2 through the generation of proof certificates and verifying these certificates with a qualified proof checker, in lieu of qualifying the model checker itself.\n\nKeywords\n\nQualificationCertificationModel checkingSoftware verification\n\n## 1 Introduction\n\nCivilian aircraft must undergo a rigorous certification process to establish their airworthiness. Certification encompasses the entire aircraft and all of its components, including the airframe, engines, and on-board computing systems. Many of these systems utilize software. Guidance for the certification of airborne software is provided in DO-178C: Software Considerations in Airborne Systems and Equipment Certification [1].\n\nFormal methods tools have been shown to be effective at finding and eliminating defects in safety-critical software [2]. In recognition of this, when DO-178C was published it was accompanied by DO-333: Formal Methods Supplement to DO-178C and DO-278A [3]. This document provides guidance on how to acceptably use formal methods to satisfy DO-178C certification objectives. However, there are a number of issues that must be addressed before formal methods tools can be fully integrated into the development process for aircraft software. For example, most developers of aerospace systems are unfamiliar with which formal methods tools are most appropriate for different problem domains. Different levels of expertise are necessary to use these tools effectively and correctly. Further, evidence must be provided of a formal method's soundness, a concept that is not well understood by most practicing engineers. Similarly, most developers of formal methods tools are unfamiliar with certification requirements and processes.\n\nDO-178C requires that a tool used to meet its objectives must be qualified in accordance with the tool qualification document DO-330: Software Tool Qualification Considerations [4]. The purpose of the tool qualification process is to obtain confidence in the tool functionality. The effort required varies based on the potential impact a tool error could have on system safety. The qualification of formal verification tools poses unique challenges for both tool developers and aerospace software engineers.\n\nPrevious NASA-sponsored work has described in detail how one might use various formal methods tools to satisfy DO-178C certification objectives [5]. This paper presents the results of a subsequent study designed to address the qualification of formal methods tools. The goal of the effort was to interpret the guidance of DO-330 and DO-333 and provide critical feedback to the aerospace and formal methods research communities on potential pitfalls and best practices to ensure formal methods tool users and developers alike can successfully qualify their tools.\n\nWe are aware of several commercial tool vendors who have successfully qualified formal methods tools. For example, Polyspace by MathWorks and Astre\u00e9 by AbsInt both have DO-178C qualification kits available. In the early stages of this project we helped to organize a Dagstuhl Seminar on Qualification of Formal Methods Tools [6] to engage both formal methods researchers and certification experts. The seminar included presentations on qualification work for the Alt-Ergo theorem prover [7], SPARK verification tools [8], and the CompCert compiler [9], as well as experience reports on qualification guidance and efforts in other industries. A good summary of tool qualification requirements in other domains is found in [10].\n\nIn this paper we examine the qualification of a model checker for use in verification of avionics software. The success of model checking is largely due to the fact that it is a highly automated process, generally requiring less expertise than an interactive theorem prover [11]. One clear strength of model checkers is their ability to return precise error traces witnessing the violation of a given safety property. However, most model checkers are currently unable to return any form of corroborating evidence when they declare a safety property to be satisfied. When used to satisfy certification objectives for aircraft software, a model checking tool would therefore need to qualified.\n\nAn alternative is to instrument the model checker so that in addition to its safety claims, it generates a proof certificate, which is an artifact embodying a proof of the claims. Such a certificate can then be validated by a qualified certificate checker. By reducing the trusted core to the certificate checker, this approach facilitates the integration of formal method tools into the development processes for aircraft software. It redirects tool qualification requirements from a complex tool, the model checker, to a much simpler one, the certificate checker.\n\nThe main contribution of this paper is presentation of these two approaches to qualification as applied to the Kind 2 model checker [12]. Section 2 provides a brief overview of the certification guidance for software in commercial aircraft. Section 3 describes the tool qualification process that is used to establish trust in the tools that are used in avionics software development. Sections 4 and 5 describe two case studies that illustrate different approaches to qualification: direct qualification of the Kind 2 model checker and qualification of the certificate checker for a proof-generating enhancement of the model checker. Section 6 provides conclusions and lessons learned from the project. The complete NASA technical report and qualification artifacts are available at [13].\n\n## 2 Aircraft Software and Certification\n\nCertification is defined in DO-178C as legal recognition by the relevant certification authority that a product, service, organization, or person complies with its requirements. In the context of commercial aircraft, the relevant certification authority is the FAA in the U.S. or EASA in Europe. The requirements referred to are the government regulations regarding the airworthiness of aircraft operating in the National Airspace System (NAS). In practice, certification consists primarily of convincing representatives of a government agency that all required steps have been taken to ensure the safety, reliability, and integrity of the aircraft. Certification differs from verification in that it focuses on evidence provided to a third party to demonstrate that the required activities were performed completely and correctly, rather on performance of the activities themselves.\n\nThe stakeholders in the civil aviation domain (regulators, airframers, equipment manufacturers) have developed a collection of guidance documents defining a certification process which has been accepted as the standard means to comply with regulations. The process includes system development, safety assessment, and design assurance. DO-178C focuses on design assurance for software, and is intended to make sure that software components are developed to meet their requirements without any unintended functionality.\n\nDO-178C does not prescribe a specific development process, but instead identifies important activities and design considerations throughout a development process and defines objectives for each of these activities. It identifies five software levels, with each level based on the impact of a software failure on the overall aircraft function. As the software criticality level increases, so does the number of objectives that must be satisfied. Depending on the associated software level, the process can be very rigorous (Level A) or non-existent (Level E). Objectives are summarized in a collection of tables covering each phase of the development process. Figure 1 shows the objectives required for the most critical avionics software, Level A.\n\nFig. 1.\n\nDO-178C certification activities required for Level A software.\n\nOne of the foundational principles of DO-178C is requirements-based testing. This means that the verification activities are centered around explicit demonstration that each requirement has been met. A second principle is complete coverage, both of the requirements and of the code that implements them. This means that every requirement and every line of code must be examined in the verification process. Furthermore, several metrics are defined which specify the degree of structural coverage that must be obtained in the verification process, depending on the criticality of the software being verified. A third principle is traceability among all of the artifacts produced in the development process. Together, these objectives provide evidence that all requirements are correctly implemented and that no unintended function has been introduced.\n\nWhen DO-178C was developed, guidance specific to new software technologies was provided in associated documents called supplements which could add, modify, or replace objectives in the core document. New supplements were developed in the areas of model-based development, object-oriented design, and formal methods, as well as an additional document containing expanded guidance on tool qualification. DO-178C and its associated documents were published in 2011 and accepted by the FAA as a means of compliance with airworthiness regulations in 2013.\n\n## 3 Qualification\n\nGuidance governing tool qualification is provided in Sect. 12.2 of DO-178C. A tool must be qualified if the following two conditions are met:\n\n 1. 1.\n\nAny of the processes of DO-178C are eliminated, reduced, or automated by the use of a software tool, and\n\n 2. 2.\n\nThe output of the tool is used without being verified.\n\nThis means that if a tool is used to identify software defects rather than, for example, demonstrating that source code satisfies its low-level requirements (a DO-178C objective), then qualification is not required. Similarly, if a tool is used to generate test cases, but those test cases will be manually reviewed for correctness, then qualification is not required.\n\nWhen it is determined that tool qualification is required, the purpose of the qualification process is to ensure that the tool provides confidence at least equivalent to the processes that were eliminated, reduced, or automated by the tool.\n\nTool qualification is context-dependent. If a tool previously qualified for use on one system is proposed for use on another system, it must be re-qualified in the context of the new system.\n\nDO-330 outlines a process for demonstrating a tool's suitability for satisfying DO-178C objectives that it is being used to eliminate, reduce, or automate. The qualification process is similar to the software verification process defined in DO-178C. Qualification amounts to accomplishing a set of activities with corresponding objectives to:\n\n * Identify the DO-178C objectives that the tool is eliminating, reducing, or automating\n\n * Specify which functions of the tool are being relied upon\n\n * Create a set of requirements that precisely identify those functions\n\n * Develop a set of test cases showing that the tool meets those requirements.\n\n### 3.1 Tool Qualification Level\n\nAs in the certification process itself, there are varying levels of rigor associated with tool qualification. The Tool Qualification Level (TQL) is similar to the software level in DO-178C and defines the level of rigor required by the qualification process. TQL-1 is the most rigorous, while TQL-5 is the least rigorous.\n\nThe required TQL is determined by identifying the tool's impact on the software development process. The impact is characterized by determining the impact of a error in the tool. DO-178C provides three criteria to characterize the impact of an error in the tool:\n\nCriterion 1\n\nA tool whose output is part of the airborne software and thus could insert an error.\n\nCriterion 2\n\nA tool that automates verification processes and thus could fail to detect an error, and whose output is used to justify the elimination or reduction of:\n\n * Verification processes other than those automated by the tool, or\n\n * Development processes that could have an impact on the airborne software.\n\nCriterion 3\n\nA tool that, within the scope of its intended use, could fail to detect an error.\n\nA code generator in a model-based development process is an example of a Criterion 1 tool. We expect that most formal methods tools will be used as part of the software verification process and will, therefore, fall into Criteria 2 or 3. That is, they will not be used to generate airborne software, but will be used to verify that the airborne software is correct.\n\nThe distinction between Criteria 2 and 3 depends on exactly which processes the tool is eliminating, reducing, or automating. For example, if an abstract interpretation tool determines that division-by-zero cannot occur and this is used to satisfy DO-178C objectives related to the accuracy and consistency of the source code (Objective A-5.6), then the tool is Criterion 3. However, if those results are also used to justify elimination of robustness testing related to division-by-zero in the object code (Objectives A-6.2 and A-6.4), then the tool becomes a Criterion 2 tool. An unofficial rule of thumb is that when a tool addresses objectives from multiple tables of DO-178C (corresponding to different development phases), it is likely a Criterion 2 tool.\n\nThe required TQL is determined by the combination of its impact and the DO-178C software level to which the tool is being applied, as shown in Table 1.\n\nTable 1.\n\nDetermination of tool qualification level.\n\nSoftware level | Criterion\n\n---|---\n\n1 | 2 | 3\n\nA | TQL-1 | TQL-4 | TQL-5\n\nB | TQL-2 | TQL-4 | TQL-5\n\nC | TQL-3 | TQL-5 | TQL-5\n\nD | TQL-4 | TQL-5 | TQL-5\n\nIn summary, formal methods tools used to satisfy verification process objectives of DO-178C will usually need to be qualified at TQL-5. TQL-4 qualification would only be required if the tool is determined to fall into Criterion 2 and it is being used in the verification of Level A or B software.\n\n### 3.2 DO-330 and Tool Qualification Objectives\n\nOnce the TQL is determined, the required tool qualification objectives are defined by DO-330. Like DO-178C, these objectives are summarized in a collection of tables. Table 2 shows the number of objectives to be satisfied in each area for TQL-4 and TQL-5. Note that objectives for a particular TQL are cumulative, so that the TQL-5 objectives are a subset of the TQL-4 objectives.\n\nTable 2.\n\nDO-330 tool qualification objectives.\n\nTable 2 highlights an important distinction between the qualification objectives. The gray rows (qualification objective tables T-1 through T-7) are objectives related to the development processes of the tool itself. The other rows (T-0 and T-8 through T-10) are objectives related only to the use of the tool. Thus there is a clear distinction between the tool developer context and the tool user context. Furthermore, TQL-5 qualification only requires objectives from the tool user context. This means that TQL-5 qualification is significantly simpler than TQL-4 because it does not require information about how the tool was developed. If a tool was built by a third party, TQL-4 qualification may be difficult to achieve. In particular, since many formal methods tools arise from academic research activities, the artifacts required for TQL-4 qualification may not be available.\n\nAnother interesting point is that tool qualification is always performed in the context of a particular aircraft development effort. This means that certain tool functions may not be utilized or addressed in a qualification. For example, qualification of a model checker may only need to cover variables of primitive data types while ignoring composite types such as arrays, records, and tuple types, if those are not relevant for the given application.\n\nOnce the proper TQL is determined and the objectives have been identified, qualification is simply a matter of demonstrating that each objective is satisfied. For a TQL-5 qualification, the bulk of this effort is associated with DO-330 Table T-0, Tool Operational Processes, and involves defining and verifying Tool Operational Requirements which describe tool capabilities necessary to satisfy the claimed certification objectives.\n\n## 4 Case Study: Kind 2 Model Checker\n\nThe first case study describes the activities and artifacts necessary to complete a TQL-5 qualification of the Kind 2 model checker based on the guidance in DO-330. Our goal is to provide a concrete example that illustrates the qualification process for a typical formal methods tool and could be used as a pattern by others. We also identify challenges or lessons learned in the process. The qualification package is available as part of the NASA final report for the project.\n\nKind 2 [14] is an open-source, multi-engine, SMT-based automatic model checker for safety properties of programs written in the synchronous dataflow language Lustre [15]. It takes as input a Lustre file annotated with properties to be proved, and outputs for each property either a confirmation or a counterexample, a sequence of inputs that falsifies the property.\n\nThis case study is based on earlier work [5] in which various formal methods were used to satisfy DO-178C and DO-333 objectives for verification of a representative Flight Guidance System (FGS). In one of the examples, the Kind 2 model checker was used to verify that a model of the FGS mode logic satisfies its high-level requirements. This qualification case study extends that work by performing the activities needed to qualify Kind 2 for accomplishing the certification objectives described in the earlier work.\n\nFig. 2.\n\nVerification using qualified Kind 2 model checker.\n\nIn this example, the mode logic was expressed as a state machine model in Simulink Stateflow, and serves as low-level requirements for the source code that will be generated from it. A Rockwell Collins tool was used to translate this model into Lustre for analysis by the Kind 2 model checker. Textual high-level requirements for the model logic were manually translated to Lustre and merged with the mode logic Lustre model. The overall tool chain is shown in Fig. 2. This case study is limited to qualification of the model checker and ignores (for now) the model translation tools.\n\n### 4.1 Need for Tool Qualification\n\nIn this case study Kind 2 is being used to automate processes that satisfy the objectives of Verification of Outputs of Software Design Process (DO-178C Table A-4). This includes, for example:\n\n * A-4.1 Low-level requirements comply with high-level requirements.\n\n * A-4.2 Low-level requirements are accurate and consistent.\n\n * A-4.7 Algorithms are accurate.\n\nFurthermore, the outputs of Kind 2 will not be independently verified. This establishes the need for qualification.\n\nThe required TQL is established by determining the impact of Kind 2 on the software development process. In this context the tool:\n\n * Cannot insert an error into the airborne software.\n\n * Could fail to detect an error in the airborne software.\n\n * Is not used to justify the elimination or reduction of other verification processes or development processes that could have an impact on the airborne software.\n\nTherefore, Criterion 3 applies so Kind 2 should be qualified to TQL-5.\n\n### 4.2 Tool Qualification Objectives\n\nThe work performed to satisfy TQL-5 qualification objectives is summarized below:\n\nT-0.1. Tool qualification need is established. (Rationale for tool qualification and determination of the required TQL is described in Sect. 4.1.)\n\nT-0.2. Tool Operational Requirements are defined. Definition of the Tool Operational Requirements (TOR) and their verification in objective T-0.5 are the key qualification activities. The Tool Operational Requirements identify how the tool is to be used within the software life cycle process. This objective requires the identification of the tool usage context, tool interfaces, the tool operational environment, tool inputs and outputs, tool operational requirements, and the operational use of the tool. The focus here is on the tool performance from the perspective of the tool user and what capabilities the tool provides in the software development process.\n\nWe have specified 111 TORs that must be verified for Kind 2. These requirements cover:\n\n * The features of the Lustre language used by Kind 2 in this context\n\n * Input validation features\n\n * Properties that must be correctly analyzed as true or false.\n\nSince the requirements will be verified by testing performed on Kind 2, they cover a finite subset of the Lustre grammar. Conservative bounds on the length of inputs are established and validated.\n\nT-0.3. Tool Executable Object Code is installed in the tool operational environment. Identification of the specific versions of the tool and its dependencies, instructions of how to install the tool, and a record of actually installing the tool are required to meet this objective. Qualification was based on Kind 2 version 1.0.1 and the Z3 SMT solver [16] (version 4.4.2).\n\nT-0.5. Tool operation complies with the Tool Operational Requirements. This objective demonstrates that the tool complies with its TORs. This objective is covered in three parts. First, the review and analysis procedures used to verify the TORs are defined. Secondly, we identify a set of tests, referred to as the Tool Operational Test Cases and Procedures, that when executed, demonstrate that Kind 2 meets its TORs. Finally, the results of actually executing the test procedures within the Tool Operational Environment must be collected.\n\nT-0.6. Tool Operational Requirements are sufficient and correct. This objective is satisfied by ensuring that the TORs adequately address the tool usage context, the tool operational environment, the input accepted by the tool, the output produced by the tool, required tool functions, applicable tool user information, and the performance requirements for the tool.\n\nT-0.7. Software life cycle process needs are met by the tool. This objective is satisfied by the review, analysis, and testing results used to satisfy the TORs.\n\nOther Objectives (T-8, T-9, T-10). Tool configuration management, quality assurance, and qualification liaison process. Most of the data required by these objectives are highly dependent on the context and the processes of the applicant organization and can only be meaningfully defined for an actual software development and tool qualification effort.\n\n### 4.3 Results\n\nThe purpose of this qualification package was to provide a complete case study containing a detailed set of tool operational requirements and test procedures. It is anticipated that this qualification package contains all of the necessary information such that it could be used within an avionics certification effort. No barriers were found that would prevent qualification of Kind 2.\n\nOne interesting result from the Tool Qualification Liason process is T-10.4 Impact of Known Problems on TORs. During verification of the TORs, some errors were identified. These have either been corrected or will be corrected in the near future. However, such errors do not preclude use of the tool in certification activities, as long as the impact and functional limitations on tool use are identified.\n\nThe qualification package and results were reviewed by certification experts at Rockwell Collins and determined to meet the requirements of DO-330. Successfully using it would require an applicant to provide detailed information to support the tool qualification objectives from Table T-8, T-9, and T-10, which are specific to an organization's configuration management, quality assurance, and certification practices respectively. We expect that it could be used as the starting point for tool qualification in an actual avionics software development effort or as a pattern for qualification of another tool.\n\n## 5 Case Study: Proof-Generating Model Checker\n\nThe second qualification case study is based on a proof-generating version of the Kind 2 model checker that is supported by a separate proof checker [14]. In this approach, the proof checker verifies the output of the model checker. This removes the need to qualify a complex tool (the model checker) and instead requires qualification of a much simpler one (the proof checker). By reducing the trusted core to the proof checker, we may be able to reduce the qualification effort required and enhance the overall assurance.\n\nThis case study is based on the same software development context as the first, and involves using the model checker to satisfy the same certification objectives for verifying the FGS mode logic. The qualification package developed for the proof checker tool is available as part of the project final report.\n\n### 5.1 Development of a Proof-Generating Version of Kind 2\n\nFor this effort we have used the SMT solver CVC4 [17] with Kind 2. CVC4 is a solver for first-order propositional logic modulo a set of background theories such as integer or real linear arithmetic. Our work relies heavily on the proof production capabilities of CVC4. A unique aspect of CVC4 proofs is that they are fine grained. This means they are very detailed and checking them is only a matter of carefully following and replaying the steps in the proof certificate. In contrast, proofs produced by other solvers require the final proof checker to perform substantial reasoning to reconstruct missing steps.\n\nThe proof checker which was qualified in this case study, named Check-It, is an instantiation of the Logical Framework with Side Conditions (LFSC) proof checker [18]. The resulting tool architecture is shown in Fig. 3, which includes both the unqualified Kind 2 model checker and the qualified Check-it proof checker.\n\nFig. 3.\n\nVerification using Kind 2 and a qualified proof checker.\n\nKind 2 is used to generate two separate proof certificates:\n\n * A proof certificate (PC) for safety properties of the transition system corresponding to Lustre model being verified.\n\n * A front-end certificate (FEC) that provides evidence that two independent tools have accepted the same Lustre input model and produced the same first order logic (FOL) internal representation.\n\nThe PC summarizes the work of the different analysis engines used in Kind 2. This includes bounded model checking (BMC), k-induction, IC3, as well as additional invariant generation strategies. In practice it takes the form of a k-inductive strengthening of the properties.\n\nThis intermediate certificate is checked by CVC4, from which we extract proofs to reconstruct safety arguments using the rules of k-induction. Proofs are produced in the language of LFSC.\n\nTo make the whole process efficient and scalable, certificates are first minimized before being checked. An iterative process takes care of this phase by efficiently lowering the bound k and removing any superfluous information contained within the certificate.\n\nThe FEC is necessary to ensure that the proof in the PC is actually about the input model provided. Without this step, it is possible that the (unqualified) model checker could produce a valid PC that is unrelated to the input model. The FEC is generated in the form of observational equivalence between two internal representations generated by independently developed front ends. In our case, the two front ends are Kind 2 itself and JKind, a Lustre model checker inspired by Kind but independently developed by Rockwell Collins [19]. Observational equivalence between the two FOL representations is recast as an invariant property. Checking that property yields a second proof certificate from which a global notion of safety can be derived and incorporated in the LFSC proof.\n\nThe trusted core of this approach consists of:\n\n * The LFSC checker (5300 lines of C++ code).\n\n * The LFSC signatures comprising the overall proof system in LFSC, for a total of 444 lines of LFSC code.\n\n * The assumption that Kind 2 and JKind do not have identical defects that could escape the observational equivalence check. We consider this reasonable since the tools were produced by different development teams using different programming languages.\n\n### 5.2 Qualification of Check-It\n\nThe approach of using a qualified tool to check the results of an unqualified tool is not unprecedented. FAQ D.7 of DO-330 provides guidance for exactly this \"two tool\" approach. Recall that qualification of a tool is necessary when it is used to eliminate, reduce, or automate DO-178C processes and when the outputs of the tool are not verified. Kind 2 and Check-It are used to satisfy the same objectives for the FGS mode logic as described in Sect. 4. The outputs of the Kind 2 analysis, a set of proof certificates, are verified using the Check-It proof checking tool. According to the guidance in DO-330 FAQ D.7, this process is acceptable if the Check-It tool is qualified.\n\nDetermination of required TQL is the same as in Sect. 4. Check-it is used only to verify proof certificates produced by Kind 2 and so it is a Criterion 3 tool. Therefore, Check-It must be qualified at TQL-5.\n\nThe qualification objectives for Check-It were the same as for Kind 2, so we only address the differences here. Since Check-It is simpler than Kind 2, defining its TORs was comparatively straightforward. Inputs to the tool are proof certificates (PC and FEC) that are composed of proof rules defined in six signature files. We have specified 82 TORs that must be verified for Check-It.\n\nObjectives for verification of tool operation were accomplished by a combination of peer review and testing. Test cases cover presence and validity of certificates, compatibility with certificates produced by Kind 2, performance requirements, and proof rule acceptance. Peer review of the proof rules in the signatures files used by Check-It was conducted to identify any potential trust issues. Results from this review were used to identify additional test cases (for example, to preclude the acceptance of unsound rules).\n\nDO-330, FAQ D.7 provides additional information on the use of a qualified tool (Check-It) to check the results of an unqualified tool (Kind 2). This FAQ identifies factors that should be considered to prevent the possibility of errors in both the unqualified tool and the qualified tool. The primary concern is to identify the interaction between tools in the case of various failures in the unqualified tool (for example, if Kind 2 fails to produce a PC or a FEC, or if either is found to be incorrect by Check-It).\n\nThe FAQ also identifies four additional concerns that apply in this situation, and which have been addressed in the qualficiation package:\n\n * Coverage of verification objectives for the unqualified tool's output\n\n * Operating conditions of the qualified tool\n\n * Common cause avoidance\n\n * Protection between tools\n\n### 5.3 Results\n\nTo summarize, we found nothing about the \"two tool\" proof-checking approach that would prevent successful tool qualification. Checking the PC validates the Kind 2 analysis and checking the FEC provides an argument that the emitted PC corresponds to the original Lustre file. If Kind 2 produces incorrect, malformed, or missing certificates Check-It highlights the error. The tools use dissimilar technical approaches, one performing model checking and the other proof checking, minimizing the chance for any common cause failure. The TORs for Check-It were much simpler to define and verify than for Kind 2. However, the proof checking approach was more challenging to explain to certification experts and, consequently, would be inherently riskier to implement. We estimate the overall effort of this approach to be about 75% of the effort required to qualify Kind 2 itself. An added benefit, however, is that the qualified proof checker could be reused with future improved versions of Kind 2 (provided the proof format remains the same), or even with other model checkers which would produce certificates in the same format.\n\n## 6 Conclusions\n\nIn this paper we have explored the qualification of formal methods tools within the context of avionics certification. This effort produced useful examples and artifacts for two qualification case studies, and also provided insight into the qualification process for formal methods tools that should be useful to software developers, tool developers, tool users, and certification experts. Combined with the prior work on Formal Methods Case Studies for DO-333, it provides a comprehensive set of case studies for using and qualifying formal method tools for avionics software development.\n\nThe work reveals that qualification at TQL-5 can be a straightforward task. The guidance of DO-330 does not require any activities that are especially difficult or costly for qualification of a model checker. However, the guidance does suggest that tools from the research community may be difficult to qualify at TQL-4 due to the requirements for tool development artifacts including tool requirements, test cases, tool design, and architectural descriptions. Formal methods tool developers who desire to have their tools used in the avionics industry should keep this in mind.\n\nIn addition, this work highlights the need for good software engineering practices for formal methods tools used in certification. The relatively high complexity of internal translations, optimizations, and analysis algorithms increases the likelihood that defects will be identified. Bug tracking facilities are absolutely essential for users to understand a tool's limitations.\n\nLastly, we developed a proof-generating enhancement of the Kind 2 model checker, and explored the impact of this capability on tool qualification. We produced qualification packages for both Kind 2 and for the proof checker for certificates generated by Kind 2. We determined that the \"two tool\" proof checker approach was viable from a qualification standpoint and provides increased assurance. However, it was not dramatically easier or less costly to qualify and was definitely more difficult to explain and justify to certification experts.\n\nBased purely on cost and perceived risk, we expect that TQL-5 qualfication of a model checker would be the approach preferred by most avionics software developers. The qualified proof checker approach provides significant advantages in terms of greater assurance and modularity, which may be attractive for developers interested in \"future-proofing\" their verification process. By keeping the model checker separate and free from the need for qualification, improved features and functionality can be more easily incorporated without impacting the qualified (and therefore less flexible) proof checker.\n\nAcknowledgments\n\nThis work was funded by NASA contract NNL14AA06C.\n\nReferences\n\n1.\n\nRTCA DO-178C: Software considerations in airborne systems and equipment certification, Washington, DC (2011)\n\n2.\n\nWoodcock, J., Larsen, P.G., Bicarregui, J., Fitzgerald, J.S.: Formal methods: practice and experience. ACM Comput. Surv. 41, 19 (2009)CrossRef\n\n3.\n\nRTCA DO-333: Formal methods supplement to DO-178C and DO-278A, Washington, DC (2011)\n\n4.\n\nRTCA DO-330: Software tool qualification considerations, Washington, DC (2011)\n\n5.\n\nCofer, D., Miller, S.: DO-333 certification case studies. In: Badger, J.M., Rozier, K.Y. (eds.) NFM 2014. LNCS, vol. 8430, pp. 1\u201315. Springer, Cham (2014). doi:10.\u200b1007\/\u200b978-3-319-06200-6_\u200b1 CrossRef\n\n6.\n\nCofer, D., Klein, G., Slind, K., Wiels, V.: Qualification of formal methods tools (Dagstuhl seminar 15182). Dagstuhl Rep. 5, 142\u2013159 (2015)\n\n7.\n\nOCamlPro: Alt-ergo (2013). https:\/\/\u200balt-ergo.\u200bocamlpro.\u200bcom\/\u200b\n\n8.\n\nAdaCore: SPARK Pro (2014). http:\/\/\u200bwww.\u200badacore.\u200bcom\/\u200bsparkpro\/\u200b\n\n9.\n\nLeroy, X.: A formally verified compiler back-end. J. Autom. Reason. 43, 363\u2013446 (2009)MathSciNetCrossRefMATH\n\n10.\n\nCamus, J.L., DeWalt, M.P., Pothon, F., Ladier, G., Boulanger, J.L., Blanquart, J.P., Quere, P., Ricque, B., Gassino, J.: Tool qualification in multiple domains: status and perspectives. In: Embedded Real Time Software and Systems, Toulouse, France, 5\u20137 February, vol. 7991. Springer (2014)\n\n11.\n\nMiller, S.P., Whalen, M.W., Cofer, D.D.: Software model checking takes off. Commun. ACM 53, 58\u201364 (2010)CrossRef\n\n12.\n\nChampion, A., Mebsout, A., Sticksel, C., Tinelli, C.: The Kind 2 model checker. In: Chaudhuri, S., Farzan, A. (eds.) CAV 2016. LNCS, vol. 9780, pp. 510\u2013517. Springer, Cham (2016). doi:10.\u200b1007\/\u200b978-3-319-41540-6_\u200b29\n\n13.\n\nNASA: Qualification of Formal Methods Tools Under DO-330 (2017). https:\/\/\u200bshemesh.\u200blarc.\u200bnasa.\u200bgov\/\u200bfm\/\u200bFMinCert\/\u200bDO-330-case-studies-RC.\u200bhtml\n\n14.\n\nMebsout, A., Tinelli, C.: Proof certificates for SMT-based model checkers for infinite-state systems. In: FMCAD, Mountain View, California, USA, October 2016. http:\/\/\u200bcs.\u200buiowa.\u200bedu\/\u200b~amebsout\/\u200bpapers\/\u200bfmcad2016.\u200bpdf\n\n15.\n\nHalbwachs, N., Caspi, P., Raymond, P., Pilaud, D.: The synchronous dataflow programming language LUSTRE. In: Proceedings of the IEEE, pp. 1305\u20131320 (1991)\n\n16.\n\nde Moura, L., Bj\u00f8rner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337\u2013340. Springer, Heidelberg (2008). doi:10.\u200b1007\/\u200b978-3-540-78800-3_\u200b24 CrossRef\n\n17.\n\nBarrett, C., Conway, C.L., Deters, M., Hadarean, L., Jovanovi\u0107, D., King, T., Reynolds, A., Tinelli, C.: CVC4. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 171\u2013177. Springer, Heidelberg (2011). doi:10.\u200b1007\/\u200b978-3-642-22110-1_\u200b14 CrossRef\n\n18.\n\nStump, A., Oe, D., Reynolds, A., Hadarean, L., Tinelli, C.: SMT proof checking using a logical framework. Form. Methods Syst. Des. 41, 91\u2013118 (2013)CrossRefMATH\n\n19.\n\nGacek, A.: JKind - a Java implementation of the KIND model checker (2014). https:\/\/\u200bgithub.\u200bcom\/\u200bagacek\/\u200bjkind\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_30\n\n# SpeAR v2.0: Formalized Past LTL Specification and Analysis of Requirements\n\nAaron W. Fifarek1 , Lucas G. Wagner2 , Jonathan A. Hoffman3 , Benjamin D. Rodes4 , M. Anthony Aiello4 and Jennifer A. Davis2\n\n(1)\n\nLinQuest Corporation, Dayton, USA\n\n(2)\n\nRockwell Collins, Cedar Rapids, USA\n\n(3)\n\nAir Force Research Laboratory, Wright-Patterson AFB, USA\n\n(4)\n\nDependable Computing, Charlottesville, USA\n\nAaron W. Fifarek (Corresponding author)\n\nEmail: aaron.fifarek@linquest.com\n\nLucas G. Wagner\n\nEmail: lucas.wagner@rockwellcollins.com\n\nJonathan A. Hoffman\n\nEmail: jonathan.hoffman.2@us.af.mil\n\nBenjamin D. Rodes\n\nEmail: ben.rodes@dependablecomputing.com\n\nM. Anthony Aiello\n\nEmail: tony.aiello@dependablecomputing.com\n\nJennifer A. Davis\n\nEmail: jen.davis@rockwellcollins.com\n\nAbstract\n\nThis paper describes current progress on SpeAR, a novel tool for capturing and analyzing requirements in a domain specific language designed to read like natural language. Using SpeAR, systems engineers capture requirements, environmental assumptions, and critical system properties using the formal semantics of Past LTL. SpeAR analyzes requirements for logical consistency and uses model checking to prove that assumptions and requirements entail stated properties. These analyses build confidence in the correctness of the formally captured requirements.\n\nApproved for Public Release; Distribution Unlimited (Case Number: 88ABW-2016-6046).\n\n## 1 Introduction\n\nThis paper presents SpeAR (Specification and Analysis of Requirements) v2.0 [1], an open-source tool for capturing and analyzing requirements stated in a language that is formal, yet designed to read like natural language.\n\nRequirements capture and analysis is a challenging problem for complex systems and yet is fundamental to ensuring development success. Traditionally, requirements suffer from unavoidable ambiguity that arises from reliance on natural language. Formal methods mitigates this ambiguity through mathematical representation of desired behaviors and enables analysis and proofs of properties.\n\nSpeAR allows systems engineers to capture requirements in a language with the formal semantics of Past Linear Temporal Logic (Past LTL) [3] and supports proofs of critical properties about requirements using model checking [2]. Moreover, the SpeAR user interface performs validations, including type-checking, that provide systems engineers with real-time feedback on the well-formedness of requirements. Initial feedback from systems engineers has been positive, emphasizing the readability of the language. Additionally, our use of SpeAR on early case studies has identified errors and omissions in captured requirements.\n\n## 2 Related Work\n\nPrevious work has investigated the role of formal methods in requirements engineering. Parnas laid the foundation for constraint based requirements with the four variable model: monitored inputs, controlled outputs, and their software representation as inputs and outputs [11]. The Software Cost Reduction (SCR) method builds upon the four variable model using a tabular representation of requirements and constraints [10]. SCR provides tool support for formal analysis, including a consistency checker and model checker. SpeAR also builds upon the four-variable model but expresses requirements in a language that is designed to read like natural language instead of a tabular representation. In contrast to tools like ARSENAL [8] that provide formal analysis of natural language requirements, engineers use SpeAR to capture requirements directly in a formal language, avoiding the introduction of potential ambiguity.\n\nPrevious versions of SpeAR [5] used pre-defined specification patterns [4] that were found to be too rigid in practice. SpeAR v2.0 introduces a language providing the formal semantics of Past LTL that is more flexible, allowing users to capture requirements directly, rather than choosing from pre-defined patterns.\n\n## 3 Formal Requirements Capture\n\nSpeAR captures requirements in a formal language that not only provides the semantics of Past LTL, but is also designed to read like natural language. Previous versions of SpeAR required explicit scoping for temporal operators, using an awkward syntax, for example:\n\n> while signal > threshold : : always output == ON;\n\nSpeAR v2.0 eliminates this syntax and provides English alternatives for most operators, such as equal to, greater than, less than or equal to, implies, and not. Additionally, SpeAR provides aliases for many operators so that systems engineers can more naturally express their requirements. With these English alternatives, the previous example can be written as:\n\n> if signal greater than threshold then output equal to ON\n\nThis syntax is much closer to natural language.\n\nWe motivate further discussion of the SpeAR language by describing partial requirements for the thermostat of a simple heating system. As seen in Fig. 1a, the thermostat is represented by a three-state automaton describing reactions to changes in the ambient temperature.\n\n### 3.1 SpeAR File Stucture\n\nSpeAR promotes grouping requirements according to system components enabling modularity and reuse. Requirements are captured in files laid out in a common structure. Partial requirements for the thermostat, a component of the heating system, are shown in Fig. 1b.\n\nFig. 1.\n\n(a) Simple heating system with associated (b) partial thermostat SpeAR file\n\nInputs, Outputs, State: Inputs represent monitored or observed data from the environment, as well as inputs from other components. Outputs represent data to the environment, as well as outputs to other components. State represents data that is not visible to the environment or to other components. For example, the thermostat monitors the ambient and target temperatures for a room (inputs), controls the heater by sending a signal that turns it on or off (outputs), and has a counter that tracks heating duration (state).\n\nAssumptions: Assumptions identify necessary constraints on inputs from the environment and from other components. For example, the thermostat assumes that the ambient temperature rises when the heater is on (a0). This constraint is an assumption: the thermostat cannot directly control the ambient temperature.\n\nRequirements: Requirements identify constraints that the component must guarantee through its implementation. For example, the thermostat will send a signal to turn the heater on when the ambient temperature is lower than the target temperature (r0).\n\nProperties: Properties represent constraints that the system should satisfy when operating in its intended environment. Properties can be used to validate that the requirements define the correct component behavior or to prove that certain undesirable conditions never arise. For example, the heater is only on when the ambient temperature is below the target temperature (p_heat).\n\n### 3.2 SpeAR Formal Semantics\n\nThe formal semantics of SpeAR is as expressive as Lustre [9] and is based upon Past LTL [3] but omits future looking operators. We define this subset as Past-Only LTL, which allows users to express temporal behaviors that begin in the past, with arbitrarily long but finite history, and end at the current step (i.e., transition). Supported temporal operators in SpeAR are shown in Table 1, where and are propositions\u2014unlike Past LTL, SpeAR provides support for a general previous operator that can be used on all legal types in the model, not just boolean types. In addition to temporal operators, SpeAR provides basic arithmetic, logical, and relational operators.\n\nTable 1.\n\nPast time temporal expressions with SpeAR equivalences\n\nSpeAR | Past LTL\n\n---|---\n\nPrevious with initial value false | Y\n\nPrevious with initial value true | Z\n\nHistorically | H\n\nOnce | O\n\n since | S\n\n triggers | T\n\n## 4 Analysis\n\nIn addition to capturing requirements formally, SpeAR provides an analysis platform. SpeAR performs type checking, dimensional analysis of unit computations, and other well-formedness checks on the requirements in real-time. Once requirements have passed these checks, the user can analyze the requirements for logical entailment and logical consistency.\n\n### 4.1 Logical Entailment\n\nSpeAR enables systems engineers to prove that stated properties are consequences of captured assumptions and requirements. This capability provides early insight into the correctness and completeness of captured requirements.\n\nFormally, SpeAR proves that the conjunction of the Assumptions (A) and Requirements (R) entails each Property (P) as shown in Eq. (1).\n\n(1)\n\nSpeAR proves entailment by (1) translating SpeAR files to an equivalent Lustre model and (2) analyzing the Lustre model using infinite-state model checking. SpeAR presents a counterexample if the requirements do not satisfy a property.\n\nIn the thermostat example seen in Fig. 1b, there are four properties: p_heat, p_off, p_error, and p_elatch. Two properties describe the nominal behavior of the system: (1) p_heat asserts the heater is on if the ambient temperature is less than the target temperature, (2) p_off asserts the heater is off if the ambient temperature is greater than or equal to the target temperature. Two properties describe the error behavior of the system: (1) p_error asserts the system is in the error state if a timeout occurs, (2) p_elatch asserts that after the system enters the error state it remains in that state.\n\nLogical entailment allows systems engineers to prove the captured requirements and assumptions satisfy all of the stated properties.\n\n### 4.2 Logical Consistency\n\nLogical entailment is only valid if the captured requirements and assumptions are not conflicting. When there is a conflict among requirements or assumptions, the logical conjunction of the constraints is false, and thus the logical implication described in Eq. (1) is a vacuous proof (i.e., ).\n\nCurrently, SpeAR provides partial analysis to detect logical inconsistency. Logical inconsistency can exist for all steps and inputs, for example when two constraints are always in conflict. Logical inconsistency may also occur only during certain steps or as a result of certain inputs.\n\nSpeAR analyzes requirements for logical inconsistency that is provable within the first N steps, for some user-selected N. This is accomplished by (1) translating SpeAR files to an equivalent Lustre model and (2) searching for a counterexample to the assertion that the conjunction of the assumptions and requirements cannot be true for N consecutive steps, beginning at the initial state, as shown in Eq. (2). Since we use counterexample generation to check consistency, we need a minimum step count to prevent the model checker from merely confirming that the requirements are consistent on the first timestep (a 1-step counterexample).\n\n(2)\n\nIf the requirements are proven inconsistent for the first N steps, SpeAR alerts the user to the inconsistency and identifies the set of constraints in conflict. If, however, a counterexample is found to Eq. (2), SpeAR declares the requirements to be consistent even if the constraints are inconsistent at step or for some other set of inputs. This result may mislead the systems engineer to conclude that the requirements are consistent when in fact they are inconsistent. Future versions of SpeAR will address this issue by implementing the stronger concept of realizability [6]\u2014a proof that all requirements and assumptions are consistent for all steps and combinations of inputs that satisfy the assumptions.\n\n## 5 Conclusion and Future Work\n\nSpeAR is a tool for capturing and analyzing formal requirements in a language that provides the formal semantics of Past LTL and is also designed to read like natural language. In addition to type checking and real-time validation of well-formedness, SpeAR provides two analyses that depend upon model checking: logical entailment and logical consistency. Logical entailment proves that specified properties, which define desired behaviors of the system, are consequences of the set of captured assumptions and requirements. Logical consistency aims to identify conflicting assumptions and requirements.\n\nSystems engineers familiar with, but not experts at, formal methods provided positive initial feedback: SpeAR is more readable than typical formal languages and is worth the effort of learning. Additionally, applying SpeAR to requirements for a stateful protocol revealed a set of unreachable states; a decision was based on a variable whose value was overwritten on the current step. This error represented an incomplete understanding of the requirement that would have been difficult to identify through testing or inspection. After all contributing errors were found and fixed, SpeAR was used to prove that all states were reachable.\n\nWhile this paper presents current progress on SpeAR v2.0, development and improvement is ongoing. We will expand logical consistency analysis to include realizability, allowing users to prove that the requirements are consistent for all steps and inputs. We will incorporate recent work in inductive validity cores [7] to provide logical traceability analysis, allowing users to identify which requirements and assumptions are used to prove each property\u2014unused requirements and assumptions should be deleted as they overconstrain the system.\n\nWe are continuing to refine SpeAR and assess its utility by applying it to the development of unmanned autonomous systems and other research efforts. These results will be presented in future publications.\n\nReferences\n\n1.\n\nhttps:\/\/\u200bgithub.\u200bcom\/\u200blgwagner\/\u200bSpeAR\n\n2.\n\nBaier, C., Katoen, J.P., Larsen, K.G.: Principles of Model Checking. MIT Press, Cambridge (2008)MATH\n\n3.\n\nCimatti, A., Roveri, M., Sheridan, D.: Bounded verification of past LTL. In: Hu, A.J., Martin, A.K. (eds.) FMCAD 2004. LNCS, vol. 3312, pp. 245\u2013259. Springer, Heidelberg (2004). doi:10.\u200b1007\/\u200b978-3-540-30494-4_\u200b18 CrossRef\n\n4.\n\nDwyer, M.B., Avrunin, G.S., Corbett, J.C.: Property specification patterns for finite-state verification. In: FMSP 1998 Proceedings of the Second Workshop on Formal Methods in Software Practice, pp. 7\u201315. ACM, New York (1998)\n\n5.\n\nFifarek, A.W., Wagner, L.G.: Formal requirements of a simple turbofan using the SpeAR framework. In: 22nd International Symposium on Air Breathing Engines. International Society on Air Breathing Engines, University of Cincinnati (2015)\n\n6.\n\nGacek, A., Katis, A., Whalen, M.W., Backes, J., Cofer, D.: Towards realizability checking of contracts using theories. In: Havelund, K., Holzmann, G., Joshi, R. (eds.) NFM 2015. LNCS, vol. 9058, pp. 173\u2013187. Springer, Cham (2015). doi:10.\u200b1007\/\u200b978-3-319-17524-9_\u200b13\n\n7.\n\nGhassabani, E., Gacek, A., Whalen, M.W.: Efficient generation of inductive validity cores for safety properties. arXiv e-prints, March 2016\n\n8.\n\nGhosh, S., Elenius, D., Li, W., Lincoln, P., Shankar, N., Steiner, W.: ARSENAL: automatic requirements specification extraction from natural language. In: Rayadurgam, S., Tkachuk, O. (eds.) NFM 2016. LNCS, vol. 9690, pp. 41\u201346. Springer, Cham (2016). doi:10.\u200b1007\/\u200b978-3-319-40648-0_\u200b4 CrossRef\n\n9.\n\nHalbwachs, N., Caspi, P., Raymond, P., Pilaud, D.: The synchronous data flow programming language LUSTRE. Proc. IEEE 79(9), 1305\u20131320 (1991)CrossRef\n\n10.\n\nHeitmeyer, C., Archer, M., Bharadwaj, R., Jeffords, R.: Tools for constructing requirements specification: the SCR toolset at the age of ten. Int. J. Comput. Syst. Sci. Eng. 20(1), 19\u201353 (2005)\n\n11.\n\nParnas, D.L., Madey, J.: Functional documents for computer systems. Sci. Comput. Program. 25, 41\u201361 (1995)CrossRef96871-J)\n\u00a9 Springer International Publishing AG 2017\n\nClark Barrett, Misty Davies and Temesghen Kahsai (eds.)NASA Formal MethodsLecture Notes in Computer Science1022710.1007\/978-3-319-57288-8_31\n\n# Just Formal Enough? Automated Analysis of EARS Requirements\n\nLevi L\u00facio1 , Salman Rahman1 , Chih-Hong Cheng1 and Alistair Mavin2\n\n(1)\n\nfortiss GmbH, Guerickestra\u00dfe 25, 80805 M\u00fcnchen, Germany\n\n(2)\n\nRolls-Royce, PO Box 31, Derby, UK\n\nLevi L\u00facio (Corresponding author)\n\nEmail: lucio@fortiss.org\n\nSalman Rahman\n\nEmail: salman.rahman@tum.de\n\nChih-Hong Cheng\n\nEmail: cheng@fortiss.org\n\nAlistair Mavin\n\nEmail: alistair.mavin@rolls-royce.com\n\nAbstract\n\nEARS is a technique used by Rolls-Royce and many other organizations around the world to capture requirements in natural language in a precise manner. In this paper we describe the EARS-CTRL tool for writing and analyzing EARS requirements for controllers. We provide two levels of analysis of requirements written in EARS-CTRL: firstly our editor uses projectional editing as well as typing (based on a glossary of controller terms) to ensure as far as possible well-formedness by construction of the requirements; secondly we have used a controller synthesis tool to check whether a set of EARS-CTRL requirements is realizable as an actual controller. In the positive case, the tool synthesizes and displays the controller as a synchronous dataflow diagram. This information can be used to examine the specified behavior and to iteratively correct, improve or complete a set of EARS-CTRL requirements.\n\n## 1 Introduction\n\nWhen writing requirements for software systems in natural language problems such as ambiguity, vagueness, omission and duplication are common [17]. This is due to the large gap between natural language and the languages in which code is expressed. Natural language requirements describe a wide range of concepts of the real, abstract and imaginary worlds. By contrast, programming languages are used to describe precise sequences of operations inside a machine. Natural language can be partial, ambiguous and subjective, whilst code can typically be none of those things.\n\nEARS (Easy Approach to Requirements Syntax) is an approach created at Rolls-Royce to capture requirements in natural language [17]. EARS is based on practical experience, but has been shown to scale effectively to large sets of requirements in diverse domains [15, 16]. Application of the approach generates requirements in a small number of patterns. EARS has been shown to reduce or even eliminate many problems inherent in natural language requirements [17]. In spite of its industrial success, we are not aware of any published material describing tool support for EARS. The method is primarily aimed at the early stages of system construction, as a means of providing clear guidance to requirements engineers when using natural language to describe system behavior. Automating the writing and analysis of EARS requirements has not been attempted thus far. It is however reasonable to expect that, due to the semi-formal nature of the EARS patterns, automated analysis of EARS specifications can be implemented to improve software development methodologies already in place at Rolls-Royce and elsewhere.\n\nIn this paper we will describe our initial work in the direction of automating the analysis of EARS requirements. As domain of application, we have chosen to focus on the construction of controller software. In particular, the EARS requirements for the controller running example we present in this study have been validated by a requirements engineer at Rolls-Royce. Aside from being industrially relevant, the controller domain lends itself well to analyses and syntheses, given its constrained nature. The contributions described in this paper are as follows:\n\n * An editor for EARS specifications, called EARS-CTRL, based on the projectional editor MPS (Meta Programming System) [2]. Sentences written in our MPS EARS-CTRL editor have the \"look and feel\" of pure natural language, but are in fact templates with placeholders for which meaningful terms are proposed to the requirements engineer.\n\n * Automated check of realizability of the requirements as a real controller is provided at the push of a button. Additionally, when the controller is realizable, a synchronous dataflow diagram [14] modelling the specified behavior is generated. This information can be used iteratively to check whether the set of EARS-CTRL requirements correctly express the desired behavior of the natural language requirements written in EARS.\n\nFig. 1.\n\nLiquid mixing system\n\n## 2 Running Example\n\nOur running example for this study is a liquid mixing system. The controller for this system, depicted in Fig. 1, is supposed to behave as follows: when the start button is pressed, valve 0 opens until the container is filled with the first liquid up to the level detected by the liquid level 1 sensor. Valve 0 then closes and valve 1 opens until the container is filled up with the second liquid up to the level detected by the liquid level 2 sensor. Once both liquids are poured into the container, they are mixed by the stirring motor for a duration of 60 s. When the mixing process is over, valve 2 opens for 120 s, allowing the mixture to be drained from the container. It is possible to interrupt the process at any point using an emergency stop button. Pressing this button closes all valves and stops the stirring engine.\n\n## 3 Expressing and Analyzing Requirements\n\nThe first step when writing a set of requirements using EARS-CTRL is to identify the vocabulary to be used. Figure 2 depicts the glossary for the liquid mixing system we have presented in Sect. 2. The glossary defines the name of the controller being built, the names of the components of the system that interface with the controller (together with informal descriptions of their purpose), and the sensors and actuators those components make available. Rules expressing relations between signals are also expressed here.\n\nFig. 2.\n\nEARS-CTRL glossary for the container fusing controller\n\nOnce the glossary is defined, the EARS-CTRL requirements can be written. Our editor is built using MPS, a projectional meta-editor for DSL development. The projectional capabilities of the editor make it such that requirements can be edited directly as abstract syntax trees projected onto a textual view. In practice this means that each requirement can be added as an instance of a template with placeholders. These placeholders are then filled by the requirements engineer using the terms defined in the glossary.\n\nFig. 3.\n\nExample of adding an EARS-CTRL requirement\n\n### 3.1 Well-Formedness by Construction\n\nIn Fig. 4 we depict the action of adding an EARS requirement using our editor. Note that two aspects of well-formedness by construction are enforced at this point: firstly, by using EARS templates instances, we guarantee that the form of the requirement is correct; secondly, the editor provides suggestions for the terms that are added to each of the placeholders as a range of possibilities extracted from the glossary. Figure 3 illustrates some examples for the action associated with the valve 2 component of the system. Note that in the suggestions associated to this placeholder two constraints are enforced: (a) only actions associated with actuators are proposed, and (b) the actions for component valve 2 are limited to the ones that are described in the glossary in Fig. 2.\n\nFig. 4.\n\nEARS-CTRL requirements to describe the controller for the liquid mixer system\n\n### 3.2 Realizability Analysis\n\nWell-formedness by construction, as described in Sect. 3.1, guarantees a certain level of correctness of individual requirements. EARS-CTRL provides additional mechanisms for analyzing the interplay of individual requirements in a specification. In particular, at the press of a button the tool can decide whether the set of requirements is realizable as a concrete controller. Note that non-realizability is typically due to conflicting requirements. This analysis is executed by (a) transforming EARS-CTRL requirements in LTL (Linear Temporal Logic) formulas, and (b) running the GXW synthesis [6] tool autoCode4 [7] via an API to attempt to synthesize a controller for those formulas.\n\nIn Fig. 4 we depict a set of requirements1 for the running example from Sect. 2 that is actually not realizable \u2013 as can be understood from the pop-up message in the fig. obtained after running the analysis. When revising the specification, we realized that requirements Req1 and Req9 were in conflict. The reason for this conflict was that, according to Req9, the emergency button can be pressed at any moment thus closing valve 0. However, Req1 states that valve 0 opens when the start button is pressed. Thus, logically valve 0 could be simultaneously open and closed \u2013 a contradiction.\n\nFig. 5.\n\nUpdated requirement to allow realizing the liquid mixer controller\n\nTo eliminate the contradiction we have replaced Req1 in the set of requirements in Fig. 4 by the requirement in Fig. 5.2 Adding the condition until emergency button is pressed to the original version of Req1 disallows valve 0 being simultaneously open and closed.\n\nWhen a set of EARS requirements is realizable, EARS-CTRL imports a synchronous dataflow diagram from the autoCode4 tool that describes the behavior of the specified controller. The controller can be visualized inside the EARS-CTRL tool as a block diagram using MPS's graphical rendering capabilities. Due to space limitations, we direct the reader to the project's website [3] for an image of the controller generated for the running example. Note that the synthesized controller is imported into EARS-CTRL as an MPS model, making it possible to further implement automated analyses on this artifact.\n\n### 3.3 The EARS-CTRL Tool\n\nThe EARS-CTRL tool is available as a github project [1]. Note that the tool is distributed as an MPS project and requires MPS [2] to be installed as pre-requisite. Together with the functional running example, we distribute with the project the realizable EARS-CTRL requirements for a simple engine controller, a sliding door controller and quiz controller.\n\n## 4 Related Work\n\nThe quest for automatically generating controller implementation from specifications dates back to the ideas of Church [8]. However, it was not until recently that researchers investigated practical approaches to the problem. Methodologies such as bounded synthesis [19] or GR-1 [18], and the combination of compositional approaches [10] have proven to be applicable on moderately-sized examples. Based on these results that stand on solid logical foundations, several projects produced research on the generation of logic formulas from natural language, with the goal of achieving reactive control synthesis from natural language. The ARSENAL project starts from specifications written in arbitrary natural language [11] and also uses GR-1 as the underlying synthesis engine. The work of Kress-Gazit et al. focuses on the synthesis of robot controllers [13]. Their methodology is based on using template-based natural language that matches the GR-1 framework. The work of Yan et al. [20] applies to full LTL specifications and includes features such as guessing the I\/O partitioning and using dictionaries to automatically derive relations between predicates (such as ), in order to detect inconsistencies in specifications.\n\nThe workflow presented in this paper, although also targeting the use of natural language, starts with a methodologically different approach. Conceptually, the tool proposes a formal language with a fixed interpretation, while hiding the formality from end-users; in fact an end-user specifies the required system behavior using only natural language. Therefore, for scenarios such as the relation between and , the negation relation is not decided during controller synthesis phase but is given during the requirements design phase. Although our tool supports producing generic LTL formulas, our decision for using the autoCode4 tool and the GXW language subset lies on the rationale that, for iterative validation of requirements, it is necessary that designers understand the structure of controllers. For tools [5, 9, 12] supporting GR-1 or bounded synthesis, the synthesized controller is commonly a generated via BDD dumping or via creating explicit state-machines which can have thousands of states, making user interaction and inspection difficult. The work presented here largely draws inspiration from and builds on the knowledge obtained when building the AF3 [4] tool for the model-driven development of software.\n\n## 5 Conclusions and Future Work\n\nDue to the early nature of this work, two main technical issues remain to be addressed: (a) the fact that expressing and analysing complex states such as \"the valve is 3\/4 closed\" or \"the quantity of liquid in the container is under quantity X\" cannot be reasonably done within EARS-CTRL (due to the boolean representation in autoCode4 of sensors and actuators); and (b) lifting the information provided by the analysis engine autoCode4 for debugging EARS-CTRL requirements is currently manually done.\n\nThe work described in this paper is an early analysis of the gap between constrained natural language expressed using EARS and logical specifications that can be automatically transformed into controllers. Note that while the former enables humans to write requirements that are as unambiguous as possible, the latter are developed for computers to process. While these worlds may overlap, they were not necessarily designed to do so.\n\nIdeally, our tool would have as starting point \"pure\" EARS requirements. However, given the gap mentioned above, we had to slightly adapt \"classic\" EARS to make it amenable to formal treatment, as briefly mentioned in Sect. 3. The implicit question posed by the title of this paper \u2013 whether EARS is just formal enough for automated analyses (and syntheses) \u2013 is thus partly answered by this work, although additional research is needed. Future efforts will thus concentrate on automatically bridging this gap such that engineers using EARS-CTRL are as unaware as possible of the underlying automatic mechanisms of our tool.\n\nAcknowledgements\n\nThis work was developed for the \"IETS3\" research project, funded by the German Federal Ministry of Education and Research under code 01IS15037A\/B.\n\nReferences\n\n1.\n\nEARS-CTRL GitHub project. https:\/\/\u200bgithub.\u200bcom\/\u200blevilucio\/\u200bEARS-CTRL.\u200bgit\n\n2.\n\nMeta Programming System. https:\/\/\u200bwww.\u200bjetbrains.\u200bcom\/\u200bmps\/\u200b\n\n3.\n\nWiki for the EARS-CTRL project. https:\/\/\u200bgithub.\u200bcom\/\u200blevilucio\/\u200bEARS-CTRL\/\u200bwiki\n\n4.\n\nAravantinos, V., Voss, S., Teufl, S., H\u00f6lzl, F., Sch\u00e4tz, B.: AutoFOCUS 3: tooling concepts for seamless, model-based development of embedded systems. In: ACES-MB (Co-located with MoDELS), pp. 19\u201326 (2015)\n\n5.\n\nBohy, A., Bruy\u00e8re, V., Filiot, E., Jin, N., Raskin, J.-F.: Acacia+, a tool for LTL synthesis. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 652\u2013657. Springer, Heidelberg (2012). doi:10.\u200b1007\/\u200b978-3-642-31424-7_\u200b45 CrossRef\n\n6.\n\nCheng, C.-H., Hamza, Y., Ruess, H.: Structural synthesis for GXW specifications. In: Chaudhuri, S., Farzan, A. (eds.) CAV 2016. LNCS, vol. 9779, pp. 95\u2013117. Springer, Cham (2016). doi:10.\u200b1007\/\u200b978-3-319-41528-4_\u200b6\n\n7.\n\nCheng, C.-H., Lee, E., Ruess, H.: autoCode4: structural reactive synthesis. In: TACAS 2017, accepted for publication, Tool available at: http:\/\/\u200bautocode4.\u200bsourceforge.\u200bnet\n\n8.\n\nChurch, A.: Applications of Recursive Arithmetic to the Problem of Circuit Synthesis \u2013 Summaries of talks, Institute for Symbolic Logic, Cornell University (1957). Institute for Defense Analysis, Princeton, New Jersey (1960)\n\n9.\n\nEhlers, R.: Unbeast: symbolic bounded synthesis. In: Abdulla, P.A., Leino, K.R.M. (eds.) TACAS 2011. LNCS, vol. 6605, pp. 272\u2013275. Springer, Heidelberg (2011). doi:10.\u200b1007\/\u200b978-3-642-19835-9_\u200b25 CrossRef\n\n10.\n\nFiliot, E., Jin, N., Raskin, J.-F.: Compositional algorithms for LTL synthesis. In: Bouajjani, A., Chin, W.-N. (eds.) ATVA 2010. LNCS, vol. 6252, pp. 112\u2013127. Springer, Heidelberg (2010). doi:10.\u200b1007\/\u200b978-3-642-15643-4_\u200b10 CrossRef\n\n11.\n\nGhosh, S., Elenius, D., Li, W., Lincoln, P., Shankar, N., Steiner, W.: ARSENAL: automatic requirements specification extraction from natural language. In: Rayadurgam, S., Tkachuk, O. (eds.) NFM 2016. LNCS, vol. 9690, pp. 41\u201346. Springer, Cham (2016). doi:10.\u200b1007\/\u200b978-3-319-40648-0_\u200b4 CrossRef\n\n12.\n\nJobstmann, B., Galler, S., Weiglhofer, M., Bloem, R.: Anzu: a tool for property synthesis. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 258\u2013262. Springer, Heidelberg (2007). doi:10.\u200b1007\/\u200b978-3-540-73368-3_\u200b29 CrossRef\n\n13.\n\nKress-Gazit, H., Fainekos, G.E., Pappas, G.J.: Translating structured English to robot controllers. Adv. Robot. 22(12), 1343\u20131359 (2008)CrossRef\n\n14.\n\nLee, E.A., Messerschmitt, D.G.: Synchronous data flow. Proc. IEEE 75(9), 1235\u20131245 (1987)CrossRef\n\n15.\n\nMavin, A., Wilkinson, P.: Big ears (the return of \"easy approach to requirements engineering\"). In: RE, pp. 277\u2013282. IEEE (2010)\n\n16.\n\nMavin, A., Wilkinson, P., Gregory, S., Uusitalo, E.: Listens learned (8 lessons learned applying EARS). In: RE, pp. 276\u2013282. IEEE (2016)\n\n17.\n\nMavin, A., Wilkinson, P., Novak, M.: Easy approach to requirements syntax (EARS). In: RE, pp. 317\u2013322. IEEE (2009)\n\n18.\n\nPiterman, N., Pnueli, A., Sa'ar, Y.: Synthesis of reactive(1) designs. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 364\u2013380. Springer, Heidelberg (2005). doi:10.\u200b1007\/\u200b11609773_\u200b24 CrossRef\n\n19.\n\nSchewe, S., Finkbeiner, B.: Bounded synthesis. In: Namjoshi, K.S., Yoneda, T., Higashino, T., Okamura, Y. (eds.) ATVA 2007. LNCS, vol. 4762, pp. 474\u2013488. Springer, Heidelberg (2007). doi:10.\u200b1007\/\u200b978-3-540-75596-8_\u200b33 CrossRef\n\n20.\n\nYan, R., Cheng, C., Chai, Y.: Formal consistency checking over specifications in natural languages. In: DATE, pp. 1677\u20131682 (2015)\n\nFootnotes\n\n1\n\nFor analysability reasons, EARS-CTRL's syntax is slighty different from EARS'. In particular EARS disavows the usage of \"until\" clauses and composed logical expressions in a requirement.\n\n2\n\nThe requirement in Fig. 5 is an instance of template While A, when B the system shall C until D. The corresponding LTL is of the form , W being the weak-until operator.\nAuthor Index\n\n\u00c1brah\u00e1m, Erika\n\nAhrenbach, Seth\n\nAichernig, Bernhard K.\n\nAiello, M. Anthony\n\nAkili, Samira\n\nAmrani, Moussa\n\nAndr\u00e9, \u00c9tienne\n\nAr\u00e9chiga, Nikos\n\nBellettini, Carlo\n\nBensalem, Saddek\n\nBlom, Stefan C.C.\n\nBonfanti, Silvia\n\nBorges, Mateus\n\nBozga, Marius\n\nButler, Michael\n\nCamilli, Matteo\n\nCarissoni, Marco\n\nCasinghino, Chris\n\nCheng, Chih-Hong\n\nCofer, Darren\n\nDarabi, Saeed\n\nDavis, Jennifer A.\n\nDemyanova, Yulia\n\nDieumegard, Arnaud\n\nDonz\u00e9, Alexandre\n\nDreossi, Tommaso\n\nDross, Claire\n\nEnea, Constantin\n\nFantechi, Alessandro\n\nFifarek, Aaron W.\n\nFilieri, Antonio\n\nFrancis, Michael\n\nFrenkel, Hadar\n\nGargantini, Angelo\n\nGe, Ning\n\nGleirscher, Mario\n\nGrumberg, Orna\n\nHaxthausen, Anne E.\n\nHoang, Thai Son\n\nHocking, Ashlie B.\n\nHoffman, Jonathan A.\n\nHuisman, Marieke\n\nIllous, Hugo\n\nJackson, Paul B.\n\nJakobs, Marie-Christine\n\nJenn, Eric\n\nJha, Susmit\n\nJohnson, Taylor T.\n\nJones, Benjamin F.\n\nKnight, John C.\n\nKowalewski, Stefan\n\nKugele, Stefan\n\nLemerre, Matthieu\n\nLeng\u00e1l, Ond\u0159ej\n\nL\u00facio, Levi\n\nMacedo, Hugo Daniel\n\nMakhlouf, Ibtissem Ben\n\nMartel, Matthieu\n\nMashkoor, Atif\n\nMavin, Alistair\n\nMebsout, Alain\n\nMediouni, Braham Lotfi\n\nMoy, Yannick\n\nNguyen, Hoang Gia\n\nNouri, Ayoub\n\nOrtiz, James\n\nP\u0103s\u0103reanu, Corina S.\n\nPetrucci, Laure\n\nPhan, Quoc-Sang\n\nPike, Lee\n\nPinto, Alessandro\n\nRahman, Salman\n\nRaman, Vasumathi\n\nRival, Xavier\n\nRodes, Benjamin D.\n\nR\u00fcmmer, Philipp\n\nSahai, Tuhin\n\nScandurra, Patrizia\n\nSchobbens, Pierre-Yves\n\nSchupp, Stefan\n\nSeshia, Sanjit A.\n\nShapiro, Brandon\n\nSheinvald, Sarai\n\nSighireanu, Mihaela\n\nSlind, Konrad\n\nSnook, Colin\n\nSogokon, Andrew\n\nSun, Jun\n\nTappler, Martin\n\nTinelli, Cesare\n\nVojnar, Tom\u00e1\u0161\n\nV\u00f6llinger, Kim\n\nWagner, Lucas G.\n\nWehrheim, Heike\n\nZuleger, Florian\n\n9th\n\nNASA Formal Methods Symposium\n\nNFM\n\n2017\n\nMoffett Field, CA USA\n\n20170516\n\n20170518\n","meta":{"redpajama_set_name":"RedPajamaBook"}} +{"text":" \nPRAISE FOR _R ECOVER!_\n\n\" _Recover!_ goes well beyond brainless, mindless, and choiceless approaches to addiction. Dr. Stanton Peele's work offers hope for mindful, practical, and liberating addiction treatment and self-help.\"\u2014Harold J. Bursztajn, M.D., Associate Clinical Professor of Psychiatry and Co-Founder, Program in Psychiatry and the Law at BIDMC Psychiatry of Harvard Medical School\n\n\"Stanton Peele's insistence that addiction is not a disease, but a symptom of dysfunctional societies, families, and\/or psyches is compelling, compassionate, and almost certainly correct. In _Recover!,_ his most impressive work to date, he lays out a program\u2014both utterly simple and profound\u2014that will quite literally save lives by addressing the root causes of addiction rather than pathologizing its many manifestations.\"\u2014Christopher Ryan, Ph.D. & Cacilda Jeth\u00e1, M.D., authors of the _New York Times_ bestseller _Sex at Dawn_\n\n\"12-step treatment worsened my addiction to the point that I nearly died of withdrawal. Stanton Peele's books saved my life by showing me that I was not powerless and did not need to be rescued by a 'Higher Power.' For a step-by-step guide on how to overcome addiction I most highly recommend Dr. Peele's new book _Recover!_ \"\u2014Kenneth Anderson, M.A., Founder and CEO of HAMS Harm Reduction for Alcohol\n\n\"In _Recover!_ , Stanton Peele and Ilse Thompson offer a blueprint to help addicts cope with their triggers, from loneliness and feeling unworthy, anxious, and overwhelmed. _Recover!_ focuses on what's _right_ in the addict's life, and adding to it. It's a hopeful, tangible set of tools designed to give power _back_ to the addict\u2014not give it up.\"\u2014Gabrielle Glaser, author of the _New York Times_ bestseller _Her Best-Kept Secret: Why Women Drink\u2014And How They Can Regain Control_\n\n\"'I am a recovering addict' was the way someone introduced himself to me on my first visit to the USA. He explained he had been in recovery for the past 25 years. The irrationality, helplessness and disempowerment inherent in this statement shocked me. This is what the disease model of addiction does to people. I am in agreement with Stanton Peele that people are not powerless or helpless in the face of dependence on drugs, and the evidence supports this view. This book dispels that, and other myths about drugs. Stanton has come up with another must-read book.\"\u2014Professor Pat O'Hare, co-founder and former director of Harm Reduction International\n\n\"In his latest book, _Recover!_ , pioneering addiction expert Dr. Stanton Peele moves on to exciting new ground by providing practical advice and tools for dealing with addiction, based on Buddhist-inspired mindfulness techniques. It is essential reading for those who want to understand the reality of addiction and ways it can be effectively addressed. I highly recommend this book to anyone who wants to move on from their own addiction or is supporting someone else to overcome their addiction.\"\u2014Julian Cohen, author of _Drugs and Young People: Essential Information and Advice for Parents and Professionals_\n\n\"Stanton Peele's writing has been a Copernican paradigm shift in the field of recovery. With his _Diseasing of America_ , Peele emerged as a savvy provocateur with the guts to take on the recovery establishment. With _Recover!_ Peele shares his clinical wisdom and compassion with those who are on the path of change and self-acceptance. _Recover!_ is a recovery program of practical perfection _without_ the typical recovery perfectionism.\"\u2014Pavel Somov, Ph.D., author of _Lotus Effect_ and _Eating the Moment: 141 Mindful Practices to Overcome Overeating One Meal at a Time_\n\n\" _Recover!_ is a powerful new tool for helping people with addictions heal and grow. Dr. Stanton Peele is a trailblazer who has led each new progressive wave in the addictive behaviors field since the 1970s. Today, Dr. Peele is a leading voice for a new shift in the field, one that refutes the myth that addicted people are victims of a permanent disease that they can arrest only by accepting their powerlessness and lifelong abstinence. _Recover!_ is a how-to guide to recovery through cultivating mindful awareness and self-compassion. Inspiring, hopeful, and a good read as well.\"\u2014Andrew Tatarsky, Ph.D., author, _Harm Reduction Psychotherapy: A New Treatment for Drug and Alcohol Problems_ ; Director, Center for Optimal Living, NYC\n\n\"In the midst of the turbulence about defining and dealing with addiction, Stanton Peele has consistently articulated one of the few sane voices. Increasingly, research has proved that he is right. _Recover!_ continues and extends his presence at the forefront of advice and help based on common sense and efficacy for those struggling with addiction.\"\u2014Liese Recke, Manager of Clinical Treatment, Oslo Norway, and former addict\n\n\"Probably the world's most notable figure in addiction studies, Stanton Peele has written another great book. _Recover!_ really is a self-help book. Unlike most of what you read, it teaches you to help yourself, rather than telling you to rely on a treatment system because helping oneself is impossible. Stanton's work assisted my recovery many years ago, and he can help you now.\"\u2014Peter Ferentzy, Ph.D., author of _Dealing with an Addict: What You Need to Know if Someone You Care for Has a Drug or Alcohol Problem_\n\n\"Stanton Peele knows more about addiction than anyone in the world. Every one of his books is a masterpiece. So is this one. The materials in this book are factual, inspiring and helpful for anyone making for change on their own. If you need additional help, take this book to a good therapist. Ask them to help you apply Peele's materials. You will be very happy with the results!\"\u2014Robert M. Muscala, R.N., Addiction\/Chemical Health Specialist, Minnesota\n\nPRAISE FOR STANTON PEELE\n\n\"Stanton Peele is a true pioneer of addiction research and theory. His ideas must be reckoned with by anyone who is serious about understanding addiction\u2014and they offer hope to the many millions for whom current approaches are not effective or who simply prefer evidence-based alternatives.\"\u2014Maia Szalavitz, neuroscience journalist for _Time Magazine_ ; co-author of _Born for Love: Why Empathy is Essential\u2014and Endangered_\n\n\"Peele offers mindful alternatives to those suffering from addictions and to professionals seeking to help them.\"\u2014Ellen Langer, Department of Psychology, Harvard University; author of _Mindfulness_ and _Counterclockwise: Mindful Health and the Power of Possibility_\n\n\" _Love and Addiction_ was probably the first book I ever read which analyzed addiction in a way that made sense to me and echoed what I knew from my work. It still reads absolutely true as an understanding of addictive behavior all these years later.\"\u2014Rowdy Yates, Ph.D., Department of Addiction Studies, University of Stirling\n\n\" _The Truth About Addiction and Recovery_ is an unusually well-researched and persuasively presented book on some of the main myths about addiction and recovery. Required reading for addicts, their associates, and those who try to treat them.\"\u2014Albert Ellis, Ph.D., founder of Rational-Emotive Therapy; ranked in a survey of psychologists as the second most influential psychotherapist in history\n\n\"Stanton Peele is the only author who has effectively challenged the consistent failure of the mental health establishment, the huge AA and Synanon-type 'religions,' the drug enforcement bureaucracy, and the medical profession.\"\u2014Nicholas Cummings, Ph.D., Past President, American Psychological Association; Chief of Mental Health, Kaiser Permanente Health Maintenance Organization\n\n\" _Diseasing of America_ is a provocative review of the uses and abuses of the disease model in the past three decades. This important book has significantly added to my education and clinical understanding of addiction in my professional practice.\"\u2014Richard R. Irons, M.D., FASAM, the Menninger Clinic\n\n\"Peele makes it clear that the disease model of addiction is an emperor without clothes. By placing addictive behaviors in the context of other problems of living, he emphasizes personal responsibility for one's habits. The book empowers the reader to view addiction in a new optimistic light.\"\u2014G. Alan Marlatt, founder of Addictive Behaviors Research Center, University of Washington; co-editor of _Relapse Prevention_\n\n\"Dr. Peele's work has influenced my professional work and changed my personal life for the better.\"\u2014Anne M. Fletcher, M.S., R.D., L.D., author of _Thin for Life_ , _Sober for Good_ , and _Inside Rehab: The Surprising Truth About Addiction Treatment\u2014and How to Get Help That Works_\n\n\"Stanton Peele's books have been instrumental in helping me understand my own underlying causes of addiction and how, however well-intentioned the 12-step model is, it led me to focus on the wrong aspects of addiction.\"\u2014Marianne Gilliam, author of _How Alcoholics Anonymous Failed Me_\n\n\"After years of being in and out of rehab, I read _Diseasing of America_. It showed me that I have the power to decide whether or not to drink. More than a decade later, I still have not had another drink.\"\u2014\"Adam Smith\"\n\n\"We have more than enough diseases without inventing new ones to relieve us of moral responsibility to deal with the complexity of the human condition. _Diseasing of America_ is an important book that should be read by all concerned about addiction. An added bonus\u2014Dr. Peele writes exceptionally well.\"\u2014Neil A. Kurtzman, M.D., Chairman, Department of Internal Medicine, Texas Tech University Health Sciences Center\n_Recover!_\n**A LSO BY STANTON PEELE**\n\n_7 Tools to Beat Addiction_\n\n_Love and Addiction_\n\n(with Archie Brodsky)\n\n_How Much Is Too Much_\n\n_Addiction-Proof Your Child_\n\n_The Science of Experience_\n\n_The Meaning of Addiction_\n\n_Visions of Addiction_\n\n(edited volume)\n\n_Diseasing of America_\n\n_The Truth About Addiction and Recovery_\n\n(with Archie Brodsky and Mary Arnold)\n\n_Alcohol and Pleasure_\n\n(edited volume, with Marcus Grant)\n\n_Resisting 12-Step Coercion_\n\n(with Charles Bufe and Archie Brodsky)\n\nStop Thinking Like an Addict and Reclaim\n\nYour Life with **The PERFECT Program**\n\nSTANTON PEELE, Ph.D.\n\nwith ILSE THOMPSON\n\nA Member of the Perseus Books Group\nCopyright \u00a9 2014 by Stanton Peele\n\nAll rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. For information, address Da Capo Press, 44 Farnsworth Street, 3rd Floor, Boston, MA 02210\n\nDesigned by Cynthia Young\n\nCataloging-in-Publication data for this book is available from the Library of Congress.\n\nFirst Da Capo Press edition 2014\n\nISBN: 978-0-7382-1676-8 (e-book)\n\nPublished by Da Capo Press\n\nA Member of the Perseus Books Group\n\nwww.dacapopress.com\n\n* * *\n\nNote: The information in this book is true and complete to the best of our knowledge. This book is intended only as an informative guide for those wishing to know more about health issues. In no way is this book intended to replace, countermand, or conflict with the advice given to you by your own physician or therapist, if you currently have or plan to consult with one. The ultimate decisions concerning care should be made between you and your doctor and therapist. We strongly recommend you discuss any actions you plan to take as a result of reading this book with either your physician or therapist, if you currently have or plan to consult with one, and keep any health care professional with whom you consult informed about the actions you take and your ongoing health and mental health status. Information in this book is general and is offered with no guarantees on the part of the authors or Da Capo Press. The authors and publisher disclaim all liability in connection with the use of this book.\n\n* * *\n\nDa Capo Press books are available at special discounts for bulk purchases in the U.S. by corporations, institutions, and other organizations. For more information, please contact the Special Markets Department at the Perseus Books Group, 2300 Chestnut Street, Suite 200, Philadelphia, PA, 19103, or call (800) 810-4145, ext. 5000, or e-mail special.markets@perseusbooks.com.\n\n10 9 8 7 6 5 4 3 2 1\n_To the memory of Alan Marlatt_\n\n_Always at the forefront_\n\nContents\n\nAcknowledgments\n\nIntroduction: What _Recover!_ is about, and how to use this book\n\nPART I: The Meaning of Addiction and Recovery\n\n1 The Story of Rose\u2014An Addict\n\n**_How one becomes an addict, then recovers_**\n\n2 Explaining Addiction and Recovery\n\n**_How Americans learn to think like addicts; how to stop_**\n\nPART II: _The PERFECT Program_\n\n3 Preparing for Change\n\n**_Getting yourself ready for_** The PERFECT Program\n\n4 Pause\n\n**_Mindfulness\u2014Learning to listen to yourself_**\n\n5 Embrace\n\n**_Self-acceptance and forgiveness\u2014Learning to love yourself_**\n\n6 Rediscover\n\n**_Integrity\u2014Finding and following your true self_**\n\n7 Fortify\n\n**_Coping\u2014Learning the skills for life management_**\n\n8 Embark\n\n**_Equilibrium\u2014Proceeding on an even keel_**\n\n9 Celebrate\n\n**_Joy\u2014Honoring your accomplishments while living mindfully and meaningfully_**\n\n10 Triage\n\n**_Realignment\u2014Resources and actions for regaining lost footing_**\n\nAfterword: Write Your Own Conclusion\n\nNotes\n\nIndex\nAcknowledgments\n\nI thank primarily two people for their help in writing this book. Ilse Thompson, whose role is acknowledged on the title page, did significant original thinking and writing, especially concerning the linkage between the downsides of current American practice regarding addiction and an alternative way of conceiving of humanity in relation to addiction and righting people's relationship to the universe. Ilse is a treasured colleague and friend\u2014moreover, one whose efforts on our joint behalf never flagged. Her contributions to this book, from start to finish, are invaluable, incalculable, and irreplaceable\u2014 _Recover!_ would not exist without her.\n\nAnd, as always, Archie Brodsky played an essential role in conceiving and executing _Recover!_ Since we worked together to write _Love and Addiction_ , published in 1975, Archie has helped with every major project I have embarked on\u2014and not only writing projects. No idea or word that appears in the book has escaped his attention. Archie's wife, Vicki Rowland, played a vital part in our working sessions, contributing insights and technical resourcefulness along with unflagging hospitality during my visits to Archie's and her home.\n\nAlong the way, a remarkable number of people have made inputs, read sections of the book, corrected my misunderstandings, and tried to help in any way they could. This list includes Chris Ryan, Alan Cudmore, Ruth Gasparik, Sylvia Carlson, Mylissa Emrick, Kenneth Anderson, Adi Jaffe, Nona Jordan, Maia Szalavitz, Alta Ann Parkins Morris, and others I may have missed.\n\nMy editor Ren\u00e9e Sedliar and agent Andrew Stuart have been steadfastly supportive in the always-challenging enterprise of creating a book. Their calm confidence, good spirits, and good judgment have buoyed Ilse and me whenever necessary\u2014which has been more than once. In our editorial exchanges Ren\u00e9e has managed to be both consistently encouraging and helpfully critical. Also in our corner have been Merloyd Lawrence, Ren\u00e9e's colleague and a longtime supporter of Archie's and mine, and Hara Marano, _Psychology Today_ editor-at-large and longtime friend and colleague. Hara\u2014who both assisted me in publishing my work in _Psychology Today_ magazine over five separate decades and with Lybi Ma enabled me to garner several million readers of my posts at _Psychology Today_ Blogs*\u2014introduced me to her and now my agent, Andrew, and thus started the process of publishing _Recover!._\n\nAt any age, but especially now, it is both important and extremely gratifying to have people\u2014more than those named\u2014who wish me well and who want to see my ideas reach and help more people. Thank you.\n\n_Stanton Peele_\n\n_November 2013_\n\n_*_ I am likewise exceedingly grateful to the _Huffington Post_ for giving me an equally visible and positive platform to present my ideas about addiction and much else.\n\n_Introduction_\n\nWhat _Recover!_ is about, and how to use this book\n\nThis book is written to clarify what addiction is, and how you or a loved one can overcome it. You are coming to this book for one of three reasons: to deal effectively with your own addiction, to help someone you care about who struggles with addictive problems, or out of interest in and curiosity about the subject.\n\nThere are two competing views of addiction out there. The one you are used to hearing is that addiction is a disease, meaning that it is a biological force over which you have no control. This is what we have been told for decades. This view is wrong.\n\nThe other view, which is the basis for The PERFECT Program outlined in this book, is that addiction is a natural but destructive expression of a person's outlook in reaction to his or her life circumstances. I will show that this view is scientifically valid, true to life, and much more helpful than the disease view. People get themselves into addictions for understandable reasons, and people can get themselves out by being mindful of who they are and who they can and want to be.\n\nThe title _Recover!_ is in the form of an imperative because you need to know that you will recover if you follow the typical path addicts experience. Science tells us this. You need to know this truth to clear away the underbrush impeding your recovery and to maximize your chance to recover\u2014not to mention expedite the process\u2014which requires that you galvanize your own resources. This book is the manual for how to accomplish your own recovery.\n\nThis way of looking at addiction makes possible an entirely different approach to overcoming addictions, one that is both more hopeful and more practical. It plays to your strengths, not weaknesses. But before I present this empowering approach to addiction, you need to discard some myths, old and new, about addiction.\n\nContrary to the medical-sounding idea of addiction as a \"disease,\" the 12-step catechism of Alcoholics Anonymous originated in America's deeply held fears of alcohol (and later, other drugs) and is steeped in religious ideas and irrationality. Why, then, have you been hearing so much lately about brain science proving that addiction is a disease? Neurobiological studies of dopamine and the limbic system do little to inform us of the ways and means to overcome an addiction, and they most assuredly do not justify a 12-step approach that appeals to God to cure your disease.\n\nMoreover, how does it help you to believe that your brain can be \"hijacked\" by addiction\u2014a highly publicized, supposedly scientific idea? If that were so, then people wouldn't be able to wait until break time to go outside to smoke, or they wouldn't only resort to their drug addiction in the company of certain people and in certain places. In fact, addicts exercise control over their addictions all the time, and most addicts outgrow their addictions. It is also true that everyone experiences an addiction in their own way, and everyone must\u2014and can\u2014find their own way out of addiction.\n\nBy reinforcing the myth that addiction is uncontrollable and permanent, neuroscientific models make it _harder_ to overcome the problem, just as the 12-step disease model has all along. Telling yourself that you are \"powerless\" over addiction is self-defeating; it limits your capacity to change and grow. Isn't it better to start from the belief that you\u2014or your spouse, or your child\u2014can fully and finally break out of addictive habits by redirecting your life? It may not be quick and easy to accomplish, but it happens all the time. In this book I will show you how it happens and what it takes to do it.\n\nMindfulness is a key component of The PERFECT Program. It is both a Buddhist and a modern psychological concept. Combining the two, mindfulness means being in the moment by being aware of your circumstances\u2014your surroundings, yourself, the here and now\u2014all of which determine how you feel and act. It strengthens your ability to bring into your consciousness the key elements of your addiction\u2014your motivation, your situation, your needs, and your ability to make alternative choices. Mindfulness gives you the space, the ability, and the self-confidence to outgrow your addiction. You can improve this ability, as you can any mental or physical capacity, by learning about and practicing it\u2014including using the meditations provided throughout this book.\n\nOne claim often made for the disease theory of addiction, now dressed up in neuroscience, is that explaining the cause of your addiction as being outside your control frees you of guilt. Yes, but at the cost of telling you that you are a slave to your addiction. The PERFECT Program invites self-acceptance, or the belief in your underlying value\u2014troubled as you may be\u2014as a human being. For it is only by combining mindfulness\u2014genuine awareness\u2014with faith in yourself that you can finally empower yourself to grow beyond addiction. This process entails self-acceptance, another modern version of a Buddhist concept, this one called loving kindness.\n\nThe PERFECT Program allows you to achieve a better life not by _escaping_ anything, but rather by _embracing_ who you are, who you wish to be, and who you can be. Regarding yourself as \"perfect\"\u2014yet another Buddhist idea\u2014again corresponds with the best contemporary psychological thinking. Embracing your perfection (which is not the same as smug self-satisfaction and denial) encourages your faith in your ability to change and accelerates the change process.\n\nHere is a concrete example of the difference between AA's disease theory and The PERFECT Program. AA's first step commands you to accept that you are powerless: \"We admitted we were powerless over our addiction\u2014that our lives had become unmanageable.\" Step One, then, is the justification for the cadres of counselors who come down like a ton of bricks on addicts in treatment programs, telling them that they can't manage their lives. In other words, if you are addicted, that is all you are, and your life has become worthless, and only the \"helpers\" can make you whole.\n\nThe PERFECT Program rejects this kind of thinking, expressed in the self-labeling mantra, \"I am an addict.\" It starts instead from two assumptions: every human being is already worthwhile, and you will succeed best when you feel best about yourself, your potential, and your core value. You still need to take responsibility for your actions and practice the discipline required to put your life on track. But you are not your addiction; you are a valuable human being whose qualities endure and exceed your addiction.\n\nThese fundamental differences translate into different helping techniques. Instead of focusing solely on the object of addiction and its all-conquering force, as AA and neuroscience do, The PERFECT Program directs you to contemplate your addiction from a broader perspective that takes in your life history, environmental influences, and personal relationships, as well as your feelings, beliefs, and outlooks.\n\nAddicts regularly respond to challenging situations by panicking\u2014after all, they have \"admitted\" that they are incapable of managing their lives. The most natural immediate reaction when you are so overwhelmed is to resume your addiction\u2014or else seek protective refuge in the group (the 12-step solution). The PERFECT Program instead helps you manage stress and anxiety without resorting to your addiction. The PERFECT Program believes you _can_ help yourself\u2014indeed, it is _based_ on the assumption that you are the crucial, the only, agent of your own change.\n\nHow to Use This Book\n\n_Recover!_ is divided into two parts. The first part of the book is an orientation for people with addiction problems and also for people who want to get inside the mind of an addict. Part I prepares you for The PERFECT Program. It provides first the story of a methamphetamine addict, Rose, so that you can understand the personal experience of addiction and recovery through the eyes of one woman. It then presents a history and scientific understanding of addiction, so that you will know what it is that you are confronting and how often\u2014and how\u2014people overcome it. This section is less prescriptive, and sometimes less experiential and more expository, than the second part of the book, which prepares you to embark on PERFECT and then presents The PERFECT Program itself. If you are coming to this book for help with an addiction, since you have your own addiction narrative, you may feel that Rose's story in Chapter 1 isn't relevant, or that the analysis in Chapter 2 isn't for you. You may be tempted to jump ahead to Part II and directly into PERFECT. But, be assured, there is value for you in these early chapters as preparation for launching The PERFECT Program\u2014not least in getting out from under the dead weight of misguided and counterproductive ideas.\n\nPlease also note that, while the nature of a book requires that it progress in some logical order, you will have a path out of addiction that is unique to you. You may have to linger longer in some phases of PERFECT; some parts may be more difficult for you to practice than others. Fine, this isn't a race. At the same time, Chapter 10, \"Triage,\" is your go-to chapter for crisis moments. If you find yourself at a loss or in urgent need, jump right into that chapter as your immediate reference and guide to your options.\n\nTaken as a whole, The PERFECT Program demystifies addiction. It offers a practical application of the best research, neutralizes the mythological power of inert substances and self-destructive behaviors, and gives you the knowledge and power to express intentionally the freedom you already sense inside you. It is a self-directed process of fortifying your life from the ground up and making addiction obsolete. It's an accessible, layered program, based on what we know to be true about addiction and what has been proven to overcome it.\n\nThe tools we offer you to achieve freedom are a synthesis of the best practices for changing how you respond to addictive urges, developing the skills to live fully and prevent relapse, and replacing paralyzing assumptions with positive options. Through PERFECT, you will learn new habits of mind and heart that reclaim your genuine self, expand and strengthen your life skills, and embrace a life of engagement, meaning, and purpose.\n\nThe origins of addiction are as complex and unique as the people who find themselves in its grip. But rather than homing in on what may have gone wrong in your life, The PERFECT Program teaches you how to build the foundation of your recovery on _what's already right_. You have a healthy inner core that instinctively rejects self-destructive behavior. You know this; you hear it cry out time and again. It may even have caused you to try to quit\u2014and to quit for a time. People are often discouraged when they fail to stay off an addiction, and such setbacks are often used to prove they have a disease they will never overcome. In fact, however, having quit previously for a time is a _positive predictor that you will recover_. Efforts at quitting show the most important thing about you in relation to your addiction\u2014that you _want_ to quit.\n\nThe PERFECT Program is presented in Part II in seven chapters, preceded by the preparations and materials you will need. Each chapter lays out a distinct part of the program that corresponds to a letter in the acronym \"PERFECT.\" These chapters incorporate three phases of change you will undergo: foundational (deep inner work), structural (creating a framework of life skills and values), and operational (living with balance and intention). Each chapter lays out clear goals for you to pursue, journal exercises, guided meditations, progress tracking, and other powerful tools you can use in your daily life. So, hear this: you are _not_ a passive spectator to your brain's functioning or an unfortunate victim of it. You are the primary generator of how your brain functions\u2014of how you function\u2014both in the here and now, and certainly over the long run.\n\n**PAUSE**\n\n_Mindfulness\u2014Learning to listen to yourself_\n\n**EMBRACE**\n\n_Self-acceptance and forgiveness\u2014Learning to love yourself_\n\n**REDISCOVER**\n\n_Integrity\u2014Finding and following your true self_\n\n**FORTIFY**\n\n_Coping\u2014Learning the skills for life management_\n\n**EMBARK**\n\n_Equilibrium\u2014Proceeding on an even keel_\n\n**CELEBRATE**\n\n_Joy\u2014Honoring your accomplishments and milestones_\n\n**TRIAGE**\n\n_Realignment\u2014Resources and actions for regaining lost footing_\n\nTo show how PERFECT works and to get you started, \"P\" stands for \"Pause\"\u2014a mark of mindfulness. This pause allows you to establish your calm inner essence. It also gives you space to consider your options\u2014including rediscovering and mobilizing your core resources. PERFECT focuses you on those things you know how to do, and to do well, so that you can generalize the competence and confidence you feel in these areas and build on hard-won feelings of self-worth and capability. Let's say you are an excellent car mechanic or athlete\u2014you can borrow the skills and self-command you bring to bear on these activities into areas where you feel insecure and perform poorly, so that you become less likely to turn to an addiction.\n\nAfter and along with pausing to consider and apply your mind to a problem, you \"Embrace\" (the \"E\" in PERFECT). Whom and what do you embrace? Yourself and all that you stand for and can do, now and in the future. _Embrace_ embodies the critical psychological idea of self-acceptance, which\u2014along with mindfulness\u2014is the essential foundation for living free of addiction. As with other key tools in _Recover!_ this is a contemporary psychological idea that corresponds closely to a Buddhist-inspired concept\u2014that of \"loving kindness.\" In addition to compassion for yourself, loving kindness conveys compassion for others\u2014which leads in turn to forgiveness.\n\nThe absence of self-acceptance\u2014in fact, the indoctrination in its opposite\u2014is the worst thing about the 12 steps. As practiced in addiction treatment throughout the United States, the steps hammer home that you are not worthy of your own and others' love. Self-acceptance, which takes you in the opposite direction from this self-denigration, is at the heart of The PERFECT Program.\n\nUsed as a guide for applying mindfulness and self-acceptance, _Recover!_ is your manual for asserting your power to overcome your addiction. In the following chapters, you can prepare for, then proceed mindfully through, The PERFECT Program and into your addiction-free life.\n* * *\n\nPART I\n\nTHE MEANING OF ADDICTION AND RECOVERY\n\n* * *\n\nCHAPTER 1\n\n_The Story of Rose\u2014An Addict_\n\nHow one becomes an addict, then recovers\n\n* * *\n\n**CHAPTER GOALS**\n\n\u2022 To describe what an addict's life looks like\n\n\u2022 To understand what caused her addiction\u2014what does she _get_ from it?\n\n\u2022 To learn whether she is doomed if she doesn't get with the 12 steps\n\n\u2022 To trace how she recovered through The PERFECT Program approach\n\n\u2022 To learn how to apply these insights to your own addiction\n\n**Purpose:** In order to combat addiction, for yourself, for a loved one, or in society as a whole, you need to see into the heart of addiction. This chapter will put you inside the mind of an addict, Rose, so that you can understand and appreciate her life and her thinking, and then will show you how she emerged from addiction through the course of her life. In this way, Rose is showing the way for you\u2014for all of us. Although Rose was addicted to meth\u2014what some consider to be a \"real\" addiction (a distinction with no meaning)\u2014her story illustrates _all_ addiction and recovery. Perhaps you'll find similarities between Rose's story and yours, regardless of the particular substance or activity to which you may be addicted. What's important for you is how Rose used The PERFECT Program to overcome addiction.\n\n* * *\n\nTo illustrate both how and why people become addicted, and how people recover according to the principles and practices of The PERFECT Program, consider Rose, who became an injecting meth addict. Rose was sidetracked from a promising academic career by an unexpected pregnancy. Weighed down by demands of part-time college attendance, single parenthood, and work, she turned to meth (also known as \"speed,\" \"crank,\" and \"ice\") for a \"pick-me-up\" to enable her to carry through her responsibilities, and especially her obligations to her daughter, to whom she was committed above all else.\n\nStruggling to support herself and her daughter, Rose felt constantly exhausted and on the verge of a breakdown. Her grades in college were marginal, not because she wasn't a good student but because she couldn't find enough time and energy to study. Meth seemed to offer redemption. After first taking meth, Rose felt invincible. She immediately cleaned her entire apartment. Stunned by how much she had accomplished\u2014it was still only 3 a.m.\u2014she brought out her textbooks and started working on her school assignments. At 6 a.m., done! By the time the sun came up Rose had formulated a new strategy for achieving the goals she had set for herself and her daughter. She saw the drug as giving a boost to her productivity and contentment so that she could carry the weight of her combined obligations. When the school year was over she would quit the drug, Rose figured.\n\nAnd meth served her purposes for a time. But given the stress in Rose's life, this balance didn't hold. Gradually, she stopped getting high to accomplish things. Instead, getting high became a goal in itself. Now she pushed her responsibilities aside to make time for her drug use. As the drug took center stage in her life, Rose fell farther behind, and she started to lose the things that were important to her. She abandoned her schooling, the reason she thought she began taking meth in the first place. Then she cut back her working hours. Although her co-workers could see that something was amiss, Rose still managed to be responsible\u2014only now for limited periods of time, after which she turned to her drug of choice. It was all she could do to hold on.\n\nWhen meth started to become her first priority, fearing her own behavior, Rose sent her daughter to live with her parents for a _temporary_ period (as she imagined it). It wasn't so much that she neglected her child as that she was overcome with worry that her daughter would notice something was wrong with her mother. This created in Rose a constant sense of shame whenever she looked at her child. But, of course, with her daughter gone, Rose could now use the drug without constraints. She associated exclusively with people who shared her use of meth. Her inhibitions lowered and her adrenaline elevated, she found it easy to make seemingly profound connections with other users, especially men. After spending all day and night talking nonstop, the interactions often turned sexual. But the deep connections she thought she was making invariably turned out to be one-night stands.\n\nNow she was taking the drug to feel alive and well, perhaps to hook up and feel\u2014if not loved\u2014at least desirable, and to forget her actual state of affairs. Rose no longer had any other way to make life seem okay to her. She deteriorated physically: her skin was an eerie shade of gray, marred by eruptions. She lost twenty pounds. _Who could find me attractive now_ , she thought, with what insight remained to her.\n\nAlthough she experienced panic attacks, Rose viewed sleep as an enemy to be avoided at all costs. She ignored the normal sequence of nights following days, since her energy came from a drug that disregarded the usual time schedules. Her user friends were awake and busy 24\/7. Days went by at hyper-speed, and she couldn't recall how many nights she had been awake. When her body and mind could not be pushed farther, Rose crashed. She and her friends often passed out in the middle of a sentence, dropped what they were holding, and fell asleep. Upon awakening, Rose repeated the whole process\u2014using, staying up for days on end, then falling into a stupor.\n\nBy now, Rose no longer gained the level of energy and feelings of escape that had formed the experience to which she had become addicted\u2014she had seemingly become immune to the drug's familiar effects. Instead of feeling nonstop motivation, staying up all night getting things done, Rose now needed the drug just to conduct daily activities\u2014she could no longer wake up and start a day without speed. At this point, Rose began injecting\u2014rather than snorting\u2014the drug. Rose's problem had morphed into self-induced narcolepsy, for which the only antidote was methamphetamine. She felt like she had become the victim of a kind of bait and switch\u2014that the drug and its effects had defrauded her!\n\nEach time Rose injected, she was filled with revulsion and guilt. Yet she carried on. She wished for a do-over; she promised herself that she was going to stop as soon as she finished the drugs she had on hand. Or next week. Or as soon as she found a better job. Rose missed her child more than anything. When it was time to go home for a visit, Rose obsessively primped her hair and makeup so that, she forlornly hoped, nothing would seem amiss to her daughter or her parents. Of course, they knew something was wrong, and Rose knew that they knew.\n\nThen she returned, guilt in hand, to her apartment and her drug. Despite her painful moments of awareness, the drag of addiction always managed to pull her back under. The regret and guilt of using in and of itself, especially after she began injecting, became her major motivation to use, since she was overwhelmed with a sense of dread when the effects of the drug wore off. Thinking of what she had given up to her addiction\u2014primarily her daughter\u2014triggered a pain for which she had only one remedy: meth. Rose could not see any way out of this mess. At least by using, she got relief for a time from her overwhelming emotional pain and guilt. She _needed_ to return to her drugged state. It was, in a paradoxical way, her comfort zone.\n\nBecause Rose failed to act against her addiction, she thought this proved her drug use was an illness. After all, everyone knew that drug addicts are powerless and out of control. That message was reinforced when Rose for a time attended 12-step meetings\u2014the only way she knew of to begin to address her problem. Rose came to believe she was not a normal person and could never be one, just a recovering person. But whenever she contemplated recovery, she rejected it. It was overwhelming and demoralizing: detox, rehab, meetings, steps\u2014 _forever_. Although what she was doing was no life for her, neither were the 12 steps. Besides, she knew so many people who cycled through recovery programs that she and her friends joked: \"Joe's in the spin-dry. He'll be back any day now.\"\n\nWith her addiction now so disabling, Rose decided not to attend her daughter's fifth birthday party. She couldn't stomach the masquerade and, mostly, didn't want to face the emotional pain of being a bystander at the event. Then, for weeks afterwards, she regretted missing this milestone in her child's life. This must mean she had hit \"rock bottom\" (a meaningless term to which we will return). Some time after that, she was revolted by what she saw in the mirror. _I'm far gone_ , she thought. Rose was hooked, without a doubt, especially since she had progressed from snorting the drug to shooting it intravenously in order to get more bang for her ever-diminishing buck. Her self-disgust and fear were now without bounds.\n\nMissing her daughter's birthday party had a special impact for Rose, and her thoughts constantly returned to it. It made clear to Rose, as nothing else could, that the costs of her drug use outweighed any benefits that remained from it\u2014even as this would have been obvious all along to anyone with an outside perspective. This experience, for Rose, finally made it intolerable for her to consider getting high. Rose didn't take the drug one day when she usually would have. She pulled out her daughter's pictures and mementos to give her a touchstone to cement her commitment to quitting. As one day without meth stretched to two, Rose was as amazed as anyone could have been that she didn't use. She had almost unintentionally detoxed, something she had always feared she could not do.\n\nAt first, Rose simply slept hard, then woke up angry. Then she slept more. She was ravenous, but didn't have the energy or the stomach to eat. Nonetheless, every hour she passed without getting high was as precious as gold in the bank, and each deposit made the idea of cashing out harder to conceive. When Rose felt that the worst of it had passed, she called her mother. As terrified as her mother had become through Rose's whole ordeal (the dimensions of which she could only surmise), she began crying as Rose explained what had been going on and asked her for help. Her mom came over with a homemade meal. Together they came up with a plan for Rose to reestablish her life, placing what was important at its center.\n\nIt might seem strange that Rose could form such ideas so quickly. But, really, they had been floating through her mind all along. All addicts have some kind of alternative, non-addicted identity waiting to surface. For Rose, this identity was always with her. Before she ever became hooked on meth, Rose felt that she was failing at what was most important to her: creating a comfortable, secure life for her daughter. Everything she did by working and going to school had been in the interest of achieving that dream, which somehow always exceeded her capacity.\n\nWith what she was struggling to achieve firmly reestablished in her mind, Rose moved back into her parents' house, rejoining her daughter's daily life. Rose returned to school and found a part-time job at a dentist's office (which was good, because she required considerable dental work). Although she had given up quite a bit of freedom, Rose now shared child-care responsibilities while living with her parents, and that support took enough of the burden off her that she could pursue her studies while sustaining her recovery from addiction. This arrangement contrasted with the level of responsibility Rose had previously thought she could assume as a single parent and student, but that had created an imbalanced life (too much output, not enough reward), which, in turn, had primed her for addiction.\n\nAll of this was by no means an easy journey for Rose. In addition to the painful way she had arrived at her current resolution, Rose still struggled with depression when she thought of what she had done and how far behind she had fallen. Her thoughts would sometimes sneak back to the drug, romanticizing her former life. But she quickly regained perspective and realized how really dreadful her life actually had become.\n\nMost important was that Rose was able to see the positive results of her changed life and to savor being clean. She was living in harmony with the goals that had been eluding her even before she became addicted. Rose was able to fit both play and quality time with her child into her schedule, as well as spending time with her family. Given where she was coming from, the situation seemed like a dream come true. Beyond this, Rose made space to run and do yoga. Her new circumstances honored the vision she had been working so hard for before her addiction. Now every facet of her life reflected her heart and brought her sense of purpose into sharper focus. She was using her values as a guide to create a place in the world for herself that she had dreamed of.\n\nAfter quitting meth, Rose began attending an Alcoholics Anonymous group in a church near her parents' home. But if she had hated the 12-step meetings she attended before, they seemed worse to her now. How could it be good for her to feel that she was powerless over her addiction after she had just quit meth? That made no sense. But these people were the experts, she thought, and their ideas worried her. Rose also entered a community program run by recovering addicts. There she always got the impression that she was a broken, horrible, incapable person whose core elements had to be ripped down and rebuilt according to a standard only the long-recovering addicts understood. She hated that feeling. Rose left the program and AA.\n\nInstead, Rose started attending a group for single mothers. She found that many of these women shared the same feelings of helplessness and loss of control that she had succumbed to, even if they hadn't become crank addicts. Feeling deeply ashamed, she finally brought up her former addiction to the group. It was a surprise to Rose when the other women told her that quitting meth the way she had was remarkable, and something she should be deeply proud of. Nor did they quibble with her having done so without 12-step support.\n\nRose also started seeing a psychologist. This woman didn't follow the 12 steps. Instead, she worked on Rose's self-esteem, which was essential to rebuilding her mothering and other skills. Rose used her therapy in support of turning her life around, of changing its entire trajectory. She progressed in school and later got a job that made use of her skills as she moved into a good career. In her late thirties now, she fell in love with a man and married him. Of course, despite the crushing addiction she experienced, there is quite a bit of life left for Rose, as there is for you.\n\n***\n\nWe see in Rose's case the basis of an addict's experience\u2014the stressful, overwhelming situation leading to drug use, then dependence on the drug; her sense of inadequacy and guilt; needing the rewards provided by the drug even _after_ these became a substitute for true satisfaction and instead caused further degradation. Yet somehow the addiction _protected_ Rose from recognizing how far she had fallen and how degraded her life had become. More important, we see through Rose's case the essential elements that led to her recovery, a recovery not dependent on an addiction-focused support group or belief system, other than a belief in herself and in the life she could create for herself and her daughter. For Rose, this meant learning to live her life in the moment, being aware of what the world had to offer her, while becoming aware of how her addiction deprived her of these pleasures and opportunities. The fundamental elements of recovery for Rose were her values, derailed for a time, then recaptured; the support and help she got from her parents, her group for single mothers, and her therapist; and her purpose in life\u2014her love for her daughter and a desire to further her and her daughter's life together.\n\nYou can use this method, too, by incorporating the values, purpose, motivation, support, skills, and\u2014underlying these\u2014the mindfulness and self-acceptance that comprise The PERFECT Program. Your story may differ substantially from Rose's. After all, you may not be addicted to a powerful illicit street drug, and you may not be able to move back with your parents as Rose could. But, in other ways, the path you travel may be quite similar to hers. _Recover!_ will enable you, like Rose, to reach into yourself and look around you in a mindful way to find all the elements of a satisfying, constructive, connected life that are essential for true recovery. _Recover!_ will also help you do another thing Rose did: to replace self-doubt and searing self-criticism with self-acceptance and self-love.\n\nCHAPTER 2\n\n_Explaining Addiction and Recovery_\n\nHow Americans learn to think like addicts; how to stop\n\n* * *\n\n**CHAPTER GOALS**\n\n\u2022 To understand what addiction is\n\n\u2022 To learn how the disease model originated and perpetuates itself\n\n\u2022 To grasp the downsides of thinking that your addiction is a disease\n\n\u2022 To examine the implications\u2014pro and con\u2014of the new brain science\n\n\u2022 To learn that people usually recover\u2014why and how they do so\n\n\u2022 To recognize your resources for recovery and launch PERFECT\n\n**Purpose:** This chapter discusses how we have come to think about addiction the way we do\u2014and how this isn't dictated by science, but by American tradition and cultural ways of thinking. It will take you through the history of the development of the disease concept of addiction, how this idea has been sold as \"science\" but (1) isn't science and (2) isn't helpful. You will learn that nothing is more natural than recovery and that you will recover if you follow the usual path addicts experience. Science tells us this. Understanding this truth allows you to maximize your opportunities to recover by clearing away the underbrush impeding your recovery.\n\n* * *\n\n* * *\n\n**CASE:** Alan, at age thirty-five, had smoked since he was a teen. He had been reading up on research on brain images of drug users. He summed up what he had learned: \"Smoking lights up the pleasure center of your brain. That's because nicotine activates the same reward pathways in the brain that other drugs of abuse like cocaine and amphetamines do. Research has shown that nicotine increases the levels of dopamine and adrenaline in the brain, neurochemicals that are responsible for feelings of pleasure and well-being. I can't produce enough of these chemicals anymore to feel okay without smoking, so I'd go through withdrawal if I stop smoking. I might never be able to experience pleasure again, in fact! How _could_ I quit?\"\n\n* * *\n\nThinking Like an Addict\n\nHere's the story: a way of thinking about addiction has grown up in the United States based on our temperance history. It is furthered by our modern \"brain revolution,\" supposedly steeped in the biology of behavior and reinforced by an economic juggernaut, that purports to find in neuroscience a full and tidy explanation for addictive behavior. Unfortunately, these cultural beliefs bear little resemblance to the reality of addiction and are not just unhelpful\u2014but detrimental\u2014to people who develop addictions. This is because both the 12 steps and the \"new\" neuroscience strive to convince you that you are an addict and will always remain an addict, which, by and large, isn't true. And if you dispute any part of this story, you are in denial, proof positive of everything they say.\n\nHow can I say that the standard addiction treatment is detrimental? I can prove it. A study compared people trying to stay off cigarettes, having quit, with or without nicotine replacement therapy (NRT)\u2014nicotine gum or patches. The neuroscientific model of nicotine addiction is that addicts become so accustomed to having nicotine in their systems that to deplete their accustomed level of nicotine disrupts their bodies and minds, creating irresistible cravings that cause them to light up. It _is_ true that smoking is a serious addiction; those experienced in multiple addictions place smoking at the top of the list of difficulty of quitting\u2014alongside heroin, above cocaine, alcohol, and amphetamines.\n\nThe quitting study, conducted by the most prestigious anti-tobacco group in the United States, the Center for Global Tobacco Control at Harvard, tracked a group of eight hundred smokers trying to quit who either did or did not use gum or patches. The investigators found that those who used NRT to quit didn't do better than those who quit without it. In fact, the most dependent smokers\u2014for whom NRT is supposed to be most helpful\u2014were twice as likely to relapse to smoking if they relied on NRT than if they did not.\n\nThere were howls of outrage from NRT specialists. Here's a typical response from a professional in the field who read my _Huffington Post_ story on the subject: \"What this article tells us is what we already know: that simply providing the availability of over the counter NRT without the guidance and support of a trained tobacco treatment specialist is not very effective.\" Except that's not what happened. \"Odds of relapse were unaffected by use of NRT for 6 (or more) weeks either _with_ or without professional counseling.\" The researchers who conducted the study were deeply invested in NRT. \"We were hoping for a very different story,\" said Dr. Gregory N. Connolly, director of the Harvard Center. These committed anti-tobacco warriors thus wasted millions of dollars\u2014and years of effort.\n\nHow is it possible that such advanced medical technology for ending smoking is _more often than not_ counterproductive? Certainly, some people succeed at _quitting_ with Nicorette gum or patches, and some remain tobacco free\u2014but the bulk do not, and there are more productive treatment investments. The key to quitting an addiction is motivation, along with a belief in the possibility of succeeding\u2014these factors are essential whether quitting addiction with, or without, treatment. Those who depend on NRT believe both (1) that they can quit without the necessary personal commitment, and (2) that they _cannot_ quit by means of their own personal strength and resources. In other words, they think like addicts\u2014 _which NRT forces them to do_. The moment of truth comes if and when these quitters also quit the nicotine replacement (which, of course, is addictive itself). _Most quickly relapse_.\n\nWhat Is Addiction?\n\nAddiction is not a by-product of the effects drugs have on your neuro-chemistry. It is also not your inherited neurochemical destiny. Addiction is a reliance on an involvement to run interference for your experience of your internal and external worlds. Addiction is a normal part of human experience, as is recovery. Addiction occurs when a person seeks out an experience, ritual, or reward to the exclusion\u2014and detriment\u2014of all other goals and activities. The measure of addictiveness is how absorbing, compelling, and harmful to the person an involvement is. Nothing else matters. Addiction can take the form of substance abuse or of compulsive behaviors like sex, gambling, or overeating. Whatever the involvement, to qualify as addictive it must lead to \"significant impairment or distress.\" But it does occur on a sliding scale\u2014yes, you can be more or less addicted.\n\nThe fifth edition of the American Psychiatric Association's _Diagnostic and Statistical Manual of Mental Disorders_ ( _DSM-5_ ), released in 2013, officially recognizes for the first time that addiction can occur with something other than drugs and alcohol\u2014that \"something\" is gambling. But we are all aware of many more addictions than drugs and alcohol. That food can be addictive\u2014that people struggle against compulsive eating impulses that make them unhappy and harm them\u2014is, seemingly all at once, being discovered by everybody. By a recent crop of neuro-diet doctors who claim that people become addicted to sugar\/carbohydrates\u2014that those foods light up the brain just as cocaine does, by authors of popular memoirs, and by analyses of American food production. Another evident example is love addiction. I wrote _Love and Addiction_ with Archie Brodsky in 1975 (in which we also discussed gambling and food addictions). Since that time, the discovery that love and sex are addictive has been an expanding universe in American psychiatry and psychology, drawing in neuroscientists, health writers, and filmmakers (the referenced sources are only a small reflection of their number).\n\nAddiction is a response to life circumstances ranging from trauma to an inability to deal with everyday demands to being in a depressed-traumatic time in your life. It can be short-term and limited in time and place or a chronic pattern. The most important thing for you to know about addiction\u2014knowledge the disease theory denies you\u2014is that most people, sooner or later, naturally outgrow it. Research continually demonstrates this truth. For instance, the National Institute on Alcohol Abuse and Alcoholism (NIAAA) discovered through a massive national survey of Americans' drinking histories that 75 percent of alcohol-dependent people recover and that the large majority do it on their own, without treatment or AA. The director of the research project, Dr. Mark Willenbring, noted: \"It can be a chronic, relapsing disease. But it isn't usually.\"\n\nYou don't need a study to tell you this about addiction. You have witnessed\u2014or even experienced\u2014this yourself: You must know someone who has quit smoking. Or maybe _you_ have quit. As I noted above, smoking is certified by multi-substance addicts as among the most difficult drug addictions to overcome. Why has it been so hard\u2014and still is for many\u2014to accept that smoking is addictive in the same way as other drugs? Because our very familiarity with the substance allows us to reject myths about it\u2014although pharmaceutical companies and associated physicians still insist that you need their products and services to quit. Yet, even with such ubiquitous marketing, most people quit smoking on their own, without treatment, as they have always done.\n\nHere's a scenario that will make sense to you:\n\nPhil, who had begun smoking in his early teens, had tried to quit smoking numerous times in his life but had finally resigned himself to being \"a smoker.\" In his late sixties, Phil awoke in a hospital bed after a heart attack. His first impulse was to light a cigarette. He asked his daughter, whose face he saw above him, to get him a cigarette and wheel him outside so that he could smoke. She told him that if he touched another cigarette, she would never speak to him again.\n\nPhil never smoked again.\n\nHow did Phil's experience relate to Alan's view of his addiction\u2014a view pushed by the leading figures in the addiction field? They fundamentally contradict one another. Here's what happened for Phil. Phil's core life wasn't about being a smoker. When push came to shove, it turned out he was prepared to sacrifice smoking when it was counterweighted by what was most meaningful to him\u2014being a father to his daughter. In fact, prioritizing parental love has cured more addictions than all other \"methods\" in the history of addiction combined\u2014and will always do so.\n\nThis isn't to say Phil did it easily\u2014after all, he had been smoking for half a century\u2014or that any smoker can or will quit quickly. But it doesn't help anyone to declare the task impossible! People may say, \"I just can't live\u2014be\u2014without smoking, drinking, pill taking . . .[*].\" It's a common sentiment, one that you might share. The truth is, however, that the qualities that make you _you_ are much more powerful and abiding than any addiction. When people overcome addiction, it's because they align their behavior with who they really are. When people recognize that something they are doing interferes with their deepest values or goals, they can leave destructive compulsions behind. It's a natural life process. Of course, there are many people whose natural recovery process needs a boost, and those are the people for whom The PERFECT Program is designed.\n\nThe PERFECT Program offers the information, guidance, and tools to ignite and accelerate your natural recovery process. It is supported by the best research in the field. If you have been through the recovery mill, or even if you are just a normal consumer of pop culture and pop science, you have been steeped in a heady concoction of misinformation and superstition about addiction, like the following primal addiction tale:\n\nI was always different from normal people. I was out of control, but I was in denial. When some horrible thing happened, I asked for help. I continued to fight the truth, but finally \"let go\" and admitted that I have a disease that I am powerless over. So, I stopped trying to run my own life; I turned my life and will over to a Higher Power. I am now \"grateful in recovery,\" counting every sober day as a gift, because my disease is always growing and I could relapse at any time and end up dead.\n\nThis redemption narrative\u2014or \"drunkalog\"\u2014is part of our cultural landscape. It's also a good place to start unraveling the history of addiction recovery in America, because the whole fairytale is bundled in this neat little package. Before I explain where these ideas originated, let's unpack the mythology:\n\n\u2022 **Myth:** Addicts are different from normal people, because they're fundamentally incapable of controlling themselves (anyone who can is not a \"real\" addict).\n\n\u2022 **Myth:** Addicts can never be like other\u2014normal\u2014people.\n\n\u2022 **Myth:** Recovery requires \"hitting bottom\"\u2014a do-or-die scenario.\n\n\u2022 **Myth:** Recovery is a blessing, bestowed by an entity outside oneself.\n\n\u2022 **Myth:** Addicts are powerless and cannot trust themselves, even when abstinent.\n\n\u2022 **Myth:** Addiction is always an incurable, progressive, fatal disease.\n\n\u2022 **Myth:** Recovery is a one-day-at-a-time proposition that _must_ include absolute abstinence and lifelong 12-step work.\n\nYou may believe that addiction is a disease that you are powerless over. You may also believe that recovery requires you to place your belief that you are an addict at the forefront of your consciousness at all times and that your addiction explains every dumb thing you have ever done. Maybe you believe that recovery is an unending, lifelong process, that it requires a spiritual awakening and perpetual maintenance, including total dedication to meetings and \"quit anniversaries.\" Meanwhile, you must avoid normal people, social situations, and mouthwash containing alcohol. Finally, you may think that the disease of addiction progresses full force, despite long periods of abstinence. That means that, if you drink a beer after twenty years on the wagon starting as a teen, you'll fall right back into your addiction as if you had been drinking uncontrollably the whole time.\n\nAll of this has been updated in the guise of modern neuroscience conflating the AA ideology with brain chemistry. But none of it is true. When you apply these ideas to other addictions\u2014like sex, love, shopping, gambling, the Internet\u2014you can see them as laughable. Addiction experts seem incapable of dismissing the obvious inconsistencies and self-evident untruths of the disease model, even with the wide swath of research that has undermined it. But _you_ must reject these ideas because, otherwise, they will keep you from outgrowing your addiction.\n\nThink of this question, \"Is love or food an addiction?\" How can something that all healthy people do be addictive? Then someone tells you how obsessed they were with a lover, not being able to sleep, devoting every waking minute to worrying and lamenting first about the relationship, then about its breakup, while avoiding all other activities and relationships. Or consider Mika Brzezinski, who admitted that she \"has been battling a junk-food addiction since she was 13 years old. She has spent much of her adult life consumed with food, operating on a disastrous cycle of binge eating, purging, and over-exercising to maintain an impossibly skinny figure.\" The truth about addiction is that food and love are addictive in the same sense that pain-killers (including heroin), cocaine, and alcohol are\u2014they are addictive for some people in some situations or at some moments in their lives. Nothing is itself inherently addictive.\n\nSo how useful is it for you to consider that you have a disease and abstain from all contact with that experience? As I discuss in Chapter 3, of course you can't abstain from love and food. And, on the other hand, the success rate for disease-oriented, abstinence-obsessed 12-step treatment\u2014along with its neurochemical equivalents\u2014is not better, and may actually be worse, than not receiving treatment at all. I showed this above in the case of smoking. Research has likewise found significantly higher rates of relapse among alcoholics in AA than among alcoholics who go about quitting on their own or who are treated with other methods. If you believe that taking one drink is identical to having one hundred drinks and that you have a progressive disease that makes you powerless to control yourself, you won't just hop off the wagon\u2014you will swan dive off it. Indeed, William Miller and his colleagues at the University of New Mexico tracked subjects following outpatient treatment for their drinking problems. The researchers found two primary factors predicted the likelihood of relapse\u2014\"lack of coping skills and _belief in the disease model of alcoholism_.\"\n\nRelying on the recovery-world idea of addiction\u2014now cloaked in neuroscience\u2014as an unconquerable disease instead of as part of normal experience has hurt us badly. As new brain discoveries uncover new addictions all the time, all presumably as uncontrollable as the original addictive diseases, we nonetheless congratulate ourselves on our modernity and medical progress. Yet we have no fewer addicts now than we did a century ago, and probably more, many more. Why, then, do we feel so confident that we have a handle on addiction, while our addictive problems expand endlessly?\n\nWhere Did the Disease Model Come From?\n\nAmerica has a temperance tradition. Carry A. Nation\u2014the axe-wielding, saloon-busting zealot\u2014is the best-known figure in the Temperance Movement, which was the engine powering the passage of national Prohibition in the United States in 1920. Temperance was\u2014and is\u2014a large part of our thinking. For us, Carry Nation may be the face of rigid sanctimony. But her conception of alcohol's impact on society arose from the wellsprings of American culture. Temperance resonates powerfully with attitudes that took hold in America in the nineteenth century, continued to grow in the twentieth, and are still expanding in the twenty-first. At the same time, they catch in many people's throats, as they did during Prohibition. And they always will.\n\nTemperance envisioned an epic battle between Good and Evil. On the eve of national Prohibition, in a national radio hook-up heard by millions, the Reverend Billy Sunday expressed the Temperance viewpoint:\n\nThe reign of tears is over. The slums will soon be a memory. We will turn our prisons into factories and our jails into storehouses and corncribs. Men will walk upright now, women will smile and the children will laugh. Hell will forever be rent [split asunder].\n\nBilly Sunday's legacy in our lives is a tragedy. (Sunday's demonization of alcohol didn't work at home\u2014while he himself lived a long life and was a moderate drinker before donning the cloth, his two sons died prematurely due to their alcoholism.) Our Temperance tradition has effectively nailed one of America's feet to the floor, and we have been marching in circles ever since. Addiction to legal and illegal drugs and alcohol certainly remains with us, and by all measures is increasing. The growth in addiction includes many new drugs unknown during Temperance and many things that weren't even imagined, or that at least weren't so effortlessly accessible so that their addictiveness wasn't as obvious as it is today (Internet pornography, games, and gambling, among others).\n\nThis moralism cum science that pervades addiction theory and practice (as Alan Marlatt so succinctly put it, \"The disease model is the moral model in sheep's clothing\") cripples us. Why should we saddle ourselves with ideas about substance use and addiction that plainly and simply don't work, and that actually hobble our ability to deal with them individually and as a society? On top of our quirky American outlooks and cultural inertia, we have added a multi-billion-dollar addiction treatment industry that aggressively maintains the status quo. Thousands of treatment facilities, addiction counselors, publishers, and \"recovery landlords\" (people who run sober living facilities) are financially dependent on the revolving door created by their staggering failures. Onto this juggernaut have been added the pharmaceutical industry's and addiction medicine's claims about addiction\u2014primarily the claim that we are doomed without their products and services.\n\nAA treats addiction with an appeal for divine intervention. The emergent but hidden truth is that current disease approaches reflect the same magical thinking that inspired Temperance activists a century ago\u2014our supposedly modern genetic and neuroscientific approaches are actually more of the same. The abject failure of Prohibition did not fundamentally change our approach to substance abuse. Instead, it shifted our point of attack. In place of a universal ban on drinking, alcohol was transformed from a public demon to the personal one of alcoholism. The battlefield is not the nation at large so much as it is the individual. Our view has shifted from the addict as a moral failure to the addict as a disease victim, although the two ideas remain inextricably similar. As the devil takes control of evil-doers, internal genetic and biological forces take control of addicts. It's not their fault but, underneath it all, these theories still blame addicts for their weakness.\n\nThe remnants of Temperance and Prohibition are everywhere evident in the United States\u2014in dry counties and cities, state alcohol monopolies, and alcohol \"blue laws.\" Many people\u2014including public health officials\u2014still hold that alcohol is inherently \"evil\" or the equivalent view that it's a poison with inexorably bad health effects. This remains true even now that the _Dietary Guidelines for Americans_ in 2010 noted strong evidence that regular, moderate drinkers live longer because alcohol reduces heart disease. Of course, most Americans believe that cocaine, heroin, and methamphetamines are evil incarnate and that once people use these substances, or use them regularly, the drugs' effects make addiction, brain damage, and other destructive consequences inevitable. But as I have shown in my books from _Love and Addiction_ on, and am now joined in proving by others like Columbia University psychopharmacologist Carl Hart, the effects of illicit drugs are sensationalized to confirm our cultural beliefs. Hart's and my purpose isn't to encourage drug use; people evidently have plenty of motivation for that on their own. It is to locate and address the source of the problem where it exists\u2014for Hart, this is especially in inner-city environments.\n\nThe Brain Revolution\n\nHasn't all of the prior discussion been rendered moot by stunning advances in brain science\u2014haven't brain scans, MRIs, and PET scans located exactly where in the brain addiction takes place? Can't we _see_ it there? The short answer is \"No.\" There is no brain scan according to which a person can be said to be addicted, as opposed to showing the acute or chronic effects of cocaine or another drug or powerful experience. No one is diagnosed as \"addicted\" based on a brain scan. And no one ever will be.\n\nScience is not science when it is handmaiden to mythology, received opinion, entrenched business and professional interests, and ongoing government policy and, _especially_ , when it isn't effective in the realm it was designed to handle. Ergo, we have the modern era of addiction science and medicine, as represented in the newly minted (in 2011) American Board of Addiction Medicine (ABAM). According to the _New York Times_ , in an article entitled \"Rethinking Addiction's Roots, and Its Treatment,\" addiction has finally been resolved by neuroscience\n\nThis is an old, old story. In fact, the science already tells us that addiction can never be resolved neurochemically, genetically, or biologically. And everyone\u2014even the neuroscientific experts who flack the new disease approach\u2014knows that this is true, and that addiction is increasing and will continue to increase. Let's take a trip back over the decades to 1977, when a prominent neurologist, Richard Restak\u2014the excitement catching in his throat\u2014called the newly discovered neurochemicals, the endorphins, \"a group of substances that hold out the promise of alleviating, or even eliminating, such age-old medical bugaboos as pain, drug addiction, and, among other mental illnesses, schizophrenia.\"\n\nWhat fruits have we reaped so far from the neurochemistry revolution? Have mental illness and addiction disappeared? Have they decreased? In fact, they've increased dramatically beginning almost exactly at the time those words appeared.\n\nAs for genes, you have heard about the Human Genome Project, which mapped all of the chemical sequences on human DNA\u2014the stuff that determines our biologically inherited selves. That mapping was completed on April 14, 2003. But there is still no gene for addiction. Although the Human Genome Project has provided a wealth of information, its bottom line is that single genes\u2014or even groups of genes\u2014 _cannot account_ for complex conditions, behaviors, and mental dispositions.\n\n_Pleasure and brain scans_\n\nThere is a voice of the new addictive brain revolution\u2014it's the voice of Nora Volkow, head of the National Institute on Drug Abuse (NIDA), heard on _60 Minutes_ , in the _New York Times_ , and inside all of our heads. And that voice says, \"Addiction is all about the dopamine.\" According to Volkow, drugs operate through dopamine receptors in impacting the pleasure centers of the brain. Since drugs stimulate people's pleasure centers, the person's brain becomes dependent on drugs in order to achieve pleasure. Or, genetically, addicts are initially deficient in their dopamine production and processing and therefore require drugs to achieve the pleasure the rest of us experience normally.\n\nSimple and appealing, right? And it's science to boot. But does it make sense? Do people get addicted to pleasure? Don't we all experience more or less pleasure from many different things? And doesn't how we react to that pleasure depend on a myriad of factors? Perhaps you think that cocaine is different, much more pleasurable. Recall my discussion earlier that experienced addicts find cigarettes harder to quit\u2014more addicting\u2014than cocaine. But you don't have to use drugs to stimulate your dopamine levels: Volkow and associates \"have used PET scans to show that even when cocaine addicts merely watch videos of people using cocaine, dopamine levels increase.\" Researchers \"demonstrate similar dopamine receptor derangements in the brains of drug addicts, compulsive gamblers and overeaters who are markedly obese.\"\n\nVolkow's brain revolution is headed into every serious area of our lives. Many activities stimulate the brain's pleasure centers. And, now, Volkow and others are saying these are addictive in the same way drugs are because they activate the same parts of the brain. I noted that the new edition of American psychiatry's bible, _DSM-5_ , for the first time recognizes as addictive a non-drug-taking activity\u2014gambling. In addition, the DSM committee is contemplating adding gaming as an addiction. But why stop there? As the authors of _The Chemistry Between Us: Love, Sex and the Science of Attraction_ make clear, \"Dopamine is involved in reward and motivation for everything we do in life\u2014whether we're eating good food, drinking good wine or interacting with our kids and family.\"\n\nSo, we learn, these groups of people\u2014drug addicts, compulsive eaters, and gamblers\u2014respond with brain changes to seeing, even thinking about, their addictive activities. Does this really explain why people become addicted\u2014ruining their lives and those of their families? Does everyone whose brain lights up due to using cocaine become addicted, and do those who do stay addicted? Maybe they will become more restrained as they mature. Maybe they will occupy themselves with other things\u2014leading more productive lives, doing the right thing, taking responsibility for the well-being of children\u2014that will cause them to restrain themselves, as love of a child did for Rose and Phil.\n\nIf so many things stimulate dopamine production and the pleasure parts of the brain, and since all of us eat, have sex, and at some time were exposed to gambling or gaming (another activity to which many become addicted), are we all addicted to one thing or another at some point? Perhaps we are. Then what might once have been considered human frailties to be worked on, alleviated, and perhaps even accepted become lifelong disease diagnoses. But, of course, we recognize that some people become addicted to the same activities while others do not. What, then, accounts for these individual differences?\n\n_Self-control and the brain_\n\nCan we locate addiction in the brain? Dopamine implicates the limbic system. But in addition to finding pleasure centers, neuroscientists must add another layer when they talk about addiction. These scientists recognize what you and I do\u2014that not all people who experience pleasure from doing something, even very intense pleasure (think sex again, or eating), simply go out and repeat that activity ad infinitum. For instance, many people consume cocaine without being addicted to it\u2014even though they, too, find it very pleasurable. You know this is true, too, because people may become addicted to amphetamines in the same way they do to cocaine (remember Rose), and yet amphetamines are used in popular prescription drugs such as Adderall.\n\nWhy don't most become addicted? Addiction theorists focus on the frontal lobes as the center of \"executive\" control functions:\n\nAlcohol and substance abuse disorders involve continued use of substances despite negative consequences, i.e., loss of behavioral control of drug use. The frontal cortical areas of brain oversee behavioral control through executive functions. Executive functions include abstract thinking, motivation, planning, attention to tasks and inhibition of impulsive responses. Impulsiveness generally refers to premature, unduly risky, poorly conceived actions. Dysfunctional impulsivity includes deficits in attention, lack of reflection and\/or insensitivity to consequences, all of which occur in addiction.\n\nAnd so addicts are marked by impulsivity, which is associated with the frontal lobes.\n\nAs with all such claims, this one involves a simplified and schematic idea of the brain. Figure 1 in the quoted reference is titled \"A Simplified Schematic of Frontal Cortical and Limbic Brain Region Circuitry That Contribute to Addictive Behavior.\" You and I couldn't make sense of this \"simplified\" schematic, let alone the actually functioning brain, whose activities defy description. The limbic system is very, very complex and is associated with, among other things, emotions, pleasure, and memory. But Joseph LeDoux and many other neuroscientists regard it as impossible to map specific human experiences onto designated places in the brain\u2014so many parts are involved in so many functions. For LeDoux, this thinking traces back to ideas about brain anatomy that neuroscientists now know are inaccurate and no longer use. Do you remember phrenology?\n\nIn 2012, a study in the prestigious scientific journal, _Science_ , reported finding a neurogenetic basis for substance abuse. The _Time_ headline about the study read, \"Siblings Brain Study Sheds Light on Roots of Addiction.\" Subjects were identified based on their chronic use of various drugs: most often cocaine, but also amphetamines, heroin, and alcohol. These individuals were compared with their siblings, who weren't substance abusers. Presented with cognitive tests, both the chronic substance abusers and their non-abusing siblings showed poor impulse control compared with most people. \"Brain scans also showed that siblings had similar abnormalities in the connections between their inferior frontal gyrus, an area of the brain involved with self-control.\"\n\nNow, the question is, why did half the siblings become addicts if all were poor at controlling their impulses? Apparently not only were the drugs not responsible for addiction, but neither were the siblings' brain deficits, which the sibling subjects shared. What we still don't know from this study is why the siblings with similar brain structures and weak self-control differed in their substance abuse. Apparently, people don't control themselves or fail to do so solely because of the \"connections between their inferior frontal gyrus.\"\n\nThe insightful author of the _Time_ article, Maia Szalavitz, wrote:\n\nInterestingly, the authors note, these connectivity problems are similar to those seen in the brains of teenagers, a group that is characterized by impulsive behavior. It is almost as if the brains of addicts are less mature. Perhaps that helps explain why some addiction wanes with age. Studies find that most people who struggle with alcohol and other drugs in their 20s \"are out\" of their problems by their 30s, typically without treatment.\n\nBut if this impulsiveness\/addictiveness is naturally outgrown, then why talk about a lifelong disease? We're in an entirely different realm altogether, the realm of _Recover!._\n\n_Can people control themselves\u2014how?_\n\nAt the beginning of this chapter, I wrote that addiction is a consuming behavior or involvement that you rely on, but that detracts from your life by making you miserable or limiting your ability to engage the world freely and effectively. How does that fit with modern neuroscientific discoveries, such as that drugs and some experiences activate the limbic system and cause the body to produce pleasurable brain chemicals, such as dopamine? The body and brain thus become accustomed\u2014acclimated\u2014to this stimulation and production, and _can't live without it_.\n\nOf course, that last phrase is the key. Alan figures he can't live without cigarettes stimulating his limbic system and producing dopamine; Phil seemingly acted that way\u2014until he quit for his daughter's love. In fact, that drugs and gambling and shopping\u2014and, as we have seen, not only these things\u2014cause brain and neurochemical changes is really no great revelation. _Every_ stimulus and human experience translates to some action of the brain. And the more powerful and engaging for you the experience, the greater the brain changes are likely to be. In this sense, then, _you_ control your brain's reaction through how strongly you respond to something or how appealing you find it to be.\n\nYour brain and neurological system adapt to this stimulation. Remember homeostasis in tenth-grade biology? The body, down to the cellular level, responds to stimulation by retracting its natural responses and creating counteracting responses, to achieve balance. You become inured to an experience, less sensitive to the stimuli, so that you need more of the external stimulation to achieve the same level of that experience that you initially attained with less effort. If that stimulation stops, the body springs back the opposite way, the more so as our body acclimates to the initial stimulus. Here is the neuroscience of all pleasure-addictions from Nora Volkow: \" _Once the brain becomes less sensitive to dopamine, it 'becomes less sensitive to natural reinforcers' such as the 'pleasure of seeing a friend, watching a movie, or the curiosity that drives exploration_. _'\"_ Volkow's definition of addiction here is actually quite close to mine, but for its being couched entirely in terms of your nervous system.\n\nWhat is the most stimulating, pleasurable experience humans can have? For most, the answer is sex. The psychiatric diagnostic manual hasn't quite gotten around to recognizing sex as addictive. _DSM-5_ also rejected _hypersexual disorder_ , which sounds a lot like sexual addiction (not to mention the now-discredited _nymphomania_ ). It is defined by \"evidence of personal distress caused by the sexual behaviors that interfere with relationships, work or other important aspects of life.\" Yet it turns out that people with hypersexuality don't find sex any more stimulating\u2014\"They look just like normal people with high sex drive.\"\n\nMost of us\u2014even with high sex drives\u2014fit sex into the normal course of our lives, as pleasure subordinated to the rest of our needs, like making a living, raising children, fitting in with society, avoiding being classified as a sexual predator, and so on. Most of us control our sexual urges much of the time\u2014although many of us have had our moments of uncontrollable delight, and misery, around sex and its deprivation. We wouldn't rape someone, kill for it, spend ourselves into insolvency, or otherwise ruin the rest of our lives to satisfy that itch in our loins. _This has always been true; it will always be true; nothing discovered in the brain can change this reality._\n\nExcept now the advent of free Internet porn has led to a remarkably large number of addictions. We all become used to\u2014sated with\u2014sex with the same partner. Most of us accept this\u2014more or less. Sexual and marital best-sellers, marriage manuals, and _Cosmopolitan_ are full of methods for keeping sexual desire alive and for restimulating couples' sex lives. Others remedy the loss of desire within long-term relationships by seeking the stimulation that comes with extramarital sex. Do those people experience more pleasure from sex, more satiation from long-term relationships, have deficient (or excessive) dopamine levels, or have bad inferior frontal gyru connections? Or are they just more likely to have extramarital affairs, for one reason or another?\n\nSexual addictions often take the form of addiction to Internet porn: \" _I sold porn on the Internet for over 10 years. It ruined relationships and led me down a dark road of heavy use.\" Marnia Robinson (who writes a Psychology Today_ blog alongside mine) has focused on Internet porn and addiction, finding it the dominant addictive problem of our time. She describes men who masturbate throughout the day, lose the ability to engage in normal sex with, or be aroused by, spouses and other lovers, and become slaves to porn.\n\nCan no one then overcome an addiction to porn? Of course they can. The above quotes come from a blogpost by Robinson and Gary Wilson called: \"Guys Who Gave Up Porn.\" Here's what happens to them:\n\nMost experience weeks of uncomfortable, temporary withdrawal symptoms [note from me: withdrawal symptoms _are_ temporary\u2014that's the definition of withdrawal], such as mood swings (irritability, anxiety, despair, apathy, restlessness), insomnia, fatigue, very frequent urination, intense cravings or flat libido, etc. One man charted his ups and downs. Happily, recovering users often become more responsive to pleasure even before the withdrawal symptoms and hypersensitivity to porn cues stop: _After 34 days I tested myself. I could masturbate to orgasm without thinking about anything for the first time of my life. And erections came much more frequently and stronger. At the same time I knew with absolute certainty that the process wasn't finished yet._\n\n_How and why do people stop being addicted?_\n\nI've used the term \"neuromeme\" to mean the style of representing human experience, motivation, and behavior in neurological\u2014brain chemistry and mechanics\u2014terms and images. As a culture, we increasingly seek explanations for our behavior in neurochemicals and brain activation, as though that were the total answer. The most important part of this neuromeme, I have shown, is the idea that we have no control over whether and how the addictive process starts and, once it's occurred, whether or not we quit. This is the \"hijacked brain\" invented by Volkow's predecessor as NIDA director, Alan Leshner (and popularized by Bill Moyers's 1998 PBS series, _Close to Home: Moyers on Addiction_ , on which I was a consultant).\n\nThese neuromemes are repeated constantly in popular broadcast media, magazines, and Internet sites. We now as a culture think in these terms. Yet nothing in those PET scans indicates that something has happened to a person's brain to finally hijack it, the exact moment this happens, and when it stops\u2014which, as we shall see, is the typical outcome for addicts.\n\nOne addict who personifies this mystery\u2014how the brain is apparently hijacked, but then recovers\u2014is Marc Lewis, who writes about his life as a drug addict in _Memoirs of an Addicted Brain_ : _A Neuroscientist Examines His Former Life on Drugs_ (Perseus, 2011). Lewis is a neuroscientist. He quit his drug addiction. Here's what Lewis says about that:\n\nSo this time was obviously hugely different. How did it work? I'm really not sure. Basically, I reported what happened. The details are accurate. I didn't have an instruction manual, so I can't really say what was going on or precisely what I did that time that unlocked a new door. But here, I'll try. I had recently endured two particularly shitty events. My girlfriend left me, which broke my heart, and my friends found me, semi-comatose, on a toilet seat in a public building with a needle sticking out of my arm, which was intensely shame-inducing. I think by then I had built up a lot of rage, not just self-contempt and all that but real rage\u2014toward drugs.\n\nA lot like Rose and Phil, really, when you think about it\u2014love and physical illness and shame caused both of them to quit their addictions. All three of them, including Lewis, were addicted, and thought they were stuck. But events proved them wrong.\n\nLewis deals with what we would all agree was the most important part of his addiction\u2014quitting it\u2014as almost an afterthought, as reflected in his title for the piece: \"How I Quit. . . . At Least, How I Think I Quit.\" Lewis says he didn't have the manual for brain change\u2014even though he is a neuroscientist and his book is full of discussions of the brain. But, really, at its base, Lewis's book is about his awkward and isolated growing up and the relief that drugs provided him. What he is really doing is trying to translate experiential psychology into neuroscience. That actually can't be done\u2014as Lewis finds: despair, love, and shame just don't come stamped with labels on brain scans. Experience and brain dynamics remain forever distinct entities.\n\nMoreover, as Carl Hart and Maia Szalavitz note about media images of permanent drug-induced brain damage in the case of methamphetamines,\n\nThe problem is that the hype may do serious damage to those struggling with methamphetamine problems. \"One of the major reasons I did the review is that one of the most effective treatments is cognitive behavioral therapy,\" says Hart. \"The argument has been made that these people can't benefit because they are cognitively impaired and can't pay attention. There's no scientific evidence to support that position.\"\n\nIndeed, the idea that those who take methamphetamine are more likely to fail at treatment or need longer-term care than people with other addictions is not supported by the data, either. Unfortunately, by pushing the idea that methamphetamine damages the brain, researchers may inadvertently deter treatment seeking, both by making people with addictions feel hopeless and by making providers have less faith in their ability to help.\n\nOf course, treatment may consist of convincing addicts of exactly these myths, which is one reason Rose felt she had to reject the treatment she was offered in order to recover.\n\n_The abuse trap_\n\nLewis's painful upbringing and subsequent drug abuse are not unusual\u2014although, as we will see, his experience is far from the typical substance abuser's or addict's case. But the abuse explanation has become another prominent theme in the addiction lexicon, and many unwary addicts have dead-ended on this sidetrack. Let me note without hesitation that childhood abuse is bad for human beings and produces bad outcomes. But, in the overwhelming majority of cases, it is surmountable and people do overcome it. Nonetheless, there is now an entire subcontinent of addiction clinicians who seek out unremembered childhood abuse as the explanation for every case of addiction they encounter. Moreover, many trace back such re-imagined abuse to imagined brain chemistry. Even such a prominent addiction specialist as Gabor Mat\u00e9, the Canadian physician and author of _In the Realm of Hungry Ghosts_ , believes that early abuse, neglect, and even\u2014casting a wide net\u2014stress and lack of affection permanently impair people's ability to process brain chemicals that provide us with pleasure and pain relief.\n\nMat\u00e9 then claims these deficiencies in addicts' neurosystems cause them to self-medicate to replace their missing neurostimulation. This is actually a specialized version of the brain\/neurochemical model we saw, but now steeped in childhood abuse, in which people are addicted to drugs as replacements for missing brain chemicals brought on by the abuse. As important as is Mat\u00e9's work with addicts, his simplistic vision of addiction in which abuse history and imagined biochemical changes become the essential causes of people's self-destructive behavior can be as incapacitating as genetic neurochemical deficiency models.\n\nIt is not enough to say that this model is highly conjectural. It also isn't true\u2014that is, it makes little sense of the world. A huge epidemiological study of early childhood experiences found that 3.5 percent of people with four or more adverse childhood experiences ever injected drugs. It was a higher number than for the general population, but still only a tiny portion of the group. Of course, few people in the overall population become heroin addicts, but the same research included alcohol dependence. With drinking as with drugs, the rates of dependence follow the same elevated trajectory depending on the number of adverse childhood experiences. But they are still only slightly higher for abuse victims\u201416 percent versus around 10 percent. So abuse models of addiction like Mat\u00e9's tell us little. And even when abuse victims become addicts, there is no way to separate out negative psychological consequences of their dysfunctional upbringings. These consequences, even though they can't be translated into identifiable brain malfunctions, could nonetheless fuel a person's addiction.\n\nWorst of all, focusing on childhood as the determinant of addiction detracts from our awareness of people's natural tendency to overcome abuse and addictive experiences. We might ask, first, what protects the other 96.5 percent of abuse sufferers who don't inject drugs and the 84 percent who do not become alcohol dependent? On top of this, what about the strong tendency described throughout this chapter and _Recover!_ for people with addictions to recover naturally? Focusing on abuse as an irreversible cause of your addiction does not support your efforts to confront your abuse and overcome its effects on your life.\n\n* * *\n\n**CASE:** Suzanna was a doctoral student, age twenty-seven, who\u2014it might seem ironic\u2014worked with an alcohol research group. Ironic because she worried about her drinking. She drank daily\u2014rarely becoming intoxicated\u2014but needing to have three to four drinks of alcohol to feel okay, and sometimes on weekends drinking more. She felt guilty about her drinking and didn't let other people know about it. Reading writers like Marc Lewis, the neuroscientist quoted above, she decided her drinking was permanently lodged in her brain due to her childhood experience. For Suzanna had been abandoned by her mother.\n\n* * *\n\nSuzanna, like many modern Americans, seeks an answer to her problems in a childhood that her reading tells her has irreversibly altered her brain. How _helpful_ is that for her? There will never be\u2014never can be\u2014a way to find lesions in the brain that stand for Suzanna's abandonment, ones that could clearly point to her drinking issues. And, please do recall, Lewis himself overcame his drug-injection addiction, more or less spontaneously. But Suzanna was caught up in this sidetrack, to the exclusion of those avenues she might have pursued successfully.\n\n_Your brain changes when you change_\n\nNeuroscience doesn't explain addiction nearly as well as it explains recovery. This is because neuroscience has the most to say about the brain's ability to be reshaped\u2014and to reshape itself\u2014while forming new connections, which is called _neuroplasticity_. Researchers time and again have discovered how adaptable the brain is\u2014for example, brain-injured people typically replace lost functioning by shifting these functions to other parts of the brain (\"rewiring\") and through new neural development. People's brains change all the time due to external and internal stimuli. _All_ of the various experiences you have compete, counteract, and disallow one another. Most important, you control which of these experiences are seminal or dominant, as when Phil (or anyone) quits smoking because his values override a mindless habit.\n\nNow that brain chemistry has become a runaway train, serious writers and clinicians believe they must point at their brains and talk in neurospeak when discussing every kind of behavior. In their brilliant book, _Brainwashed: The Seductive Appeal of Mindless Neuroscience_ (Basic Books, 2013), Sally Satel and Scott Lilienfeld detail the extent to which neuroscientific theories pervade modern thinking. Calling this the \"neurocentric\" view of the mind, Satel and Lilienfeld detail how this view is based on simplistic and inaccurate ideas about what brain scans can actually tell us. At the same time, they show that this view denies the reality of choice and personal responsibility and leads to bad decision making throughout society, including not only psychiatry, but also the legal system.\n\nObviously, the same reliance on brain concepts and neuromemes is occurring in the addiction field. High-end practitioners use brain scans or similar tests to show that individuals' frontal lobes aren't sufficiently activated. What is sufficient frontal lobe activity, how complex neural patterns in the prefrontal cortex in combination with other parts of the brain express themselves in thinking and behavior, whether drug takers who use and don't become addicted show similar MRI results\u2014all those considerations are irrelevant to these practitioners. It is a way of thinking people often want to hear. The crucial difference is between those, like Dr. Drew of \"Celebrity Rehab,\" who claim that \"hypofrontalism\" is a permanent brain disease that means people's self-restraint is dead and can't be revived and those who understand that self-restraint is an area for addicts to work on using cognitive-behavioral techniques.\n\nPeople may find it useful to think in terms of their brains when they change old patterns. But you don't need to see a brain graphic to know that people initiate change. Because you know people like Phil and Rose, and you may be one of those people, who quit smoking or other addictions. The \"hijacked brain\" and \"chronic brain disease\" memes ignore this natural ability of the brain to reform itself. The idea that a person's brain scan depicts their addictive past, present, and future is poppycock.\n\nSome of the ways to change brain function that have been measured include meditation and through related mindfulness, breathing, and relaxation techniques and self-acceptance. One way to think of mindfulness practices to defeat craving is that they disconnect existing brain patterns, what some call the neural craving network, while creating new neural pathways. But your principal concerns are the practices that you consciously control\u2014the more often you engage in such techniques, the more readily your brain adapts and responds to them. What is critical is to start, practice, and continue these new ways of thinking and acting.\n\n_Working against people's own natural growth_\n\nAs I have indicated, AA and the 12 steps are popular out of all relation to their ability to address and to remedy addiction. But, nowadays, the public relations behemoth in support of chronic brain disease-ology has even more backing than from celebrity recovering addicts\/alcoholics who promote the 12 steps. Many more institutions, livelihoods, and reputations depend on the disease of addiction today than when Bill Wilson and Bob Smith reached into American religious mythology to create the 12-step philosophy. These include now addiction medicine, manufacturers of an emerging array of pharmaceuticals, and the neuroscientific research industry itself, all in addition to the vast network of Betty Ford\u2013style, 12-step rehabs. Only, now, the usual 12-step bromides and treatment are couched in neurochemical and brain terms while simply performing the same ancient rituals based on the same faulty logic, data, and visions of the sources and trajectory of most addiction. This large\u2014and growing\u2014industry requires that more of us believe that we are suffering from lifelong addictive diseases. What is happening to the idea that we can outgrow, that we can be encouraged to outgrow, and that we should outgrow addiction?\n\n_Outgrowing addiction_\n\nThe ability to change an addiction is something we all know about. As in Maia Szalavitz's analysis of the decline in impulsivity as people mature (and maybe experience changes to their inferior frontal gyrus), we have all seen and experienced it. When interviewing sociologist Thomas Vander Ven, who, in his book _Getting Wasted_ , described how most college binge drinkers (more than 40 percent of undergraduate students) are drinking to overcome social anxieties and to gain a sense of belonging in their first time living away from home, an interviewer for the online magazine _Salon_ had an affecting reaction:\n\nA lot of what you say really rings true. I definitely had a lot of social anxiety when I was in college. I was on a varsity rowing team, and I was gay, and I drank partly to get over the awkwardness that came with that. . . . And as soon as I left college\u2014it was almost instantaneous\u2014the idea of being hungover just became extraordinarily unappealing and I stopped drinking so much.\n\nVander Ven responded to his young interviewer: \"That's a lot of people's experience\u2014drinking in college is just a very different enterprise than once you graduate.\" That is, unless you are convinced you have a lifelong disease. In the meantime, Hazelden and other treatment providers are expanding big-time into treatment facilities dedicated to adolescents\u2014in the case of Hazelden, to the tune of a new multi-million-dollar campus for teens.\n\nWhy don't we hear from all of the people who outgrow their alcoholic\/addictive phases? On the one hand, it's so natural that we don't find it exceptional or noteworthy\u2014even as Hazelden and others hard-sell the opposite, counterintuitive idea. For example, now that Angelina Jolie is a transcendent movie star, world-moving humanitarian, mother, and role model, who focuses on her troubled youth, when she was suicidally depressed, cut herself, and used heroin along with other drugs? Or, do you remember now that Drew Barrymore appeared on the cover of _People_ in 1989 (January 16), age thirteen, as America's youngest addict? She had been in rehab and confessed, \"I'm Drew, and I'm an addict-alcoholic,\" and that now she was embarked on recovery. She subsequently relapsed, attempted suicide, and reentered rehab, as she described in her 1990 memoir, _Little Girl Lost_ , published when she was fifteen.\n\nThe _People_ article included an analysis by a psychiatrist and adolescent addiction expert, Dr. Derek Miller: \"Although there is nothing available clinically to test for genetic dependence,\" Dr. Miller admitted, \"parents should be very careful to keep their children off of all alcohol if there is a history of either alcoholism or biologically based depression in the family.\" In other words, Drew inherited her alcoholism-addiction from her substance-abusing parents and forebears (like grandfather John Barrymore). Miller continued: \"Abstinence is the key to all treatment.\" Although, he added, \"the younger the adolescent, the harder it is for them to understand they have a problem.\" You know, the problem that they were born addicts-alcoholics, a destiny they can never escape.\n\nFlash forward to 2012, when Barrymore once again appeared in _People_ (June 4), with the announcement: \"Drew Barrymore: She's a Vintner!,\" one who had \"lots of knowledge and was passionate about her wine.\" But everyone is so aware\u2014it is so obvious\u2014that most people successfully outgrow their youthful substance abuse that no one cares to reflect back to the earlier _People_ treatises on Drew and addiction to reevaluate their ideas about alcoholism and other addictions. Do you think Dr. Miller has greatly revised his theories based on his monumental miscalculations about Drew? Not likely. Believing the disease theory of addiction means never having to say you're sorry\u2014just as no one worries about a few miscalculations about how the discovery of endorphins and a special alcoholism gene would soon end addiction and solve alcoholism, or about how nicotine replacement holds the key to quitting smoking addiction, even though it actually fosters it.\n\nChange, Change, Change\n\n* * *\n\n**CASE:** Dori had been drinking alcoholically for twenty years, since her early teens. Most nights of her life she fell asleep in a drunken blackout. She also smoked for all that time. If anyone were a candidate for permanent, debilitating alcoholism, it was Dori. She had been in and out of 12-step programs her entire life, as well as psychiatric treatment. Nothing had changed for her.\n\nDori was extremely concerned about her appearance\u2014she always dressed well, exercised, and was hyperconscious about her weight and diet. One night, Dori walked into a bar and stared at several women arrayed along the bar's counter. In the harsh light of the place, Dori\u2014already a little bit drunk\u2014saw herself in the row of run-down women. Dori quit drinking that night. And smoking. And psychiatric meds. She had a rough several weeks dealing with the upheavals in her system that withdrawal caused. But more important for her to deal with was the giant empty space at the core of her life that alcohol had filled for more than half of that life. Yet recovery proved to be enduring for Dori.\n\n* * *\n\n_The truth, and how to harness it for your recovery_\n\nNot only must you reject the fear-mongering addiction madness of the last century, brought up-to-date by Dr. Drew, the American Society of Addiction Medicine, and neuromemes\u2014you can replace it with a sane, empowering understanding based on principles grounded in reality. A truly human view of addiction accepts that a wide range of factors contribute to the development of addiction. But what most concern you\u2014what offer you the best chances in life\u2014are those factors that you can address and change. You stop being addicted by expanding your psychological horizons, creating new interests, and maturing (remember, Nora Volkow characterized addiction as when people lose the \"pleasure of seeing a friend, watching a movie, or the curiosity that drives exploration\") and by focusing on your values, working on skills you need to improve your life, and developing larger purposes.\n\nRemember our list of myths about addiction? Let's replace them with these essential truths, and explore each in turn.\n\n\u2022 Addiction and recovery are common\u2014typical\u2014in human experience.\n\n\u2022 Addiction, by its nature, is artificial and, therefore, can be overcome.\n\n\u2022 You have the resources within you to overcome addiction, completely, forever.\n\n\u2022 There is nothing and no one more able than you to begin and sustain your recovery.\n\n_Addiction and recovery are common\u2014typical\u2014in human experience_\n\nAre Angelina Jolie, Drew Barrymore, and Dr. Adi Jaffe (a therapist who Dr. Drew claims couldn't have been really addicted since he now drinks moderately after a major amphetamine addiction) the only people who have come down from addiction to become moderate substance users? In fact, they are in the majority. As I wrote at the beginning of this chapter, the National Institute on Alcohol Abuse and Alcoholism has conducted a giant survey of Americans' drinking lives. This study is called NESARC (National Epidemiologic Survey on Alcohol and Related Conditions). NESARC interviewed more than 43,000 representative Americans eighteen and older about their lifetime of drinking\u2014interviews were conducted in 2001\u20132002 and a second wave in 2004\u20132005.\n\nAbout one in ten Americans qualified for a diagnosis of alcoholism at some point in their lives, the government's alcoholism researchers determined. Here's what happened to them: \"Twenty years after onset of alcohol dependence, about three-fourths of individuals are in full recovery; more than half of those who have fully recovered drink at low-risk levels without symptoms of dependence. . . . Only 13 percent of people with alcohol dependence ever receive specialty alcohol treatment\" (this includes attending AA). And no higher a percentage of treated than of untreated alcoholics recover (28 percent of treated alcoholics are currently alcoholic, compared with 24 percent of the untreated) These untreated alcoholics are the invisible Americans we _don't_ hear about because they violate most Americans' beliefs. But, unless the United States is wasting a fortune utilizing its best researchers and interviewers, most people overcome alcoholism themselves, as they do smoking and every other addiction.\n\nPerhaps, you feel, drug addiction is very different from alcoholism and smoking. According to NESARC, which also measured drug abuse, it is. _Drug addicts more readily give up their addictions than do alcoholics and smokers_! NESARC reports, \"26 years after first becoming dependent, half the people at some time dependent on nicotine were in remission, a milestone reached for alcohol after 14 years, for cannabis six years, and for cocaine five years.\" Although there were not enough heroin addicts in this population to analyze, the investigators found that other data showed their remission point likewise to be quicker than for alcohol and cigarettes. In other words, Rose's relatively quick recovery from her meth addiction and Phil's lengthy effort to quit cigarettes, with Dori in between, are typical. The reason, as Rose's case shows, is that it is harder to maintain an illicit-drug lifestyle.\n\nAnother study of the NESARC data found that 80 percent of people who had been dependent on an illegal drug were in recovery. Moreover, investigator Gene Heyman showed, \"no matter how long ago someone became dependent on an illegal drug or alcohol, their chances of achieving remission remain the same.\" Heyman thus emphasized that, contrary to AA's idea of addiction as a progressive disease\u2014or claims that neurochemical changes fix an addiction permanently in the brain\u2014people are just as likely to quit at any point in their addiction career. Heyman found that addicts quit at the point when they can finally realize their values and aspirations.\n\nThese analyses of the drug addiction data from NESARC were summarized in an issue of the _Effectiveness Bank Bulletin_. This issue labeled a third large study \" **Recovery is the norm** ,\" in which the renowned alcoholism scholar William White synthesized the results of hundreds of studies of drug addicts and alcoholics: \"Recovery is not an aberration achieved by a small and morally enlightened minority of addicted people. If there is a natural developmental momentum within the course of these problems, it is toward remission and recovery.\" What a powerful message this is, if only it were broadcast as loudly as is the one that addiction is embedded in our brains and our lives, presumably forever for most people. But such recovery from drug addiction goes unrecognized, as it does with alcoholism, because it usually occurs without treatment.\n\nNonetheless, most people understand\u2014or at least live out\u2014this message for themselves. Another massive study of drug abuse, the National Survey on Drug Use and Health, is conducted annually by the Substance Abuse and Mental Health Services Administration. Here are the figures for abuse of, or dependence on, either alcohol or drugs by age group for 2011 (these figures remain essentially the same year after year):\n\nTABLE 2.1 **Percentage of Americans Who Abuse or Are Dependent on Drugs or Alcohol for Each Age Group**\n\n**_Age Group_** | **_% Abuse or Dependent_**\n\n---|---\n\n18\u201319 | 17\n\n20\u201322 | 20\n\n23\u201325 | 17\n\n26\u201329 | 13\n\n30\u201334 | 12\n\n35\u201349 | 8\n\n50\u201359 | 5\n\n60+ | 3\n\nWe see again from government data that substance abuse is a common trait among the young, but that large numbers of people cease their abuse and dependence after their early twenties. Twenty percent (one in five) of those at this age are clinically diagnosable as either abusing or dependent on alcohol or drugs, compared with 12 percent in their early thirties, and down to 5 percent in their fifties.\n\nENVIRONMENTS THAT ENCOURAGE\u2014OR DISCOURAGE\u2014ADDICTION\n\nThere are many scenarios in which people are rendered unable to cope. Some people are thrust into traumatic situations that are beyond anyone's ability to control, and some people simply do not have the skills to manage their obligations and the vagaries of everyday life, at least for the time being. Whether they are having trouble navigating traumatic circumstances like war or abuse or simply having difficulties in daily coping, people may seek a ready escape in mind-altering substances and other addictions. And, once they have turned to addictive remedies, the possibility of regaining control of their lives can seem even more remote.\n\nHistory has provided the example of addicted Vietnam GIs. Heroin use was rampant among American soldiers in Vietnam, where the drug was readily available. Among those addicted in Vietnam, only a fraction (one in eight, or 12 percent) became re-addicted stateside. This was true even though _half_ tried a narcotic when they returned. What explains this? Turning to and relying on a powerful analgesic to relieve stress made sense in Vietnam, but not afterwards. As Vietnam fades into history, we can still readily discern the powerful addictive urges produced when normal routes to escape and advancement are blocked in our inner cities. But it is no more permanent a condition there than it was for most veterans when they returned to manageable environments.\n\nVietnam demonstrated that addiction doesn't define a person, that being able to gain satisfaction through engagement with the world trumps addiction. There is no better \"treatment.\" The Vietnam heroin experience showed us the recipe for recovery: people avoid and overcome addiction when they have positive options, meaningful goals, and control of their lives.\n\n_Addiction, by its nature, is artificial and, therefore, can be overcome_\n\nLike the soldiers who depended on heroin to release them from horrific circumstances that they could not change, addicted people seek refuge in any powerful, consuming experience that allows them to cope with a life that feels meaningless or out of control\u2014a feeling that is both worsened and relieved by their addiction. The addiction further fills countless hours beyond those eaten up in altered states of consciousness or compulsions. Think of all the mental and emotional energy an addiction wastes: days planned around purchasing and consuming the substance or practicing the activity; fielding negative fallout (like angry co-workers, family members, and friends; mounting bills; health problems); making solemn promises to stop; remorse and guilt.\n\nYet, as painful and self-defeating as these feelings are, their predictability sustains addicts and even lends a bizarre sense of purpose to their lives. Rather than being a medical mystery, _addiction makes complete psychological sense._ It's a natural human response to unmanageable life circumstances, one through which people mistakenly attempt to find purpose and a sense of well-being. They're wrong, of course, and can't succeed at it. But this is more of a perverted effort to balance one's life than a permanent addicted place in your brain. _Addiction is not who people are_. And most people figure this out as they go along, because\u2014contrary to claims of denial\u2014it's not that hard to figure out. People perceive the mounting negative consequences for their lives and, if given half a chance, they clamber out of the addiction. We have seen through the best, most comprehensive research about people's real lives that this is what happens for most people, and not only Vietnam vets.\n\n_You have the resources within you to overcome addiction, completely, forever_\n\nWhen I point out that people recover without treatment, this of course doesn't mean they didn't get help, or that people recover completely on their own. They rely on community, family, personal resources. Thus, becoming connected with others is one of the best predictors that you will recover. Likewise, as I will show in succeeding chapters, everything you bring to the effort\u2014your knowledge, education, work skills, values, commitments, friends, family, community involvements, interests, health\u2014offers a helpful boost. And, so, along with the types of therapy that can be helpful, along with the passage of time and maturity, any resource you possess aids in achieving your own, true-to-yourself recovery. And any of these assets you acquire or improve as you work for recovery will contribute to achieving it.\n\nSo, we see that people have the wherewithal, or can gain it, to overcome addiction for themselves\u2014you included. Why do they recover? You know what happens: people settle down emotionally, they develop responsibilities\u2014work, children, financial obligations\u2014the usual. It comes with the human territory of growing up or, in addiction terms, \"maturing out.\" You may have failed to mature out when you might have had the chance. You may even have developed your addiction later, after supposed maturity, even\u2014unfortunately\u2014as a parent (like Rose). Perhaps you lacked the necessary skills or emotional resources that come to most people in adulthood. But that's water under the bridge. The PERFECT Program is your second chance\u2014your second emergence into maturity.\n\nEFFECTIVE TREATMENT\n\nResearch also shows you the best way to get help to help yourself. Should you seek or need treatment, or even if you just want to learn what sorts of treatments work so that you can use their best elements, we turn to research on _evidence-based treatment_. Psychological investigators have repeatedly found evidence for the effectiveness of therapies steeped in real human functioning. Researchers have performed a series of meta-analyses, which combine results from all investigations of treatment effectiveness. One such comprehensive analysis ranked 12-step therapy and AA thirty-seventh and thirty-eighth among forty-eight possible treatment options. More critically, combining the results of several such analyses, these addiction therapies are the five steady winners:\n\n\u2022 Cognitive-behavioral therapy\n\n\u2022 Community reinforcement approach\n\n\u2022 Motivational interviewing\n\n\u2022 Relapse prevention (which is also cognitive-behavioral)\n\n\u2022 Social skills training\n\nAll of these effective treatments approach addiction as ingrained behaviors and habits of mind, fostered by life situations. Although people with even the most intense addictions\u2014like Dori\u2014may ultimately solve their addictions for themselves, others\u2014including you\u2014may seek and benefit from effective treatment (unlike all of the programs Dori went through). What you find is that the evidence-based treatments in this list all reject the notion of an incurable disease and instead harness and fortify people's own resources. They fuel people's motivation to quit, counteract or change their environment, rely on their social community, and develop their life skills. And all _create a sense of personal empowerment_. That's what _you_ need to do.\n\nAlong with this research on effective treatments comes mindfulness research. Mindfulness is learning to be aware of your thoughts and impulses, to stand outside of them in order to gain control of them. The thoughts might be there (along with urges, cravings, compulsions), but you learn that you do not have to let them lead you. Mindfulness allows you to see that _you are not your addiction_. This approach also includes meditations that enhance people's positive feelings, particularly towards themselves\u2014something we all recognize in psychology as self-acceptance or self-esteem. The mindfulness approach has been used effectively with mental illnesses like schizophrenia, and it is now being applied to addiction along with mental illness. Alan Marlatt's group at the University of Washington has used mindfulness to combat cravings that lead to relapse.\n\nApproaches focused on your ability to function, how you cope with the world, and your ways of thinking about yourself align perfectly with what we know about human behavior. Here research agrees with what seems logical, even irrefutable. You are enormously more likely to beat addiction if you feel strong and capable\u2014if you embrace and nurture your own power. This is what The PERFECT Program does.\n\n_There is nothing and no one more able than you to begin and sustain your recovery_\n\nThe disease model presents itself as an enlightened view of addiction that does not stigmatize or undermine the addict. But that claim is bogus. The PERFECT Program takes the opposite approach to the impossible disease model idea that you must accept that you're powerless in order to begin recovery. In order to recover, you don't need to learn to think like an addict. Instead, _you need to learn to think like a non-addict_. And your life-seeking, healthy core is the engine of your recovery.\n\nMoving Forward\n\nSo now you know these facts: (1) thinking of yourself as an addict isn't necessary and serves only as an additional burden to overcoming your problem, (2) the best science shows that you are more likely to overcome your addiction than not, (3) the seeds for doing so are already within you\u2014everything human about you and everything you know of life is part of what will enable you to overcome addiction. From here on, The PERFECT Program\u2014building on the best evidence from effective treatments\u2014will help you harness and direct your life force toward recovery.\n\n*Please be aware of and observe the cautions in quitting cold turkey reviewed in Chapter 3.\n* * *\n\nPART II\n\nTHE PERFECT\n\nPROGRAM\n\n* * *\n\nCHAPTER 3\n\n_Preparing for Change_\n\nGetting yourself ready for The PERFECT Program\n\n* * *\n\n**CHAPTER GOALS**\n\n\u2022 To gather yourself, your materials, your resources for The PERFECT Program\n\n\u2022 To assess your addiction, your values, your resources for change\n\n\u2022 To define your terms of recovery, to consider your options, and to set your goals\n\n**Purpose:** This chapter brings you to the starting point of your change effort. It gets you prepared, sharpens your pencils, and sets aside the space\u2014emotionally and physically\u2014to begin to change and to quit your addiction. You will start by assessing your addiction, defining recovery, and setting your goals. Once you start in this positive direction, you will begin moving forward steadily.\n\n* * *\n\n* * *\n\n**CASE:** Alex had been getting drunk most nights for several years, stumbling home from his neighborhood bar, often not remembering doing so. Sometimes he found bruises and cuts that he had no memory of incurring. He decided\u2014recognized\u2014he was an addicted alcoholic. This wasn't an intellectual calculation. It was a decision to change.\n\nAlex had heard terrible stories about detoxing\u2014that it was horrid, even life-threatening. Beyond that, what would he do instead of drinking? But the fear of withdrawal overshadowed the latter concern in Alex's calculations\u2014after all, if he could kick his alcohol habit, surely he'd find new things with which to fill his time!\n\nAnd, so, Alex prepared himself well, at least for detoxing. He loaded his refrigerator with fruit juice and mineral water. He had on hand large quantities of fruits and cereals. The cereals, he reckoned, were the easiest things he could get down no matter how nauseous he became; the fruits, the healthiest things. And he recruited his brother, Paul, to stay with him in his spare bedroom.\n\nThe first weekend was hell on wheels, especially at night. Alex couldn't find comfortable sleep and he awoke throughout the night with nightmares. His hands shook when he tried to read. Several times he thought of getting his brother in the next room to drive him to the hospital.\n\nBut he also slept\u2014fitfully\u2014over several days. Alex actually didn't come out of his bedroom until Monday morning and then reluctantly, his eyes bloodshot, feeling sluggish and ill. Paul looked up and, calling him \"sleeping beauty,\" told Alex he had looked in on him several times and found him sleeping\u2014albeit sometimes thrashing.*\n\n* * *\n\nThis case is simply an affirmation of truths borne out by history and science. Many, many people have quit many, many addictions before the creation of the Betty Ford Center. The most important reality for you to embrace is this: You are not your addiction. You are not _an addict._ Your true self is the engine of your recovery. The essence of The PERFECT Program is to fortify the _real you_ to take the reins of your life.\n\nGetting Ready\n\n_Materials_\n\nThis chapter is going to put you to work delving into the essence of your addiction, getting you back in touch with the things that give your life value and purpose, and establishing some goals. Let's get started by clearing some space and gathering supplies. Here's what you'll need:\n\n_Two journals._ One is for personal writing and one for completing the PERFECT exercises and tracking progress. We'll call them your Personal Journal and your PERFECT Journal. You can use any kind of notebook or pad, but make sure that it is something that appeals to you and is functional so that you'll be inspired to use it. Most importantly, dedicate your journals to this process and keep them free of extraneous notes like to-do lists or random phone numbers\u2014anything that will distract your mind with unfinished tasks. You might even get a **third notebook** for jotting down tasks and items that occur to you as you are using your dedicated journals. This will allow you to clear them from your mind for the time being and put them in a safe place that you can revisit later. Similarly, choose **writing implements** that feel good to use, with free-flowing ink, and keep them with your journal so you don't have to go scrounging for pens. If you prefer, you can start a journal on your computer or start a private blog. Keep it front and center on your desktop so that it is easily accessible, or set your computer to open your journal at start-up.\n\n_A timer._ This will come in handy for some of The PERFECT exercises. Don't use your alarm clock, unless you have one with a pleasing tone that won't jangle your nerves. Egg timers can be purchased for under five dollars, or you can even use the timer on your cell phone set to a gentle chime. There are also meditation timer apps for cell phones.\n\n_A meditation spot._ Meditation is a central element of The PERFECT Program (don't panic\u2014we'll walk you through it), and you'll want to create a space where you can sit without distraction. You don't have to create a shrine or invest in an expensive silk and buckwheat cushion\u2014unless you are inspired to do so. All you need is a quiet spot and half an hour to yourself. You can sit on a pillow on the floor, on a straight-backed chair, or even under a tree. (Now, if it's under a tree, you'll need an indoor and an outdoor spot, for when weather forbids communing with nature!) Make sure it's a spot where you can relax. For instance, if you choose a place next to the cat box or a pile where you collect dirty laundry, you won't want to spend time there.\n\n_How does addiction appear in your life?_\n\nAddiction manifests differently in everyone, and for different reasons. Addiction includes a wide range of involvements, whether with substances or behaviors, and its causes and effects are both specific and complex. Rather than tell you what your problem is and present you with one solution, we're going to guide you through the process of assessing your addiction and the impact it has on your life\u2014remembering that it can be more or less severe. Once you are clear about where you stand, you can begin to set some goals, and PERFECT will guide you through that process, too.\n\nRecovery does not have to look like endless days of white-knuckle abstinence and a procession of tedious meetings. If addiction is a treadmill, then recovery is a grand adventure. Understanding that addiction is a destructive, self-negating, ingrained behavior chosen in response to life circumstances and that recovery means infusing your life with a sense of purpose, personal agency, and new skills, you can create a broader vision of what your personal recovery will look like. Through The PERFECT Program, you will be creating a life for yourself that is utterly incompatible with addiction, replacing self-destructive patterns with life-affirming pursuits. Recall Rose (in Chapter 1) as an example. Despite her reverence for her child, her lifestyle allowed addiction in. She rebuilt a life around family (parents, child, and eventually husband), positive social groups (her single mothers' group), education, marriage, and a career that ruled out her addiction forever.\n\nLet's begin by assessing your addiction and making some decisions about what freedom from addiction will mean for you. You will need your PERFECT Journal for this.\n\nADDICTION SELF-ASSESSMENT QUESTIONNAIRE\n\n1. What substance(s) or behavior(s) are you addicted to?\n\n\u2022 If you have more than one, list them from the one that has the most negative and consuming impact on your life to the least.\n\n2. Focusing on the addiction at the top of your list:\n\n\u2022 How often do you engage in your addictive behavior?\n\n\u2022 If you use a substance, how much do you use at a time? If it is a behavior, describe your involvement in detail. How often do you rely on it?\n\n\u2022 At what times of the day or under what circumstances do you do it, typically?\n\n\u2022 When you are not engaged in the substance or behavior of your addiction, when and how much do you think about it?\n\n\u2022 For how long have you had this level of involvement with your addiction?\n\n3. Now go through all the questions in #2 with the next most virulent addiction on your list.\n\n4. What experience are you seeking through your addiction(s)? Describe your feelings when using, or when you're involved in the activity. Summarize what it does for you or gives you.\n\n\u2022 Do you actually achieve this experience? If so, how often and for how long?\n\n\u2022 What other experiences come with your addiction? List both positive and negative.\n\n5. How does your addiction impact your daily life?\n\n\u2022 Family and friends?\n\n\u2022 Responsibilities?\n\n\u2022 Leisure time?\n\n\u2022 Finances?\n\n\u2022 Health?\n\n\u2022 Self-esteem?\n\n6. When is your addiction at its peak? What is going on in your life at those times?\n\n7. Are there periods during which your addiction seems to be less powerful? If so, when? What is different about these times?\n\n8. Have you ever stopped your addiction for a period? For how long? How did your stopping affect your life? How did you feel?\n\n9. Do you believe that you can overcome your addiction? Why do you think you can or can't?\n\n10. At this moment, imagine what it would be like living without this addictive involvement, and describe that life.\n\nVALUES QUESTIONNAIRE\n\n1. Name three things that are important to you, whether or not you are actively honoring them right now.\n\n2. What activities would you be pursuing if you were not so occupied with your addiction?\n\n3. Have you abandoned any dreams because of your addiction? If so, name these.\n\n4. What are some things you value that you could lose in the future due to your addiction?\n\n5. What do you hold close to your heart that most opposes your addiction (religious faith, parenthood, political activism, health, self-respect, regard for others, etc.)?\n\n6. What key skills or talents do you have?\n\n7. What are your most positive qualities?\n\n8. Name at least two accomplishments or events that you are proud of: Did you help someone? Did you win a competition? Did you build or create something? Did you stand up for something you believe in?\n\n9. Who are the most important people in your life, either people you really care about, or people you can really count on, or both?\n\n10. Which three human values do you elevate most, such as kindness, generosity, friendship, honesty, hard work, creativity, independence, integrity?\n\nWithdrawal\n\n_The physical journey_\n\nIf you think of your body as a collection of chemicals responding to one another and working in unison, it makes sense that introducing a new chemical into the mix is going to force all the other chemicals to respond to it. Many people remember feeling disgusted by their first encounter with cigarettes\u2014nauseous and light-headed, perhaps. That's simply the body's response to a chemical interloper disturbing the body's balance. But after continued use, the body will adjust and begin working with this new chemical in order to reestablish its equilibrium. Now, the body comes to expect this chemical and complains if it doesn't receive it. That complaint takes the form of withdrawal.\n\nIt's standard to call this situation \"physical dependence\" or \"chemical dependence,\" but the word \"dependence\" is misleading. The body is dependent on water for survival, but could never be dependent on nicotine or alcohol for survival. \"Accustomed\" is a more accurate word. While it is true that some people have developed such a high tolerance for their drug of choice that withdrawal can be medically risky, less severe withdrawal is the rule.* The more likely scenario is that you will experience some discomfort while your body adjusts. It will be unpleasant, and then it will be over. Of course, you must be immediately sensitive if this is not the case and be prepared to get medical help. In any case, it is after this phase that you will face the long-term challenge of dealing with your real life\u2014the one beyond your addiction.\n\nIf you are giving up a drug, but not only then (see love withdrawal, below), fear of withdrawal may be a major hurdle that prevents you from pursuing recovery. The fact is that withdrawal can be miserable. You might be facing a few days of physical and mental discomfort: restlessness or insomnia, headaches, shakes, digestive problems, nausea, depression, anxiety, even grief. There are things you can do to help you cope in the short run, including having someone aware of your situation who can look after you as needed, but even more importantly for the duration:\n\n\u2022 Arrange to have positive outings and experiences, things that always bring you pleasure\n\n\u2022 After your initial adjustment, taking perhaps a couple of days, make sure to see (certainly don't isolate yourself from) family and friends\n\n\u2022 Arrange to see a counselor, a therapist, or a spiritual figure\n\n\u2022 Do regular physical activity, even if minimal\u2014like walking around the block or climbing stairs\n\n\u2022 If cooking or engaging in formal meals seems like a stretch, nonetheless do maintain regular nutritious intake of food\u2014think of yourself as training for a fight or race\n\n\u2022 Remember, recall, visualize what this is all about\u2014you're not coming off your addiction for something to do\u2014you're heading somewhere, toward a different life, one that expresses who you really are and want to be\u2014have those images available for ready access\n\n_\"What if I'm not addicted to crack or heroin (or OxyContin), or alcohol dependent?!\"_\n\nIn the last section I might seem to be writing for people who have given over their lives (and all their time) to an addiction in which they've isolated themselves from civilized society. Many people who come to this book will still have jobs, families, or other daily responsibilities while facing serious addictive problems. If you are functioning in your regular roles but still anticipate disruptive withdrawal and a difficult transition and readjustment, part of your preparation will be to arrange for time off from work and\/or for people to take over what you're normally expected to do, like providing meals for your kids. There is, of course, the risk of over-preparing. This is a question no one can resolve for you\u2014including, perhaps, even you yourself. That is, anticipating great pain and discomfort that may not occur can be an unnecessary hindrance to quitting, while being unprepared for more severe withdrawal is a danger. So, always have a fallback plan in place.\n\n* * *\n\n**CASE:** Ezra was growing and wholesaling marijuana for acquaintances, mainly former co-workers he knew at the major firm where he had worked. Ezra had a family\u2014a wife and two small children. When his kids entered preschool, he foresaw the difficulties he might have conducting his business. And, so, Ezra began the laborious process of (1) cleaning up his growing operation\u2014the soil, the irrigation stones, the water hoses and outlets, the ruined floors beneath the tubs for the plants\u2014what a mess! (2) cleaning himself up from his around-the-clock pot-smoking addiction.\n\nEzra had never slept well. Indeed, his drug use was in good part aimed at alleviating his anxiety. So he anticipated\u2014and experienced\u2014quite a few sleepless nights without his drug of choice. He was concerned to be rested and focused because now that he was forced once again to get a real job, he had to concentrate on creating a resume, rekindling long-lost work skills, and reconnecting with his old work network.\n\nIt was tough going for several months. But\u2014as might be expected of someone running an urban growth operation while raising a family\u2014Ezra was smart and resourceful. He coped. After his period of readjustment, Ezra concluded, \"You know, quitting drugs wasn't all that hard.\" In fact, quitting gave him a chance to work on his life-long insomnia and to develop better ways to find sleep at night.\n\n* * *\n\n_Maintain your perspective_\n\nChildren come unhinged when they know they're going to get an injection at the doctor's office. They can work themselves up into such a panic over this impending apocalypse that they will scream and cry, anticipating the little pinch that hurts significantly less than a stubbed toe or a scraped knee. The actual discomfort is nothing compared to the terror that precedes it. Similarly, while you may be nervous about experiencing some physical discomfort, try to maintain your perspective on it, because your perception of that discomfort makes the difference between a tolerable and an intolerable situation. Also, remember that it's finite\u2014it will end. You will feel better.\n\n_Care for the whole person_\n\nThe point with Alex and Ezra is that, while your body is experiencing some physical symptoms, this is not the major part of the withdrawal experience. After all, people frequently quit addictions, only to relapse at some point farther down the road, when physical withdrawal is a distant memory. As Alan Marlatt showed through his research in his volume (edited with Dennis Donovan), _Relapse Prevention_ (Guilford, 2005), relapse occurring after immediate withdrawal has passed is the rule.\n\n* * *\n\n**CASE:** Savannah had been addicted to heroin since her early twenties. Now in her forties, she\u2014and those who knew her\u2014figured quitting the drug was impossible. Sal, a friend of many years who had always known Savannah to be addicted, was one of those who believed this to be true. As almost a chance question, he asked Savannah, \"Have you ever been off narcotics?\" \"Yeah,\" Savannah answered casually, \"I once quit for two years.\" Sal had two thoughts: \"She could quit!\" and \"Why did she go back, since it is such a misery for her to be addicted?\"\n\n* * *\n\nAs another example, peak cigarette withdrawal lasts several days, and even residual withdrawal effects not more than a month. So if you relapse, it's rarely in response to bodily readjustment due to withdrawal. Relapse is caused by psychological and life issues that both exacerbate your withdrawal and persist long after it.\n\nEzra, for example, had to cope with a quick temper that now surfaced when he had to deal with trivial issues created hourly when managing young kids\u2014anger that marijuana had warded off for him. As it does for many people, the din of an active addiction had drowned out the painful negative commentary that loops through one's mind. These are stories you tell yourself about how strange, hopeless, or worthless you are, and they can become especially loud and insistent during this period. You might, for instance, begin berating yourself for having been addicted or insisting to yourself that it's too late for you. You might feel overwhelmed by the road ahead. It's not possible to stop these thoughts from intruding, but you can diffuse their power by recognizing them when they appear and calling them what they are. For instance, \"Oh, there's that old voice telling me that I won't succeed,\" or \"My mind is running off again.\" Just be aware that it happens to us all.\n\n_\"How did I used to spend all my time?\"_\n\nIn the last chapter, I spoke of the centrality of addictions for filling and structuring one's life:\n\nDays planned around purchasing and consuming the substance or practicing the activity; fielding negative fallout (like angry co-workers, family members, and friends; mounting bills; health problems); making solemn promises to stop; remorse and guilt. . . . Yet, as painful and self-defeating as these feelings are, their predictability sustains addicts and even lends a bizarre sense of purpose to their lives. Rather than being a medical mystery, _addiction makes complete psychological sense_.\n\nTo say the least, people who are giving up their addictions often find themselves with a lot of time on their hands. You don't realize how all-consuming an addiction is\u2014how much time it devours\u2014until you're sitting there with the whole day and night stretched out in front of you, and the next fifteen minutes seem like an eternity. This is the time to indulge in some simple pleasures. Rent some movies; stock up on engrossing novels; make plans to meet with friends for coffee or breakfast; embark on a project you've been meaning to tackle, like learning to play the ukulele, starting a garden, or painting the bathroom. Plan your day and create as much structure as possible.\n\nBut, in addition, you are going to have to create\u2014or re-create\u2014a non-addicted life structure based on a larger vision of yourself. And you will have plenty of time now to concentrate on that task, which you and I will work on in the following sections of this book.\n\n_Seek support_\n\nThe Substance Abuse and Mental Health Services Administration (SAMHSA, the agency responsible for the National Survey on Drug Use and Health referred to in the previous chapter) has recently redefined recovery. In 2011, the agency reversed decades of thinking to create a \"new working definition of recovery from mental and substance use disorders\":\n\nRecovery is a process of change whereby individuals work to improve their own health and wellness and to live a meaningful life in a community of their choice while striving to achieve their full potential.\n\nSAMHSA's redefinition creates \"four pillars of recovery: health, home, purpose, and community.\" \"Purpose\" means that recovery is self-activated\u2014including finding \"meaningful daily activities, such as a job, school, volunteerism, family caretaking, or creative endeavors, and the independence, income and resources to participate in society.\"\n\nCommunity and support constitute one of the essential pillars of recovery. This is the time to begin building (and rebuilding) your personal community. In Britain (more so than in the United States\u2014go figure) a therapy measured to be as effective as the motivational enhancement that I discussed in the last chapter is called \"social network therapy\" (also social behavior and network therapy). This therapy involves finding or creating a supportive, non-addictive community and social contacts. During the immediate quitting period, you can turn to supportive family and friends; let them know how they can help. Remember Rose's mom and Alex's brother. Then there is involvement in larger communities, like Ezra reemerging into the work world, or your helping others, joining a church, finding a support group (like Rose's single mothers' group), a hiking club, and on and on. This pillar dovetails with finding meaningful activities\u2014including work, school, volunteering, family caretaking, creative endeavors\u2014that provide you with the independence and resources to participate in society.\n\nPeople Don't Really Withdraw from Love (Do They?)\n\nI was teaching at the Harvard Business School while writing _Love and Addiction_ before its publication in 1975. One of my colleagues there, who had seen an interview I had done in the _Boston Globe_ , walked by me and laughed, \"Right, love addiction!\" Yes, people become transfixed in their love affairs, sacrificing everything for them, sometimes murdering or committing suicide or tolerating ongoing abuse for the sake of what they view as a love relationship. But their chagrin, pain, and dissociation often reach highest pitch when a love affair ends. One of my most popular posts at _Psychology Today Blogs_ was \"The 7 Hardest Addictions to Quit: Love Is the Worst!\" Yes, that's right\u2014worse than heroin, cocaine, or smoking. Without repeating the arguments in my blogpost, let me reprint a comment from a reader:\n\nMy divorce has left me completely blindsided and affected every aspect of my life. It is something that I have struggled for years to get over and to this day cannot seem to move forward. It has literally destroyed so much of me and continues to take another piece day by day. I fear what the outcome will be in the end.\n\nOr, from the _New York Times_ :\n\nIn 12-step confessional style, this is what love addiction did to my life: I dropped out of college, quit my job, stopped talking to my family and friends. There was no booze to blame for my blackouts, vomiting and bed-wetting. No pills to explain the 15 hours a day I slept. No needles as excuse for my alarming weight loss. I hit bottom one sleepless night, strung out on the bedroom floor, contemplating suicide. And then I spent four months\u2014and a good chunk of my family's money\u2014in treatment for love addiction.\n\nAnd on and on. I know my colleague at Harvard would probably sneer at these. Or else you might say, \"Well, these people have preexisting psychiatric conditions.\" Yes, more or less like many other addicts. To state it briefly, people become addicted to an entire gestalt of feelings, physical reactions, and experiences. No one element can be separated from any other. Emergence from that gestalt may be earth-shattering. As I wrote in _The Meaning of Addiction_ :\n\nNeither traumatic drug withdrawal nor a person's craving for a drug is exclusively determined by physiology. Rather, the experience both of a felt need (or craving) for and of withdrawal from an object or involvement engages a person's expectations, values, and self-concept, as well as the person's sense of alternative opportunities for gratification. These complications are introduced not out of disillusionment with the notion of addiction but out of respect for its potential power and utility. Suitably broadened and strengthened, the concept of addiction provides a powerful description of human behavior, one that opens up important opportunities for understanding not only drug abuse, but compulsive and self-destructive behaviors of all kinds.\n\nChoosing Your Goals\n\nFor generations now, it's been gospel that overcoming addiction requires resigning yourself to abstaining, come hell or high water. Yet, at the same time, recovery is often punctuated with dangerous binge relapses like Amy Winehouse's. This whole sequence occurs because conventional recovery means making your addiction continue to be the absolute center of your universe by the continual, perpetual rejection or negation of it\u2014like the anorexic who used to be overweight. Life was about being addicted, and now it's about fighting being addicted, which often resembles being addicted, as some people note about the way many alcoholics use AA.\n\nEither way, the addiction is the core around which your whole life revolves. It's a grim picture, so it's no wonder so many people reject it. Even if your ultimate goal is complete abstinence\u2014which it may be, considering the nature of your addiction and your priorities in life\u2014there are more effective, empowering, and life-affirming ways of achieving it. Once you realize that addiction is not about the power that a substance or compulsion has over you, a horizon of possibilities for recovery opens up.\n\n_Self-control and free will_\n\n_Recover!_ is not a discussion of free will\u2014after all, I'm a psychologist, not a philosopher! It's about the skills and outlooks you need to recover. But the recovery field has a special angle on free will\u2014they use a term in AA called \"self-will,\" which they see as a negative. Contrary to this finger-wagging disempowerment, true recovery from addiction means reclaiming your power and free will, not giving it up. Exercising free will is not just doing what you feel like doing or acting on every whim or craving or desire. Rather, it means making choices and pursuing actions based on your values and priorities, _in spite of whims and feelings to the contrary._ Twelve-step recovery says you can't do this; I know and you know that you can. Imagine that it's the day before you're scheduled to take a certification exam. If you pass, you will qualify for a dream job that will allow you to provide for your family. You have to study and go to bed early, but you're burned out and really feel like watching all the episodes of your favorite series on CD or the Internet. Choosing to turn off the video and study is a true act of self-will, while planting yourself on the couch with a bucket of hot wings is, in this case, an abdication of will.\n\nYou can watch your series and eat hot wings another time. Delay of gratification, it's called. Its absence is central to addiction, and being able to delay gratification is often crucial for recovery. For addiction means giving in to the appeal of a simple solution, the addictive experience, whenever confronted with difficult emotions or life issues, rather than seeking out harder, long-term (real) solutions for these things. Remember, Rose couldn't confront her long-term issues and goals, and so she used meth instead. Impulsiveness\u2014yet another term for the tendency just to reach for a reward or experience\u2014has often been seen as playing a role in addiction. Remember our discussion in Chapter 2 of impulsiveness, the brain's frontal lobes, and the addicted and non-addicted siblings and their dysfunctional inferior frontal gyrus. Impulsiveness and its opposite are more than the equipment you are born with.\n\nPeople often learn\u2014or don't learn\u2014the ability to delay gratification early in life, as children. Cultural commentators have become very concerned that American children\u2014compared with those in France, for example\u2014don't learn how to delay gratification. This may be connected to the obesity epidemic in this country, among other things. Another term for this is self-control, which is kind of the down-to-earth, day-to-day version of free will. This exercise of free will takes effort. But, here's the great thing\u2014modern cognitive science shows that self-control improves with practice, and best sellers are now being written explaining this. Self-control and delay of gratification can certainly be instilled in children.\n\nAs with everything else associated with addiction\u2014indeed, with life\u2014meaning is crucial. It is when people feel that self-control is valuable and fulfilling that\u2014although it may require sacrifice at a given moment\u2014they are more willing to exercise it. Think about requiring children to dust and vacuum as chores. It works better to make them responsible for keeping an area clean and organized when completing a project or because the area is a place where they play or carry out activities. When cleaning and being responsible for an area (or the entire house) connects to their own desires and goals, the task _has meaning for them_ \u2014it is really no longer a task. Similarly, as you work your way into your non-addicted life and begin to savor its effects and benefits in areas that you enjoy and seek to improve, your motivation is reinforced and expands\u2014that is the recovery pillar called purpose.\n\nI am taking pains to make these points and to draw this distinction because the disease theory has made \"willpower\" a dirty word. Trying to develop and to rely on your own willpower seems to go against the scientific notion of the hijacked brain that we considered in Chapter 2, or the rejection of \"self-will\" by the 12-step movement. After all, relying on your own will violates the third Step: \"Made a decision to turn our will and our lives over to the care of God as we understood Him.\" This three-cardmonte switcheroo\u2014calling the exercise of free will a cause of rather than a remedy for addiction\u2014undermines success in overcoming addiction by leading people to believe that, as diseased addicts, their spirit is broken and self-direction is a path leading them back to addiction.\n\nIn fact, true recovery means shifting the balance of power _away_ from addiction and toward your own free will. Taking the focus off the substance or behavior and putting it back where it belongs\u2014on your values and sense of life purpose\u2014allows you to determine what recovery means for you. Keep in mind that the opposite of addiction is not abstinence. The opposite of addiction is intention and what you seek in your life, and there is nothing wrong with your ability to determine these things for yourself and to pursue them. Your recovery goals should represent who you are and what's meaningful to you, although you can always revisit and change your goals as you progress down this path. The PERFECT Program makes clear that your recovery is your own creation. This kind of true recovery is going to look different for every person. I use the term \"recovery\" because it's a familiar term\u2014but remember that it's also a loaded word. In fact, it might be helpful to replace it in your mind with ideas like _balance_ or _self-direction_ , and to imagine this as a process of displacing addiction with things you want that you know will improve your life.\n\n* * *\n\n**CASE:** Let's go back to the new, detoxed Alex\u2014the one who went through scary alcohol withdrawal but emerged to see his brother at the breakfast table, and then faced the rest of his life (he was thirty-two). Now what?\n\nAlong with a family (including his parents, brother, and sister), Alex had a girlfriend, Susan. He also had a job, at which he continued, only now without facing hangovers in the mornings. Susan wasn't an alcoholic, but went out many evenings with Alex, drinking far less by his side. She was younger (twenty-three), and perhaps that explained her acceptance of Alex's extreme drinking. In any case\u2014and thankfully for Alex\u2014it didn't put her off the relationship. So, when Alex told her he was quitting drinking, Susan wondered, \"How will we spend our evenings now?\"\n\nIn fact, Alex relied on Susan for much of the answer to that question. She had her own family, circle of friends, and things she did with both\u2014and on her own\u2014like going to movies, staying home and sewing, and going to the gym. Alex turned to Susan as if he was seeking a navigator through foreign territory for guidance as to what people who don't spend their nights drinking do. And she now took Alex under her wing, as much as was reasonable (he didn't begin sewing, although he did start reading while Susan sewed).\n\n* * *\n\n_Abstinence_\n\nIn regards to your addiction itself, what are you shooting for? Never to use again\u2014complete, lifelong abstinence\u2014is one goal. It is a quite difficult goal to achieve, but it may perhaps be advisable, depending upon what you're addicted to, the state of your psychological and physical health, and what is most important to you. Still, it's important to keep in mind that abstinence means _not_ doing something. Abstinence has no inherent value except as it aligns with what's valuable or meaningful for you to pursue. In other words, recovery is not a purity test, and abstinence is not the holy grail. It's important to make this distinction because recovery culture has an abstinence fetish, a belief that in order to be considered \"sober\" people must be free of all mind-altering substances, renewing their commitment to abstinence on a daily basis for the rest of their lives. And yes, this includes people in their teens or early twenties.\n\nLet's look at the word \"sobriety.\" In the real world, sobriety means not being impaired. In 12-step speak, sobriety means never taking any consciousness-altering substance, _ever_. This fixation on abstinence requires that people who recover through the 12 steps decide that their lives revolve around an empty space. Not only is that undesirable, it's unsustainable. You can't commit your life to nothingness, only to health, your goals and plans, and your belief in yourself.\n\nAs a marker of other progress rather than an essential goal in itself, abstinence is not a state of grace. If you're striving for abstinence but you go off the wagon, you have not blown your recovery or ruined everything; you do not have to \"start over.\" There is no such thing as starting over. This is your life we're talking about, not a contest. Here's an analogy: Imagine your whole life spread out in front of you like a sea of clear water. Now, imagine that you pour a bottle of red wine in. The wine will diffuse fairly rapidly and disappear into the vastness of the sea, and the impact will be absorbed. Now imagine that you have narrowed the scope to one day, represented by a single pail of water. When you pour a bottle of wine in, the water is unable to diffuse it. This is the difference between true recovery and living an endless string of one-day-at-a-time reprieves.\n\n* * *\n\n**CASE:** Alex decided to spend a night drinking again after more than six months of abstinence. He wanted to see what it felt like. Susan prepared to accompany him for the evening. And so, dressed for battle, the two went to Alex's favorite pub. For one thing, Alex didn't have to pay for a drink. All his old drinking cronies stopped by their table and ordered one for him.\n\nBut, truth be told, Alex was finding it hard to consume so many drinks. First, he didn't order anything for Susan, but passed the extras along to her. Alex ended up having five drinks, and Susan three. And it was only 9:30! Looking around ruefully, Alex indicated to Susan that it was time to go. With terse farewells to his former fellow revelers, Alex and Susan went out the door of the bar. \"Is it too late to catch a movie?\" Alex asked Susan.\n\n* * *\n\nIf you choose abstinence for yourself, make it an empowered choice, unencumbered by the neurotic trappings of conventional recovery. Choose abstinence, not because it is the only way for all addicts, but because:\n\n\u2022 It is genuinely what you desire.\n\n\u2022 You violate your values using, in the presence of, or in pursuit of the behavior or substance.\n\n\u2022 The behavior or substance is genuinely dangerous to you or others.\n\n\u2022 The substance is illegal or life disrupting in other ways.\n\n\u2022 Moderate involvement is not a realistic possibility for you.\n\nMost important to keep in mind is that abstinence serves your life plan, not vice versa. This means (1) a simple violation does not indicate that you have swerved from your plan, which you can resume instantly and completely; (2) you can revise your plan. In Alex's case, he continued to abstain, with the idea that once every six months he would go out drinking again. He did this for several years, although he never consumed on _any_ of these nights anything like the amount he used to drink regularly. Years later, he decided to quit drinking altogether. Do any real alcoholics you know follow this path? Plenty; and here's one who admitted it\u2014Christine Quinn. In a revelatory memoir she released in preparation for running for mayor of New York City, Quinn described her bulimia and drinking problem: \"By the time Ms. Quinn left college . . . bingeing and purging and drinking to get drunk were regular habits.\"\n\nQuinn entered and successfully completed rehab for bulimia in 1992:\n\nFor the first time, Ms. Quinn also examined her drinking. She arrived back in New York with a meal plan and a referral to a therapist who specialized in eating disorders and alcoholism. She cut back to drinking moderately, having only the occasional glass of wine, which she continued until about three years ago [i.e., the better part of a decade], when she stopped entirely. She says she considers herself an alcoholic.\n\nHere's a more troubling example, one that I listened to at a meeting of a recovery group devoted to abstinence.\n\n* * *\n\n**CASE:** Renee had been abstinent for six years. One night, leaving her supermarket parking lot, she noticed in the corner of the lot a bar that she knew had a fireplace. Since it was near Christmas, and her own apartment (which she shared with her husband) had no fireplace, she decided to drop in the bar. She had too much to drink, drove home, and was quickly stopped by the police, lost her license, and was unable to continue at her job\u2014which led to a divorce from her husband.\n\n* * *\n\nThis horrifying story didn't have to occur, as we will see in the relapse prevention section of The PERFECT Program. However, even taken at its worst, Renee drank too much one night in six years. She had a lot to make up for, but she didn't drink again for another four years. Getting drunk one night in a decade is about as good a record as anyone could hope for (recall the analogy of spilling a bottle of wine in the ocean). This story is not meant to make light of Renee's suffering and guilt. It is meant to put in perspective what a violation of an abstinence vow should actually mean and how it should be handled.\n\n_Moderation_\n\nIt's important to understand that addiction is a coping mechanism\u2014a destructive (but efficient) one that produces negative consequences in your life. Considering it in this way puts the emphasis where it belongs\u2014on _you_. You are the locus of addiction, not a substance, a disease, or an outside force. For a little perspective, think of all the possible substances and behaviors people can become addicted to: powerful, mind-altering drugs; milder, mood-altering drugs; dangerous or risky behaviors; recreational activities (like gambling); everyday, even life-sustaining behaviors (like eating and sex). These things are so diverse that the only element they all share\u2014besides sometimes being addictive\u2014is the human one. People are resourceful enough to make just about anything the object of their addiction. In other words, whatever you're addicted to is incidental to the condition of being addicted. Being addicted is like being malnourished or depressed\u2014it's a state you are in\u2014a condition unto itself, while your drug or behavior is just a symptom of addiction.\n\nThis is a crucial distinction because popular addiction mythology places all the emphasis on the drug or behavior itself, insisting that addicts admit their powerlessness over the thing to which they are addicted. This mythology is focused on, instead of eliminating addiction, eliminating the symptoms or the random objects of people's addictions. From this backwards perspective, lifelong abstinence is the only option, and moderation is a crazy delusion. Consider this, however: if you are no longer addicted, and you have healthy coping strategies, there is no drug that can render you helpless before it. When addiction ends, so does the compulsion to escape. The objects of your addiction remain neutral\u2014they are, and always have been, just things, behaviors, objects. They had no innate power before addiction, and certainly have none after. _Moderation is indeed possible for people who have truly recovered from addiction. You may be able to look forward to drinking a glass of wine or having a beer after work or eating a piece of chocolate cake or going to Las Vegas with your friends without fear of ruining your life._\n\nOne reason we often don't hear about people who moderate their drinking is that it happens so matter-of-factly. People usually don't make a big deal of it; it's just part of the natural evolution of their lives\u2014remember that \"more than half of those [alcoholics] who have fully recovered drink at low-risk levels,\" as discussed in the previous chapter. As a result, this common phenomenon typically takes place under the radar, occasionally popping up in a story about a celebrity. I described how New York politician Christine Quinn cut back to drinking only an occasional glass of wine, a practice she maintained for years. Less than two weeks after Quinn's story appeared in the _New York Times_ , the paper ran an interview with Billy Joel, once well known for his heavy consumption of vodka and scotch. Explaining that he doesn't \"subscribe to A.A. . . . to 12-step stuff,\" Joel reported that currently \"I have a glass of wine with a meal.\" These two stories, appearing within a couple of weeks of each other, stand for others\u2014many, many others.\n\nOne disproof of the \"frontal lobe\" theory from the previous chapter\u2014in which Dr. Drew claims that if addicted your \"brain frontality\" dies or becomes comatose\u2014is that then your brain couldn't control _any_ potentially addictive activity. Really? Thus, in his podcast with harm-reduction specialists Drs. Jaffe and Kern (harm reduction is discussed in the next section), when Dr. Jaffe said that he had had a major meth habit but now drank moderately, as well as perhaps smoking marijuana, Dr. Drew was driven to make up the Jewish exception\u2014claiming that only Ashkenazi Jews had the special genetic immunity that allowed Jaffe's feat. For the record, I know a number of non-Jewish former speed freaks who currently drink moderately\u2014including Rose. Apparently, methamphetamines are one thing, white wine and marijuana others. In any case, it's interesting to hear Dr. Jaffe describe the anxiety with which he had a glass of champagne after he had been in treatment for his addiction and thought he had to quit every kind of psychoactive substance. Many clients and others have described this apprehension to me.\n\nOf course, aiming for moderation requires self-knowledge. For instance, for some people, there is no point to moderation. There's little value in moderation for someone whose only reason for drinking is just to get drunk. Why bother? However, someone who drinks addictively sometimes, but who also has the capacity to enjoy wine with dinner or with friends, has a good reason to see moderation as a recovery goal. It contributes value to his life. Other objects of addiction may have no value in themselves. In these cases, an activity may be readily given up in its entirety\u2014like gambling. But it's not for me or anyone else to make that decision for you.\n\n* * *\n\n**CASE:** Tristan was a lifelong addicted gambler. His father had been one, and as a teenager he ran away to escape his dysfunctional home, but then started gambling himself. He progressed in his habit over decades until he married and had a young daughter. In his efforts to protect his family from his addiction\u2014in what could be termed a harm-reduction step\u2014Tristan turned his paychecks over to his wife, who allotted him an allowance. Still, a couple of nights a month, he spent all night on the Internet gambling, sometimes throwing away thousands of dollars that he and his wife planned to use to buy a home.\n\nPreviously, Tristan would quit, then edge back into gambling, perhaps lured by an online offer or ads he saw for a casino or racetrack. When he turned forty, he despaired about ever having some of the things that eluded him and his family. In addition, he was starting his own business. Tristan went to a non-12-step therapist who didn't demand that he stop gambling. During his therapy, Tristan went on several gambling binges. Finally, he told his therapist, \"I know this isn't a disease. But, whatever it is, I don't think I can control this thing. Maybe not now, or maybe ever. I need to quit.\" His therapist responded, \"Good idea. What do you think it will take for you to stop gambling entirely? Let's describe that lifestyle, its restrictions, and replacement activities. Let's make a plan.\"\n\n* * *\n\nTwo obvious points about Tristan's case are: (1) the power and meaning of his decision to abstain came from his arriving at the decision for himself, (2) his abstinence (like his urge to be addiction-free) came in the service of larger, more important goals in his life: family, career, and home.\n\nBut Tristan could give up gambling\u2014it wasn't essential for his life. Some addicts _must_ moderate, because the object of their addiction is something they cannot quit, like food, sex, or shopping. Yet, 12-step recovery has applied its short-sighted, ineffective temperance mentality to this arena of addiction, too. It does so by saying, for instance, \"You must abstain from _non-marital_ sex,\" or that one must avoid sugar, alone, of all foods. But an addiction to binge-eating cannot be cured by repeating the mantra that food is just fuel and should never be enjoyed, and that you can never have a dessert again. That's a recipe for relapse.\n\nAs to \"illicit\" (nonmarital) sex (including masturbation), isn't that a bit old-fashioned? What if you aren't married, or don't have a stable partner? Will you never be allowed to have sex, or an orgasm, again, like a monk or a nun? Nor can a sex addiction be cured by scheduling and micromanaging sexual encounters. That's like curing food addiction with an eating disorder, or trying not to think of the proverbial pink elephant\u2014all of which simply sets you up for failure somewhere down the road. The goal of The PERFECT Program is to restore quality of life, which means being able to enjoy food, sex, and necessary life experiences and pleasures in a carefree manner, as you were meant to. This will happen when you restore balance and meaning to your life and learn to live with intention.\n\nIn contemplating moderation, here are some questions for you to consider:\n\n\u2022 Is moderation a realistic option for you?\n\n\u2022 Are you addicted to something that will contribute to your quality of life if used moderately?\n\n\u2022 Would even moderate use jeopardize your or anyone else's safety or well-being?\n\n\u2022 Would moderate use be more trouble than it's worth?\n\n\u2022 What would moderation look like for you?\n\nAbstinence and moderation (or harm reduction, as we shall see in the next section) are not distinct options, and you do not have to choose one now and forever. They are very fluid approaches to pursue in your PERFECT Program; they overlap and support each other and evolve (think of Alex and Tristan). Understanding these approaches might also give you even more clarity and insight into the nature of addiction. You might, for instance, want to be able to drink alcohol normally, but don't feel confident that moderation is possible for you right now. So, you choose to quit drinking totally for the time being while working through The PERFECT Program. When you feel ready to reintroduce alcohol, you move cautiously by instituting some brakes. Or, perhaps, you are conflicted\u2014desiring abstinence, but afraid that you will be unable to give up your addiction. You might continue drinking but institute harm reduction safeguards, including drinking only in safe environments or under supervision and setting goals for yourself along the way.\n\nThere are infinite variations and possibilities. Addiction manifests differently in different people, and so does recovery. Taking what you have learned so far about the nature of addiction, the depth of your involvement, and the elements of your life that are most valuable, you need to set your goals\u2014which we'll see to at the end of the chapter. I'll guide you through this process, but since recovery is not a one-size-fits-all endeavor, it is up to you to decide what approach is most appropriate for you. Remember, nothing you decide here is set in stone. You can always reassess your goals, which Dr. Jaffe did when he started drinking moderately after quitting meth; we will now examine other examples of this.\n\n_Harm reduction_\n\nHarm reduction is a policy favored by leading experts in the addiction field. It means minimizing the damage done by addiction\u2014or any substance use\u2014and preventing its worst potential outcomes. People recover from bad nights, even bad patches and years. Some things they don't recover from. These worst outcomes\u2014like death, AIDS, accidents, and injuries\u2014must be avoided above all. As one example, many teens get drunk. We don't like this phenomenon, but nearly all these kids will recover (as you and I did)\u2014unless they have an accident. Preventing accidents by avoiding drunk driving\u2014for example, by having an arrangement that your child should call you if they have been drinking\u2014is harm reduction. Another example of harm reduction\u2014one more common for college students\u2014is to have another person nearby if someone goes to sleep extremely drunk.\n\n* * *\n\n**CASE:** Ryan was talking. \"Sybil was the most obnoxious girl in our crowd at college. I couldn't stand her! She never stopped talking, and what she said really never made sense. But, one night, I got drunker than I ever had. Sybil took me home, put me to bed, and slept on the sofa in my room. In the middle of the night, I was on my back, and I vomited. Sybil jumped up, made me get up out of my stupor, cleaned me up, and made me wash out my mouth and drink some water. Then we both went back to sleep. The next morning, we went out for breakfast\u2014on me. Later one of my friends who saw us said, 'Did you sleep with Sybil? I never thought I'd see the day!' I said, 'Oh, Sybil's okay.' And I thought, 'She's more than okay\u2014she saved my life.'\"\n\n* * *\n\nAnd, so, you should\u2014and might want to\u2014quit your alcoholism or addiction, or abstain from alcohol or another addictive substance or activity altogether. But you can't or you won't do so now. In the meantime, you must take care of yourself. For most people, drinking or using at home is safer than going out and getting intoxicated, certainly when you are in unfamiliar territory or driving. Another risk factor is using the amount (of alcohol, narcotics) to which you were formerly accustomed after a forced period of abstinence in treatment or prison. This behavior is actually encouraged by the \"in for a dime, in for a dollar\" message that one drink is as bad as\u2014the equivalent of\u2014an all-night bender. Different substances carry with them a variety of risks in different situations\u2014overdose, accidents, violence, withdrawal, illness, and communicable diseases\u2014against which you must exercise care and vigilance.\n\nThe key example of harm reduction in the drug field is the provision of clean needles to addicts, which reined in the spread of HIV and hepatitis among intravenous drug users and those who come into contact with them in countries\u2014virtually every Western nation\u2014that adopted such programs. Despite the evident common sense of harm reduction efforts, black-and-white thinking has stymied its introduction into public policy in the United States. And, so, after the initial wave of the AIDS epidemic among gay men, America became the leading economically advanced nation in numbers of new HIV cases, especially pediatric AIDS cases spread from parents to children, as the epidemic moved from homosexual men to IV drug users, often in inner cities. Tragically, this has led\u2014and continues to lead\u2014to thousands of unnecessary deaths. The tragedy is exacerbated because research has shown that, not only does the provision of clean needles prevent HIV from spreading, it also brings many addicts into contact with health care providers through whom they then progress to quitting their addiction altogether.\n\nAlthough America's abstinence fixation and perfectionism prevent us as a nation from implementing harm reduction wholeheartedly for narcotic addicts, no one is stopping you from implementing harm reduction techniques in your own life. So you must take steps to stop things from getting worse due to your addiction and to prevent incurring any permanent damage. This may mean cutting back and taking other safety precautions, even when your best goal might be to quit altogether. I don't want you, like Amy Winehouse, who died drinking heavily after leaving rehab, to kill yourself for an unachievable (for now) ideal.\n\n* * *\n\n**CASE:** Lorraine was a raging alcoholic for many years. At her worst, she went on binges, disappearing overnight, where none of her family knew where she was. Her husband took to hiding the keys to her car. She thought about suicide. When friends suggested AA, she spat out a \"no.\" Those closest to her thought she was a goner, another casualty of alcoholism.\n\nThat didn't happen to Lorraine. For a combination of reasons\u2014family support, a job she liked, just plain self-regard (or self-will)\u2014she bottomed out without hitting bottom, and pirouetted gradually upwards. As one key example, although she had regularly lost jobs over the years, now she enrolled in an ambitious professional graduate school program\u2014and passed her first two years with flying colors!\n\nBut Lorraine didn't desist from drinking, or even from periodically overdrinking. What she _did_ do was cut out the stupid drunk episodes. She didn't drive, or leave the house, when drunk. Instead, when she had too much to drink, she called her closest friend, Ellen.\n\nAt first Ellen was really troubled by these calls, thinking, \"Am I enabling her to continue drinking, and to be an alcoholic? I was concerned for a while that she was _never_ going to get better, except that she _did_ get better.\"\n\nBy chance, Ellen read about harm reduction and so learned there was such a thing as reducing really dangerous drinking and its life-threatening consequences. Only then could she relax and help a friend whom she loved, and who continued to improve.\n\n* * *\n\nAmong the myths of addiction is that alcoholics and other addicts can't control their consumption once they have begun drinking and using. Study after study has shown this to be false, that not only will alcoholics and others control themselves in specific circumstances, but that\u2014when they instead consume to the point of intense intoxication\u2014this was not an unintended consequence but their plan from the get-go. Think, for example, of rules that require people to go outside their work sites in order to smoke. Objections were raised that people couldn't limit and control their addiction that way throughout the workday, given the tension that accompanies many jobs. In fact, virtually en masse, even the most committed smokers have adapted to this requirement. We (you and I) will make use of this collection of facts and information when we plan your triage and relapse prevention techniques farther along in your PERFECT Process.\n\nThere is a larger myth: that anything but abstinence is evidence of denial or self-delusion and that you really can't make any headway in fighting your addiction or improving your life without instantly quitting forever. This purity fetishism has prevented many addicted people from making the positive changes in their lives they _are_ capable of (as Lorraine did), and has prevented friends and family (like Ellen) from helping them make changes that might save their lives or the lives of others or get them started in the direction of complete recovery. No matter what your ultimate goal, or whether you feel ready to leave your addiction behind, you can begin making improvements in your life immediately.\n\nHarm Reduction Exercise\n\nHave a look at your Addiction Self-Assessment Questionnaire, and review your answers to question 5, \"How does addiction impact your daily life?\" While you read your answers, ask yourself if there are changes you can make right now that will minimize the impact your behavior is having in any of these areas. A change might mean altering a pattern\u2014for instance, choosing to smoke outside, away from family members or pets\u2014or it might mean incorporating something new into your life, like a daily walk. Start by focusing on changing one thing. For example, you don't have to stop drinking to stop driving drunk.\n\n_Make a list of doable changes you can implement immediately that will orient you in the direction of your goals_\n\nDecide which changes you'd like to make right away and begin. It takes time for new habits to stick, so don't consider yourself a failure if you're not consistent right away. Just keep correcting, as you do with your car's steering wheel. Use your PERFECT Journal to track your progress.\n\nGOALS WORKSHEET\n\n**1. Long-Term Goals**\n\na. Visualize your ideal life and write about it in as much detail as possible. You might describe what a typical day of freedom looks like, for example.\n\n**2. Short-Term Goals**\n\nb. On one line, name three areas of your life that are suffering because of your addiction and, under each one, list some possible changes you can make right now to spark improvement in those areas.\n\nc. Read over your options\u2014some of them will be ambitious and some will be practical. Choose the one change from each list that seems most doable to you. For instance, if you are sedentary and concerned about your health, choosing to train for a 5K might sound inspiring, but a more realistic goal might be to start walking three times a week.\n\nd. Now, under each of your choices, make note of things that will help you achieve these goals. To continue with the example above, what would you need to begin walking? A pair of sturdy but comfortable shoes? Some motivating music queued up on your MP3 player? A walking schedule? A walking buddy? A dog (you can always borrow a neighbor's, and your neighbor will thank you)? Begin gathering your resources.\n\ne. Set a day to start implementing each of these changes, and set up a tracking system. You can use a calendar, a daily checklist, or your PERFECT Journal. There are even websites out there (like ) that help you set goals, track your progress, and connect with others who share your goals. A free online calendar, like Google or Yahoo, will allow you to send reminders to yourself.\n\nf. Remember that making these changes points you in the direction of true recovery. You are aligning yourself with your values. If you miss a day or slack off, just pick the ball back up. Every moment is an opportunity to make a positive choice.\n\n**3. Mid-Range Goals**\n\ng. Consider the journal entry you wrote on your vision for yourself, and make a list of goals you will need to meet to actualize your vision. For example, if you see yourself earning a degree, you will need to begin researching programs and requirements. Do you have to earn your GED or take the GRE?\n\nh. Are there things you can do right now to begin preparing? If not, when would be a realistic time to begin? Write down that date.\n\n**4. Addiction Goals**\n\nTaking all your answers into consideration, what is your ultimate goal in regard to the actual substance or behavior you are addicted to? What is the best way for you to achieve that? For instance, if you are aiming for abstinence, is it more realistic _for you_ to taper off, implement harm reduction methods, or go cold turkey? If you are aiming for moderation, is that a long-term goal? If so, how will you handle your addiction in the meantime? Compose a plan for yourself now, listing your addiction goals and the avenue you want to take there. Remember, you can always go back and revise as you gain clarity about yourself and your values. You are not doomed by your biological destiny\u2014or anything else\u2014to remain the same person you are now forever.\n\n* * *\n\n**CASE:** The rabble-rousing Irish actor, Richard Harris, came within an inch of snuffing out his life due to his cocaine addiction and alcoholism after he achieved early stardom in the 1970s. By the late 1980s, although he had survived his addictions, Harris's career had not been so fortunate, and he hadn't made a movie in years. But Harris began a concerted effort to be cast in the 1990 film _The Field_ , for which he received an Academy Award nomination, and his career was rekindled, including parts in _Unforgiven_ , _Gladiator_ , and, most notably, the role of Albus Dumbledore in the first two Harry Potter movies.\n\nHaving made it by this time to his seventies, Harris had calmed down considerably. In an interview for _People_ , Harris described resuming drinking late in life. First he described how the Dumbledore part had made him a hero to his grandchildren. And, then, he told about having a Guinness at the local pub every now and again, saying his relatives wouldn't believe it knowing he was above ground and wasn't enjoying the national beverage. Think he would blow it at this point and ruin his grandfatherly image? Apparently, that wasn't a possibility. And, so, Richard Harris died non-abstinently, but without resuming his addiction to substances.\n\n* * *\n\nBeing human means that you are a creature in flux, that you always have the potential for change, when you are in the right place and when your personal signs tell you.\n\nMoving Forward\n\nYou did a lot of challenging work in this chapter, exploring your life from several different angles and delving deeply into areas that might not have seen the light of day in a while. This is an enormous accomplishment, and you should take a moment now to congratulate yourself. You have compiled a valuable store of information. At this point, you should have:\n\n\u2022 A realistic assessment of your addiction\n\n\u2022 An understanding of how addiction impacts your life\n\n\u2022 A (re)collection of the things that bring meaning and value to your life\n\n\u2022 A vision of your life, free from addiction, that aligns with your values\n\n\u2022 Short- and long-term benchmarks, guiding you toward your vision\n\nRemember that your trajectory will be fluid. You might take a few missteps or reevaluate your goals, so it's important to broaden your scope to see that\u2014in the big picture\u2014your momentum is forward. In the next chapter, you will begin building the foundation of your PERFECT Program by rediscovering and fortifying your core self to take charge of your life.\n\nLET'S GO!\n\n* Caution: I am not recommending that people undergo medically unsupervised detoxification the way Alex\u2014or Rose (meth)\u2014did. See note 1 for a discussion of alcohol withdrawal.\n\n*In these extreme cases, particularly involving hypnotic-depressants (especially alcohol and benzodiazepines), medically supervised detox is a wise option. If you have any concerns about this, please consult with a doctor who is experienced in this area, and who is not in AA himself or herself (unless they are capable of separating themselves from their personal experience). Under any circumstances notify someone close to you about your plans, and in extreme cases arrange for them to stay with you. See note 1 for a discussion of alcohol withdrawal.\n\nCHAPTER 4\n\n_Pause_\n\nMindfulness\u2014Learning to listen to yourself\n\n* * *\n\n**CHAPTER GOALS**\n\n\u2022 To learn to distinguish between addictive and healthy urges\n\n\u2022 To recognize options and crossroads\n\n\u2022 To activate your free will\n\n\u2022 To begin a practice of mindfulness meditation\n\n**Purpose:** This chapter helps you develop the skill of mindfulness, which means paying attention to the world and to yourself, including your addictive urges, so that you can create the space in which to recognize your addictive cravings, reconsider your options, and make life-affirming choices.\n\n* * *\n\n* * *\n\n**CASE:** Ozzie had smoked four packs of unfiltered cigarettes a day ever since he was eighteen. Now forty-two, he had inhaled quite a bit of nicotine as he fixed televisions over that quarter century: \"My hands were a filthy yellow I could never wash out,\" he said. Ozzie was a union activist, a shop steward, so that it was his job to stand up for fellow workers when any got in trouble. Ozzie believed in the labor movement and resolutely defended the rights of the working man against corporations. In retaliation for these efforts, Ozzie believed, the local management of the large corporation that employed him sent him to the worst parts of the city to repair TVs.\n\nOne day, while having lunch with a group of fellow workers, Ozzie went as usual to a machine to buy cigarettes. It was the early 1960s, and the price of a pack had just risen from $.30 to $.35, which one of Ozzie's fellow employees kibitzed: \"They could raise the price to a dollar, and Ozzie would still pay it. The tobacco companies have Ozzie by the ________.\" Ozzie responded, \"You're right. After this pack, I'll never buy another cigarette or smoke again.\" And he never did, until the day he died\u2014fifty years later.\n\n* * *\n\nDistinguishing Yourself from Your Addiction\n\nHave you ever been in the middle of a heated debate with someone, and halfway into your righteous, irrefutable argument, you realize in a flash that you are wrong? What do you do? If you're like most people, you'll finish the sentence the way you started it. For some reason, that instant of clarity just isn't enough to stop you in your tracks or make you shift gears. Still, you heard it\u2014that gentle, compelling voice that sends you signals and information from some deep, still place in your mind\u2014\"you're wrong.\"\n\nThis voice seems to assert itself out of nowhere. It's like a whisper that has the power to break through a trance, or like a flash of lightning that exposes the edge of a cliff just before you step off. Whatever you call this voice\u2014God, conscience, life force, inner child, authentic (or true) self, wise mind, instinct\u2014it presents you with a window of opportunity to exercise your options, even when you feel like you're riding a rocket train to hell.\n\nAs you know, hearing that voice and heeding it are two different things. In the first chapter, we witnessed Rose reject and ignore that voice time and again. The voice is just not as compelling or demanding as the surface noise: the repetitive, negative chatter that has created well-worn grooves in your mind and body\u2014your addictive cravings, compulsions, and habits. Perhaps you've experienced being zoned out in front of the TV or the computer, deeply engrossed in the flickering images and barrage of junk information, when out of nowhere a window opens up in your mind and a vista of options appears: \"I should get up and walk the dog . . . pick berries . . . call a friend . . . read a book.\" You've probably heard some variation of this old joke: _I suddenly got the urge to exercise, so I sat down and waited for it to pass_. When that window of opportunity opens, we tend to do just that: hang tight and then reimmerse ourselves in the trance.\n\nIt can feel as if there are two of you in your own mind: One of \"you\" is being led around by the nose, while the other is watching. One is in thrall to urges, battered by incessant demoralizing beliefs and thoughts, including that your addiction is irresistible, while the other looks on in wonder and protest. When you ask yourself, \"What the hell am I doing?\"\u2014a question everyone asks from time to time\u2014this is one of your selves questioning the other. This invisible interchange _proves_ that you are _not_ your addiction.\n\nEveryone knows such conflicts. No one is in perfect alignment with their best instincts or values all the time. But many people are able to correct course to improve their alignment either naturally or intentionally. Consider overworked parents who put in long hours in order to support their families, but who eventually realize that the time they spend away from home and family betrays their primary purpose. So they make changes in their work schedules in order to honor what they truly value: spending time together as a family.\n\nWhat is unique when you are addicted, however, is that the hammering voices, urges, and cravings _overwhelm_ your deeper voice. You have built a barrier, a screen, in the channel of communication, and continuing to act on your addiction serves to reinforce this blockage. Being addicted is like existing in a frantic state of patching and mending the screen between your authentic self and your addicted self. It's as if that screen separating your two selves were the only thing keeping you alive. But what's keeping you alive is your authentic self. The good news is that, no matter how much patching you do on the screen, the voice of your authentic self can't be extinguished. It remains unaffected by the racket your addicted self is making and continues to press to escape from behind the screen.\n\nIf you have ever enjoyed playing in the ocean, then you know what to do when a huge wave is about to pummel you: You dive under it, because the water below remains still, as if nothing is happening under the tumult. It is amazing how peaceful it is down there when that powerful force is crashing overhead. If you were the ocean, your true self would reside in the calm waters under the waves.\n\nThese truths about the dual self, the true self, the trance, and conflicting inner voices are timeless. Ancient spiritual traditions from all over the world, along with modern psychology, continually return to this phenomenon. In this chapter, I introduce you to your two selves in a very basic way, which you can filter through your religious faith or understand as simply a mechanism of human nature, as you see fit. I bring these concepts into the realm of addiction because they are on stark display wherever an addiction has staked its claim. It may help to think of the two voices\u2014addiction and true self\u2014as your two hands. Addiction is like the dominant arm and side of your body that respond preemptively to the tasks confronting you. The process of overcoming addiction is like deliberately developing the skill and strength in your other arm so that it can instead assert control. As your true self becomes stronger and more adept, your addiction loosens its grip, allowing your true self to take charge.\n\nAt this moment you may have some very negative beliefs about yourself. You may believe that your true self is somehow corrupted or deviant. You may think that you simply do not have an identity outside your addiction\u2014that you are not distinct from it. You may believe that you have behaved in ways that disqualify you from positive participation in society, or that any engagement with the world beyond your addiction is a tedious masquerade. I acknowledge those beliefs and feelings now as you venture into this chapter; I will not direct you to ignore them or get over them. The purpose of this chapter is to guide you toward an understanding of this inner dynamic, to help you recognize the different voices that are competing for your attention, and to teach you how to choose where you place your attention, which voice you heed. I will also offer you exercises and practices that will help you differentiate one voice from another. You can start the exercises immediately\u2014at least contemplate those listed at the end of the chapter.\n\nMoments of Grace\n\nI've discussed how 12-step recovery and its proponents view addiction as \"self-will run riot\"; this book takes the opposite view: Authentic free will that springs from your own already healthy core is the engine of your recovery from addiction.\n\nLook at it this way: the very act of seeking addiction treatment\u2014indeed, reading this book!\u2014is evidence that your healthy life force has asserted itself. You made a decision based on your best instincts and desires for wellness and acted on them. This simple, obvious truth undermines the foundation of the standard recovery model, which requires you to embrace the idea that you will always make self-destructive decisions when left to your own devices. So let's step briskly over this recovery mythology to explore how you can begin deliberately moving in the direction of true recovery.\n\nInstead, let's think about _your power to control your destiny, your mindfulness_. To remind you, as I said in the introduction: mindfulness\u2014which is both a Buddhist and a psychological concept\u2014is the ability to focus your attention on the present moment. The benefits of mindfulness are being actively pursued in medicine for a range of medical and psychological conditions. But mindfulness is particularly relevant to addiction. Being fully aware of and noticing what you're doing strengthens your ability to surface the key elements of your addiction\u2014your motivation, your situation, your needs, and your ability to make alternative choices. You can improve this ability as you can any mental or physical capacity, by learning about and practicing it through mindfulness meditation, which brings your attention to your immediate sensations. I provide mindfulness meditations throughout this book, beginning with a basic mindfulness meditation primer, following in the exercises with a description of \"user-friendly mindfulness meditation\" that you can practice by choosing meditation options that feel right for you and your situation.\n\nThe idea of mindfulness as living in the present can be oversimplified as \"living for the now,\" as in \"We're all gonna die, so let's get drunk (stoned).\" On the contrary, the balancing perspective of psychological mindfulness is consideration of how what you're doing impacts your life now and going forward. Mindfulness is awareness of the full reality in which you are situated, not a blocking out of awareness.\n\nThink of a moment recently when you were about to mindlessly light a cigarette or pour a drink or eat some chips or place a bet. Have you ever paused in this moment? When, just for a second, it seemed as if you were at a crossroad? _Why am I doing this? I don't have to do this. I don't want to do this._ Perhaps you looked ahead to the consequences, the impact the addictive action would have on the rest of your life, and your resulting feelings (shame, etc.). But, then, perhaps you automatically repressed these thoughts and continued with what you were doing. After all, there are also consequences to taking the road less traveled, the non-addictive choice: You will have to acknowledge your responsibility, which is often painful. You will have to acknowledge your power, as well, which can be overwhelming. You will have to find something else to do with the time you might have spent lost in addictive behavior. You will have to feel whatever difficult emotions you were about to suppress: boredom, grief, or fear. You will have to face the responsibility for the choices you have made or avoided, like strained family relationships or financial or health problems that are a result of your addiction. And, if you listen to that voice just once, won't it prevent you from ever being able to pursue your addiction in peace?\n\nThe pause can be a pivotal moment\u2014it offers the chance for a shift in balance, when your deepest self breaks through the haze of your addiction, interrupting the momentum that often seems beyond your control. Recall from Rose's story how she would experience a moment of revulsion and conflict every time she injected herself. When you pause this way you are being presented with an opportunity to honor your true self. It's a _moment of grace_.\n\nThe word \"grace\" has many connotations, both religious and secular. In _Recover!_ , grace describes those moments when you hear your true voice. In these terms, a moment of grace is the sudden awareness that you are at a pivotal point; it is a vision of your ideal life, an opportunity to make a decision and act with free will, to pursue your true, healthy motivations. A moment of grace is a period or place in which you present yourself with options, when the addictive busywork, the repetitive patchwork of your life, is suspended and you see yourself from a clear vantage point\u2014not from the outside, but from the inside, from the calm under the waves. It's a chance to move your life scales out of the balance they are now in\u2014to tip them and shift the weight to the _positive, healthy arm of the scale_.\n\nThese moments may seem to happen accidentally, as they did for Rose and Ozzie. For Rose, it occurred when she dwelled on the impact of missing her daughter's birthday party. It made her feel as though she were no longer her child's mother. As for Ozzie, hadn't he noticed his nicotine-stained hands any time in the previous twenty-five years before deciding to quit smoking that day at lunch? Or Dori, in Chapter 2, who quit drinking when she saw several haggard women barflies and imagined herself as one of them\u2014hadn't she ever seen the signs of aging due to her heavy drinking and smoking before she reached her thirties? What caused all of them to see themselves as though from their mind's eye?\n\nWhether you choose to act on any given insight\u2014to make changes\u2014may also seem inexplicable. You might ask yourself why Rose didn't quit _in the first place_ , rather than miss her daughter's birthday party, or why she didn't avoid all of the steps that _led up_ to that moment. Why did she have to stew on that experience afterward\u2014one which, after all, she chose? It seems as though she needed to experience that painful moment as a message from her own heart, even though she hadn't used similar previous internal communications to elevate herself. Instead, they had caused her to berate herself, giving her more reason to use.\n\nWhile these moments can seem fleeting and illusory, The PERFECT Program helps you use them as the foundation of permanent changes you will make in your life. When your true self emerges, however briefly or quietly, this is your opening for change. As you learn to recognize and build on these instances, your core values and life purpose will become stronger, louder, more assertive, while your addiction becomes _less_ compelling, _more_ incompatible with what's important to you and, finally, _irrelevant_ , indeed, offensive, to your life\u2014as it did in the second half of Ozzie's life, and for Dori, who has become an advocate for people seeking to quit addictions on their own.\n\nShifting the Balance\n\nSometimes, the natural processes of maturing, taking on greater responsibilities, and finding meaning in life combine to make self-destructive behavior impossible. For example, an alcoholic might completely stop the dangerous practice of driving drunk once she becomes a mother. Now that her own children are in the back seat, she rejects that reckless behavior in her gut. The option of doing such a thing is permanently off the table, even if her addiction to alcohol persists. This mother experienced a significant natural righting of course when her behavior became incompatible with what she truly valued. This change in her driving habits might eventually provide her with the foundation to make further permanent changes in her life, including giving up her addiction, as becoming a parent does for innumerable addicts.\n\nMany of us live in a state of conflict or despair, eaten up by the knowledge that we are violating our core values, but unable to find the commitment or will to change course. As you may know through personal experience, a moment of grace will not be illuminated by a sunbeam from heaven. It's usually fleeting, and comes hand in hand with self-recrimination. But its ambivalent nature does not mean that the choice won't eventually be clear, or that you do not have the power within yourself to change. Nor does it mean that this voice isn't already influencing you in positive ways, even if it is not strong enough to revolutionize your life in one fell swoop. Being able to recognize when your healthy self is asserting itself is the first step toward shifting the balance.\n\nPerhaps Rose would have emerged from her trance sooner if she had been aware of the process occurring within and had been able to direct it intentionally. Remember when Rose began injecting meth? She felt acute shame and disgust each time she did so, which reinforced her belief that she was different\u2014a completely lost soul who had to surrender herself\u2014unworthy of attempting to live a productive life like a \"normal\" person. Mainstream recovery wisdom told her that she actually _was_ different, so it's no wonder that she would immediately adopt such a hopeless perspective at times like this.\n\nHow much more empowering it would have been for Rose to recognize her inner turmoil as evidence of something positive about herself rather than as something broken!\n\nThe unease Rose felt when shuttling her daughter off so that she could be alone with her drug, which never failed to arouse her deepest values, caused her emotional discomfort because she was able to feel just how far off course she was. Awareness and understanding of this dynamic would have allowed her to see this discomfort as a positive sign, a signal that her behavior was betraying her truth. The _only_ way for her to quell this dissonance was to change her behavior in line with her values.\n\n**Finding Your Mindfulness**. Now that you are aware of your inner voice, you can try an experiment: The next time you find yourself pausing before or during an addictive behavior, turn your attention to that voice and notice the options it presents to you, while acknowledging the emotions you are experiencing. This is a simple act of mindfulness, in which you consciously\u2014even if just briefly\u2014extend the duration of that pause by focusing on it. Draw it out and sit with the discomfort as long as you can, even if you ultimately turn back to your addiction. Do this exercise whenever you have an opportunity.\n\nPhil (whom we met in Chapter 2) had begun smoking at thirteen and had tried repeatedly to quit\u2014succeeding for a few months two times, with a nicotine patch and nicotine gum, each time relapsing. At age sixty-nine, he awoke from his heart bypass operation, following his second heart attack, to see his lovely, thirty-six-year-old daughter Cynthia hovering over him. \"Can you get me a cigarette, Cynthia darling?\" he asked, as he had so many times before. \"Daddy,\" Cynthia responded, \"if you smoke another cigarette I'll never speak to you.\" Phil lived fourteen more years and, like Ozzie after his moment of truth, never smoked again.\n\nBoth Ozzie and Phil are confusing for those brain-hijacking theories of addiction I reviewed in Chapter 2. In one theory, addiction specialists explain how, once the body becomes accustomed to a certain cellular nicotine level, it is impossible for the person to tolerate falling below this level. So how could one sentence cure Phil and Ozzie? For these two addicts\u2014safe within the social acceptance given smokers in their life-times\u2014the crystallizing of their values by a seemingly stray comment in retrospect makes sense.\n\n* * *\n\n**CASE:** Wilson was born considerably later than Phil and Ozzie\u2014almost three-quarters of a century later\u2014although his life overlapped with both of theirs when _he_ began smoking as a teenager. A painter, Wilson didn't fit the image many had of the carefree artist. He was conscientious and worked diligently both on his paintings and on jobs he held to put himself through school. In fact, Wilson tended to be anxious and to overworry his life.\n\nSo it seemed Marie, a carefree fellow artist he met, was a good match for him. Aside from their opposite dispositions, Wilson and Marie shared many values. They also both smoked. Then, suddenly, Marie quit (she had never been a heavy smoker). But Wilson persisted, even though Marie's example reminded him daily that he didn't really want to continue his addiction. As they reached their early thirties, the couple decided to have a child, and Marie became pregnant. Wilson quit smoking.\n\nWhile talking on the phone to her mother in another city, Marie mentioned casually that Wilson had quit. Her mother exhaled a loud \" _ThankGod!_\" Marie responded, \"I knew Wilson would never smoke after we started having children. Everyone knew he'd be a devoted dad.\"\n\nWilson, who was sitting nearby in their small apartment, heard his mother-in-law's first thankful prayer through the phone, but nothing more from her end. He shrugged inwardly. He was nonetheless proud that his wife had such confidence in him, which he had proved correct.\n\n\"How's your mom?\" he asked Marie.\n\n* * *\n\nEx-addicts like Ozzie and Phil can point to a precise pivotal moment of grace when a sudden realignment took place. Others' moments aren't so precise. Wilson's decision was a clear and necessary development in his life that he wouldn't ignore. Rose, on the other hand, circled back on her moment after she failed to heed it initially. Ultimately refusing to accept that she was no longer a mother\u2014even as she hadn't been acting like one for some time\u2014Rose finally rebelled against her addiction. The birthday party represented a flashing sign that she was crossing into territory where she refused to go. Wilson quit because he couldn't, in this day and age, imagine himself as a smoking father. Phil quit smoking when his daughter made him choose between her and his cigarettes. She spoke directly to his deepest self at just the right time and made an offer he couldn't refuse. Ozzie quit when a teasing comment from an acquaintance shifted his perspective, allowing him to see how his dependence on tobacco companies clashed with his pro-labor principles. Ozzie had never tried to quit before, unlike Phil, who had tried many times, and Wilson, who worried about quitting long before he did.\n\nThese examples demonstrate different ways people have aligned with their deeper selves. But all of these people, when they have overcome their addictions, have a reason that springs from a deep well of meaning within them. Reading these stories may make you worry, even despair, that _you_ are different from these happy ex-addicts\u2014that _your_ addicted self is stronger, more insistent, unconquerable. \"You,\" your addicted self whispers in your head, \"are so far gone that even loving your child isn't enough,\" as it said to Rose. \"What _is_ the matter with you?\" Perhaps you cannot think of _anything_ that would give your life meaning or satisfaction beyond your addiction.\n\n**Mindfulness Reflection: Meet Your Addicted Self.** If you are experiencing discouraging thoughts about yourself after reading these stories, please take the time now to acknowledge these difficult feelings and thoughts. There is no need to dwell on them, because we will address them fully in the next chapter. Accept and regard them with curiosity and the recognition that you will turn your complete attention to them soon.\n\nFor now, it is enough that you accept two things: (1) When you experience a \"pause\" in the momentum of your addiction, your inner wise mind is asserting itself; (2) When someone overcomes an addiction, it is because a shift in balance has occurred that aligns their choices with their deeply held values and purpose. And, before we go any further, you must keep this in mind\u2014Ozzie and Phil became ex-addicts only after years of active addiction. Ozzie was heavily addicted for twenty-five years, Phil for five _decades_. Dori drank heavily for two decades, stunting her adult development. And Rose gave away her _child_. So you are not the worst addict we will encounter in _Recover!._\n\nThat you can recover despite the length and severity of your addiction has been shown time and again by smokers and other addicts. Following the 1964 Surgeon General's Report labeling cigarettes as cancer-causing, it seemed like only the worst, most addicted smokers would continue their addictions. A National Cancer Institute monograph, _Those Who Continue to Smoke_ , asked, \"Are [residual] smokers less likely to quit now than in the past?\" What they found: \"Surprisingly, none of the papers provides compelling evidence that this is the case.\" So, no matter how badly addicted you are, for no matter how long, you can quit. \"Perhaps most provocative, however, are NHIS (National Health Interview Survey) data showing those aged 65 and over and 45 to 64 have the lowest rates of current smoking prevalence and highest quit ratios.\" That is, even when older people remain smokers after others have quit, they are _still_ more likely to quit than younger smokers. I believe this is due to people's (yes, even longtime addicts') sense of their mortality.\n\nHitting Bottom?\n\nDo Rose, Dori, Phil, Ozzie, and the other addicts whose lives we have glimpsed all demonstrate the phenomenon of \"hitting bottom\"? (Wilson clearly does not.) This is another piece of recovery mythology that says that only when addicts reach the absolute nadir in their lives can they possibly quit. Hitting bottom is supposed to be a do-or-die crossroad, a point at which things cannot get worse, so they have to get better. Often, people in the recovery world explain away an addict's failure to stay on the wagon by claiming that this person has not yet hit bottom\u2014that they have to keep plunging powerlessly to ever-deepening depths of humiliation, danger, and self-betrayal. Wow! Can you see how this vision of recovery actually encourages the _pursuit_ of greater degradation? Because it is only at the lowest point of existence, when the alternative is death, that you will finally surrender and work the steps. What a grim, terrifying scenario this is! It is also a complete fantasy, starting with Wilson and many addicts like him who simply refuse to go down that route.\n\n\"Hitting bottom\" in the recovery industry is simply a term used to shift the goalposts. There is nothing scientific, or even anything specific, about it. \"Bottom\" cannot be defined or pinpointed. If you die in a gutter, without seeking recovery, it shows that you have a really \"low bottom,\" that you just didn't get far enough down to reach out. And if you quit your addiction, even if nothing horribly bad has happened, then you have a \"high bottom.\" And what about the many people for whom nothing in particular has actually happened when they recover\u2014what \"event\" caused Ozzie, a shop steward and heavily addicted smoker, or Dori, an attractive woman and serious alcoholic, to quit?\n\nAside from exposing it as logical nonsense, I believe it is even more important to reject this crazy notion of hitting bottom on the grounds that it is irresponsible and dangerous. If you believe that you must hit bottom before you can recover, then you _have to_ pursue the scorched-earth policy of self-destruction that can be fully demonstrated only by bankruptcy, homelessness, communicable diseases, driving accidents, rape, prostitution, prison, brain or liver damage. . . . In fact, when you think about it, unless you are dead, things can always get worse. And, that worse things await you if you don't quit is actually a helpful insight when you consider it from a non-12-step perspective. You may be mortified by your position or your behavior, but even from the depths of depravity, you can always descend even further.\n\nLet's cut ourselves loose from this therapeutic nightmare. The truth is that as long as you can say to yourself _this is not what I want for myself_ , recovery is always possible. However low down you are or are not, you can choose to extricate yourself from that mess just as readily as\u2014more easily than\u2014you can end up at the bottom of the dung heap with your last gasp of life. Because there is no such place as \"the bottom.\" The directive to hit bottom is actually an instruction to _imagine_ what for you would be the worst thing in your life, to plumb the dark pit of your soul. But it works only if you regard that image as an elevated moment of grace\u2014a sign to look up instead of down. As sports psychologists teach people, you will head in the direction that you look _toward_ and fulfill the goals you visualize for yourself.\n\n_In short: There is no reason you must find your lowest low in order to recover. You do not have to live your worst nightmare in order to discover what is truly important to you. You can start wherever you are._\n\nIt is true that many people make a drastic change in their lives when they find themselves shocked or deeply ashamed of their own behavior. Sometimes, your first instinct is to suppress the pain by curling up and sinking deeper into your addiction. Other times, these feelings inspire a radical realignment. Rose, for instance, regularly received warning messages from outside (school, parents, work) as well as from within herself. Although, given the strong undertow of her cravings, she didn't act on these messages for some time, they nonetheless manifested in her as revulsion, regret, shame, and fear\u2014and sometimes also as a promise to herself to quit or a brief feeling of inspiration and determination.\n\nRose did not hit bottom when she missed her daughter's party. Among her low moments, this doesn't stand out as the lowest. For instance, it couldn't be considered worse than sending her daughter to live with her parents, or beginning to inject meth, or watching herself deteriorate physically, or any of the other degrading episodes she had grown accustomed to. So why did a missed party trigger a shift, when having to make a choice between her addiction and her daughter hadn't been enough to make her change her course? If missing the party wasn't Rose's absolute, do-or-die bottom, then what was unique about that situation?\n\nRose's moment occurred when she perceived the difference between what she truly valued and where she was actually headed in a way she finally could not ignore. The missed party signaled a _person she would not let herself be_. Just as Ozzie could not be a capitalist stooge, or Wilson and Phil could not bear to see themselves as unloving fathers when that image inescapably presented itself. Or think how once, after one long bout of heavy drinking, Dori was hospitalized near death, and her mother lay in bed grasping her to say good-bye. But that didn't make Dori quit. Yet imagining an old-hag version of herself\u2014the vain Dori exercised and dieted religiously\u2014did. Likewise, having seen the dark place of a mother who abandoned her child, Rose couldn't ignore her most dearly held value in order to enter it. Or, more accurately, to enter it and to remain there. After all, whatever smoking signified to Ozzie about being captured by the capitalist system, he had been enslaved there twenty-five years before he leaped out one day like a cat from a hot tin roof.\n\nIntentional Alignment\n\nAside from the fact that all the people in our stories demonstrate how overcoming addiction begins with an internal shift in balance, they appear to have another element in common: circumstance, even accident. Some-how\u2014with Phil, or Ozzie, or Dori, or Rose\u2014either they were shocked out of their addictive trance by a chance event or they experienced a sudden or subtle mental shift that they couldn't pinpoint. It is tempting to believe that none of these people had control over the positive changes in their lives any more than they had control over their addiction. And they are representative of a legion of people who have gone through similar experiences. It may seem that the shift was something that happened _to_ them and that they were lucky or blessed by some mysterious force. You must remember, however, that the authentic self is not a foreign entity. It's not an elusive, unknowable presence. When people overcome their addictions, they are not transforming into completely different people. They are merely surfacing another side of themselves, an alternative persona, one that has been hidden and yet that represents their true, abiding self.\n\nBeing addicted means that you identify so strongly with your addiction, you are so consumed with the never-ending task of patching that flimsy screen that keeps your true self from emerging, that you have forgotten how to imagine yourself living without it. You would be empty inside or a complete stranger to yourself, someone without an identity or soul, you may now believe. _Recover!_ and The PERFECT Program tell you: **This is not true.** The real you is, in fact, able to reassert itself and to take charge. He or she is the very familiar _you_ who is reading these words on this page right now. And _that_ you is not fundamentally, perpetually, or irrevocably an addict. The addicted you is disposable\u2014may even be displaced while you read these words.\n\nBut it can be as hard for you to remove your addictive thinking and identity as it is to rid yourself of the addictive behavior\u2014harder. They're probably making quite a racket in there, encouraged (as in Alan's case that begins Chapter 2) by popular misinterpretations of science\u2014often spread in the recovery world or via media\u2014that say you are unable to change. Like so many other ideas about yourself you harbor\u2014\"you can't do this; you have no authentic self; you're going to be fat forever; you are worse than Rose or anyone else; you'd never be happy if you couldn't hang out at bars with your friends; everyone secretly thinks you're weird . . . blah blah blah\"\u2014 _these ideas are false._\n\nYou know instinctively that Rose, Dori, Phil, and Ozzie did not lose an essential part of themselves when they abandoned their addictions. Rather, they grew more fully into who they truly are: within themselves, in relation to others, in connection to their worlds. Having now emerged from the cocoon of their addictions, they will not be _less_ themselves for having emerged, for making this effort, and for eventually finding their perch in the real world (that is, one not colored by their drugs or addictive experiences). What made the transformations seem accidental or external in the cases presented was only these individuals' lack of awareness of the natural recovery process unfolding within them and of their power to manage it. But, now that _you_ are aware of the inner dynamics at play, you can nurture this transformation in yourself. And you can start now, right where you are, by learning to focus on the signals from your core and to distinguish them from the cravings and urges that have trapped you until now.\n\nRecall the ocean surf analogy earlier in this chapter and imagine yourself in the calm deep water under the waves. The force and spectacle of the waves overhead is very much like your addiction\u2014rushing and crashing over everything in its path\u2014but always in flux, changing and shifting. A wave has no permanence, and neither does your addiction. Underneath the waves, where your life is rich and abundant, is the deep calm in which you reside. Of course, you cannot stop the waves, but you can learn to shift your focus away from the surface turmoil. The mindfulness meditation exercise at the end of this chapter is a technique you will use to sharpen your underwater senses and begin to recognize your real voice from deep down within you. It will also allow you to recognize that the negative voices\u2014the urges, cravings, and the vicious stories we tell about ourselves\u2014lack permanence. Just like a wave. Yes, they are powerful and potentially destructive, just like waves, but they are just as transitory and ephemeral.\n\nMoving Forward: Putting Mindfulness into Action\n\nIn this chapter, you have gathered some information that you can use as you continue your journey to true recovery. Now, when you pause to ask yourself, \"What the hell am I doing?,\" you will recognize that as a moment of grace, a communication from yourself and an interlude filled with possibility. Simply turning your attention to that voice will bring you into contact with your core, sharpen your interior senses, and begin the conscious shift of your life's balance. This is the process of mindfulness in recovery. Beginning a daily mindfulness meditation practice is a gentle way for you to initiate the process of natural recovery by learning to harness your free will. _Mindfulness skills will also be your bedrock of relapse prevention._\n\nMaybe you still believe that change isn't possible for you, that your addiction is intractable, or even that you don't deserve a full life. That is okay. For now, focus only on distinguishing the competing voices within and practice the following exercises. In the next chapter, we will explore these negative beliefs about yourself and guide you to a place of self-acceptance.\n\n_Mindfulness and addiction_\n\nYou may suspect that I emphasize the practice of mindfulness meditation throughout The PERFECT Program in order to take advantage of the mindfulness craze. As mindfulness has come to the fore in recent years, there are now manuals for mindfulness for just about everything people want to do: selling, money management, medicine, marriage, parenting, exercise, eating, pet ownership, even sewing. Clearly, mindfulness is a trend. But it is also a deep and powerful practice that has been passed down for thousands of years. And, as this chapter makes clear, it speaks directly to and combats the essential mechanism in addiction.\n\nAddiction is the mindless and relentless chasing of superficial urges and compulsions, a desperate grasping at fleeting satisfaction; mindfulness is its perfect, natural opposite and antidote. In fact, that is exactly what it was meant to achieve. Mindfulness is a respite from craving that you create through the practice of bringing your full awareness into the present moment, rather than allowing yourself to be led mindlessly by force of habit. The usefulness of the Marlatt team's mindfulness-based approach to relapse prevention illustrates this principle. Mindfulness may be the buzzword _du jour_ , but for combating addiction it is a central, crucial practice. Mindfulness has proven especially useful in dealing with binge eating, which appears both in regard to obesity and to eating disorders such as anorexia and bulimia.\n\nAs I have written: \"Addiction is the search for emotional satisfaction\u2014for a sense of security, a sense of being loved, even a sense of control over life. But the gratification is temporary and illusory, and the behavior results instead in greater self-disgust, reduced psychological security, and poorer coping ability. That's what all addictions have in common.\" There is no place where this cycle is clearer than in the case of binge eating. Binge eating points clearly to the nature of the addictive experience as a self-feeding negative relationship to an object, activity, or involvement. As one woman spoke of coalescing obese binge eaters and those with eating disorders: \"The problem [for either the anorexic or bulimic, or the obese, binge eater] is not the food; the problems are the issues in your life, and you turn to food because you can't handle them.\"\n\nAs the foundation of The PERFECT Program, developing your mindfulness practice is key. So, if the very thought of meditation makes you groan in anticipation of excruciating tedium, well . . . get that groan out of your system now. Go ahead\u2014groan!\n\nDone? Then let's get started!\n\nMeditation\n\n_Basic Mindfulness Meditation_\n\nIt is often difficult for people with addictions to meditate. The idea of just sitting with yourself for any length of time can seem overwhelming, especially when you are preoccupied with patching your addictive screen to hide your real self. This meditation is thus an exercise of your free will, as well as a technique for making contact with your core self.\n\nFind a quiet place, where you know you will be undisturbed, and a place to sit, either on a chair, a cushion, or on the floor. Don't lie down: You want to be in a state of relaxed attention, not fall asleep. Set a timer for ten minutes (if ten seems overwhelming, start with five and work up to ten). Find a comfortable position, rest your hands on your lap, close your eyes, and relax every muscle. Focus your attention on each part of your body and release the tension there. When you are relaxed, turn your attention to your breathing: listen to the sound of your breath, notice the duration of each breath, the sensation of taking air into your lungs. If it helps you to focus, you can think \"in breath\" and \"out breath.\" As you do this, thoughts and emotions will enter your mind, some random, some uncomfortable. When this happens, acknowledge them, notice them, and release them, and then deliberately shift your attention back to your breathing.\n\nThere is no right way to meditate, and no particular experience you should have. It's important to remember that, even if you spent the whole time fidgeting and distracted, that is not wrong. That was simply your experience; you are learning the skill of sitting with uncomfortable feelings. You are not obligated to act on every urge or thought that presents itself to you. Remember that no one can block out all thoughts and feelings, so don't make that your goal. You cannot control what thoughts come into your mind. Notice how fluid these thoughts and feelings are, how they come and go, and how you can turn your attention away from them. You cannot stop them from coming, but you can consciously control where you place your attention. With daily practice, you will find it ever easier to turn your awareness where you choose to and let the waves of thoughts and feelings flow over you and away.\n\n_Tips:_\n\n\u2022 Create a permanent space in your home for meditation, where you will be comfortable and undisturbed by noise or clutter.\n\n\u2022 Get an egg timer or an alarm with a gentle chime\u2014not your cell phone timer; your phone might ring.\n\n\u2022 Turn off the ringer on your phone.\n\n\u2022 Set a regular time every day for meditation, when you know you will be alert.\n\n\u2022 Challenge yourself to increase your meditation time weekly by five minutes. Set a goal of at least thirty minutes.\n\n\u2022 Find a meditation center or group in your neighborhood.\n\n**Mindfulness Variation:** You can bring mindfulness practice into your everyday life. Whenever you think of it, stop and bring your full presence to whatever you are doing. For instance, if you are washing dishes, challenge yourself to notice as many details as you can about the activity: How do the suds feel? What do they look like? What temperature is the water? How do you feel about doing the dishes? Or focus inward\u2014on your mind and your body (instead of listening to your iPod)\u2014while you exercise. Remain mindful as long as possible, and see if you can extend these periods of full awareness.\n\n**Relapse Prevention Starts Now:** Research is demonstrating the effectiveness of mindfulness techniques in relapse prevention. Studies conducted at the University of Washington, for instance, report a significant decrease in relapse as well as cravings in participants who employ mindfulness-based practices compared to those who receive \"treatment as usual.\" Starting a mindfulness meditation practice now will provide you with a strong foundation for maintaining your success, giving you a powerful skill that will aid in both preventing relapse and correcting course in the event that you do relapse.\n\nExercises\n\n**Activating Your Free Will:** Acting with free will is the ability to align your choices and behaviors with what is truly important to you. Simple enough in theory, but it takes deliberate practice. Once you have the ability to see your addictive urges for what they are and to distinguish them from your healthy core self, you can begin to choose where to focus. In other words, you can train your free will to take over. Let's begin by committing to use this powerful anti-addiction tool in your daily life:\n\n**S.P.O.T.**\n\n\u2022 **See:** When you have an addictive urge, _see_ it for what it is. Mindfully appraise the feeling as addiction, distinct from the conscious presence that you are using to recognize it. There is the urge, and there is you acting as witness to the urge. Say, \"This is an addictive urge.\"\n\n\u2022 **Pause:** Allow yourself to sit with your addictive urge, to experience the uncomfortable feelings, or even the emotional pain that results from not immediately acting on your craving. Set a time frame for yourself and commit to not acting on this urge\u2014say, thirty minutes to start. Or if that's too difficult, start smaller and work your way up.\n\n\u2022 **Override:** While you are waiting it out, engage yourself in a life-affirming activity that you know will bring you some sense of accomplishment or satisfaction. Make a list of things you can do at a moment's notice to override your addictive urge (there are some suggestions for you in the \"Triage\" chapter on page 241).\n\n\u2022 **Track:** Keep track of your S.P.O.T. progress: record how long you were able to Pause and what you did to Override your addictive urge. Focus only on your successes and on what worked for you. Do not berate yourself if you succumbed. Remember, you are strengthening your \"weaker hand,\" and that takes effort, time, and patience.\n\nJournal Exercises\n\n**Your Moments of Grace:** Can you identify any recent instances in which you experienced a \"pause\" in your addictive behavior? Perhaps you were about to indulge your addiction and were overcome with a feeling of tedium or repulsion. Maybe you extinguished a half-smoked cigarette out of a sudden feeling that you were wasting your time or making yourself sick. Perhaps you put down a cream puff or morning pastry by thinking, \"Is this really something I like?\" Or you may have looked at your friends drinking or smoking weed at a party and considered, \"Maybe I'll just sit out this shift.\" Write about these instances in as much detail as you can recall, extending for as long as you held out against your addictive urges. If you did relent and indulge, include the thoughts or feelings that eventually led you to persist in your addictive behavior. Try to answer these questions:\n\n\u2022 What did that moment of grace communicate to you? How did it present itself? As a feeling? A thought? An image? Was it a negative idea or image of the activity, or a positive one of what might be?\n\n\u2022 How long did it last? How did it make you feel?\n\nIf you dismissed it and continued to pursue your addiction, write about what you said to yourself, or how you suppressed that inner voice.\n\n**Telling a New Story:** Choose one of the moments of grace you wrote about in the last exercise and tell the story again, only this time give it a different ending. Write a new story about yourself: Imagine that you honored that voice and chose not to pursue the addiction. What would you have chosen to do instead? What would you have accomplished? Explore your new story in as much detail as you can. It is like writing a work of fiction with you at the center, except that \"fiction\" is the real you.\n\nYoga and Mindfulness\n\nYoga offers many of the same benefits as meditation\u2014indeed, many yoga classes and videos begin and\/or end with brief meditations. I practice yoga\u2014which I summarize as stretching and breathing. As in meditation, the centering focus of all activity is on your breath, along with a deep awareness of your body. For people inclined to physical exertion and for whom the restful poses of meditation don't come naturally, yoga can be a better route to mindfulness.\n\nIntroducing yoga into your routine will broaden and deepen your experience with mindful awareness. Of course, yoga is good exercise and can help you become stronger and more limber. But it has benefits beyond exercise. Just as with meditation, yoga requires you to bring your awareness fully into the present moment. As with meditation, the benefits are in simply doing it, at any level of proficiency. As you take your body into new positions, you may be aware of uncomfortable sensations or emotions, but turning your curious attention to these feelings is part of the exercise. Like meditation, yoga offers a balancing experience to your day in which you engage your mind, body, breathing, and your setting simultaneously, in the moment.\n\nIf you haven't done yoga or don't know how to begin a practice, it is an easy activity to access. Classes are readily available, either privately or at no added cost at Y's, health clubs, or other community venues. Gaiam (www.gaiam.com), Amazon, and many other sites offer numerous yoga videos, including many for beginners, some of which may be available at your library. Among many books you can find on yoga is _Moving Toward Balance: 8 Weeks of Yoga with Rodney Yee._ Yee guides you through a home-based yoga practice while delving into the mind and body benefits of this practice, a valuable addition to your mindfulness tools.\n\nOther Mind-Body Programs\n\nThere are many varieties of mind-body learning aside from yoga, some almost as well known (including tai chi, Pilates). Any of these is worth exploring, even though I can't go into detail about them here. Another form of such movement\/meditation is the Feldenkrais Method. Feldenkrais emphasizes mindful self-awareness, including visualization, in order to relearn common motions to improve performance, encourage ease and pleasure of movement and function, and reduce pain and injury. Feldenkrais involves instruction, but is also self-directed and non-routinized, relying on the person's creativity and experience. It is a gentle practice that proceeds in gradual increments. Typical Feldenkrais advisories are to be aware when practicing so as to avoid discomfort, to enjoy the practice, and to integrate new learning with everyday living and movement. You may find instruction and classes at the Feldenkrais Method website (www.feldenkrais.com).\n\nUser-Friendly Mindfulness Meditation\n\nThis additional meditation section reviews the basic meditation approach I described above, but in a more general and open way, to allow you to tailor your meditation practice as you see fit and to feel comfortable exploring your options.\n\nThe heart of mindfulness meditation practice is in willfully directing your attention to the present moment and your feelings and sensations within it. You can find your own way of achieving that experience. This will be a self-directed practice, so experiment with approaches to meditation to find what works best for you. Typically, people sit on a cushion with their legs crossed and backs erect. Your ambition might be to levitate six inches off the ground in a perfect lotus position, but (since that is only for advanced students) you may be most comfortable sitting in a straight-backed chair. Similarly, you may find it easier to keep your eyes softly focused on a candle flame than to keep your eyes closed (especially if you have a tendency to sink into a torpor when you meditate). You may want to rest your hands on your knees, palms up, relaxed and open, or you may feel more secure with your fingers touching your thumbs, palms down on your knees, or softly folded in your lap, or together at your heart. Whatever position you choose, notice how it makes you feel, what sensations or feelings each position creates for you.\n\nThe purpose of mindfulness meditation is not to empty your mind, to be clear of all thoughts. In fact, there is no state of mind you must strive to achieve, so that when you're finished you know whether or not you have been successful. Simply _doing_ it is success. What will you be doing, then, exactly? You will be paying curious, nonjudgmental attention to whatever comes up, while intentionally directing and redirecting your mind to remain fully in the present. That is it. Here's the nuance: The practice is in continually and deliberately reinhabiting the present moment, not in trying to force yourself to remain in the present moment.\n\nThink of your mind as a playful puppy that will chase after every squirrel or ball that crosses his path. It is in the puppy's nature to romp and chase. However, just because it is in his nature does not mean that his whims should always rule the roost. He must be trained to return to you when you call him, otherwise he might carelessly (mindlessly) chase a cat out into the road. As he matures into an adult dog, you don't want him to stop playing or protecting his territory, but you do want to make sure that you are the one in charge. As his master, you can call him back to your side when necessary.\n\nYou are not trying to prevent your mind from wandering or chasing after shiny objects. That's what our minds do. You simply want to train your mind to come when called. Traditionally, mindfulness practice begins by focusing your attention on your breath. It is the most convenient, ever-present touchstone\u2014a bridge between the inner and outer landscapes you inhabit at every moment. Turning your attention to your breath is easy, because it is always there and you can always find it. There are a few ways of keeping your attention focused on your breath. You may, for instance, say to yourself (either silently or out loud), \"In breath. Out breath.\" You might also count your breaths. Count to ten, then start again\u2014and again. If your mind wanders, start again. No judgment. Or, you might vocalize with each breath. You may know about chanting \"Om,\" which is an option, as is simply making a sound that feels right to you as you breathe out.\n\nAlternately, you may want to focus your attention on a part of your body or inner landscape that feels good or neutral. Or, use the sound of your refrigerator humming as your home base, if that works. You might choose to use a visual touchstone, either physical (like that candle flame) or by keeping your eyes closed and focusing on the spot between and just above your eyebrows. Some people see light or color there. In order to remind yourself to bring your attention back to the present, you can set a gentle chime to sound every ten or fifteen minutes. Or listen to a guided mindfulness meditation, which you can download from the Internet or purchase as a recording. If you find it difficult to sit, or are overcome with restlessness and do not have the tolerance for it yet, you may practice walking meditation. In walking meditation, you focus your attention on movement: your steps, your active muscles, your gait. Walk with intention, taking deliberate steps. And when you find your mind wandering, acknowledge it, and turn your attention back to your walking. The variations are endless, so to ensure consistent practice, take time to figure out what works best for you. The only correct way to practice mindfulness meditation is _your_ way. As long as you are doing it, you are doing it right.\n\n_Meditation options_\n\nHere are some options to help guide you to a meditation practice that works best for you. Each option will generate different feelings or call different thoughts to mind. Bring your mindful attention to these feelings and thoughts. For instance, does sitting on a cushion make you feel more grounded than sitting on a chair? Or does sitting on a chair allow you to remain more alert? Does keeping your eyes closed make you feel disoriented, while keeping your eyes focused on a flame helps you feel more connected to your environment? Remember, as you continue your practice, these options will remain fluid. What makes you feel insecure one day may make you feel exhilarated the next. Today, you might need walking meditation; tomorrow, you might be willing to sit still and explore your restlessness.\n\n* * *\n\nLocation:\n\n\u2022 Indoor meditation spot\n\n\u2022 Altar\n\n\u2022 Outside\n\n\u2022 Walking (inside or outside)\n\n\u2022 Meditation hall\n\n\u2022 Other_______________________\n\nSitting Options:\n\n\u2022 Floor\n\n\u2022 Cushion on the floor\n\n\u2022 Crossed legs\n\n\u2022 Lotus position\n\n\u2022 Chair\n\n\u2022 Other _____________________\n\nHand Position:\n\n\u2022 Palms down, on your knees or lap\n\n\u2022 Palms up, on your knees or lap\n\n\u2022 Fingers touching thumb, on your knees or lap\n\n\u2022 Hands at your sides or touching the floor\n\n\u2022 Palms pressed together, at your heart center\n\n\u2022 Other _______________________\n\nMindfulness Touchstone (Home Base for Your Attention):\n\n\u2022 Breath\n\n\u2022 Chant, \"Om\" or other vocalization\n\n\u2022 Physical sensation\n\n\u2022 Emotional feeling\n\n\u2022 Craving or urge (see Chapter 7)\n\n\u2022 Physical object\n\n\u2022 Inner visual image\n\n\u2022 An intention\n\n\u2022 Other_________________________\n\nGuidance:\n\n\u2022 None\n\n\u2022 Recorded guided meditation\n\n\u2022 Chimes at intervals\n\n\u2022 Meditation class or group\n\n\u2022 Other_________________________\n\n* * *\n\nCHAPTER 5\n\n_Embrace_\n\nSelf-acceptance and forgiveness\u2014Learning to love yourself\n\n* * *\n\n**CHAPTER GOALS**\n\n\u2022 To balance mindfulness with compassion\n\n\u2022 To make self-acceptance a new habit of mind\n\n\u2022 To draw a distinction between your true self and your addiction\n\n\u2022 To understand and practice forgiveness, of yourself and others\n\n**Purpose:** It may seem that mindfulness implies stark introspection, requiring you to see all your flaws with brutal clarity. In other words, it could be yet another tool you can use to beat yourself up. But clarity of perception is logically tempered by self-acceptance. It simply makes sense for you to recognize that you are a worthy and complete person, entitled to fulfillment, opportunity, and love. With this realization in place, your self-examination will be balanced\u2014both accurate and compassionate\u2014which will make it effective. The purpose of this chapter is to guide you toward self-acceptance and its sister cognitive emotion, forgiveness\u2014of yourself and others. With the joint tracks of mindfulness and self-acceptance in place, you can readily go forward with your PERFECT Program.\n\n* * *\n\nThe Weight of Negativity\n\nIt may be human nature to suspect the worst about ourselves. Sometimes this impulse achieves pathological levels, as it does with people who suffer from a condition called \"body dysmorphia.\" Those afflicted believe themselves to be so physically grotesque that they have no right to even walk outside as normal human beings do. They are unable to look in the mirror without feeling profound self-hatred, seeing shocking deformity and ugliness, even though their appearance is perfectly normal, or even beautiful, to those around them\u2014especially those who see the whole person, inside and out. Think, for instance, of dangerously malnourished anorexics who believe themselves to be obese, exploring their bodies with microscopic attention to this pocket of fat or that small curve. When they look at themselves, all they can see are these magnified imperfections\u2014they live a life of vigilance, self-denial, and self-debasement, trying to correct their overwhelming flaws, or they hide themselves away altogether.\n\nMaia Szalavitz notes, \"Being ashamed of drinking prompts relapse, not recovery.\" In a study in which alcoholics were videoed reviewing their bad drinking episodes, when they were followed up four months later, researchers found that their displays of physical shame (coded on a scale of their body language) in the first ten seconds directly predicted their likelihood of relapse: every added point they scored led to an average of eleven more drinks over the period of the study. Even alcoholics displaying moderate shame drank twenty more drinks than those who didn't convey shame. Furthermore, a review of the use of \"humiliating, confrontational tactics, which attempt to induce shame\" found that not one study over four decades supported this approach. \"The results add to a body of literature suggesting that widely used shaming and humiliating methods of treating alcohol and other drug problems\u2014such as those seen on shows like _Celebrity Rehab_ \u2014are not only ineffective but also may be counterproductive.\"\n\nYet shame and humiliation are the fundamental emotional experiences encouraged in recovery! Step 1, that you are powerless, is described as \"absolute humiliation\" by AA. _Self-acceptance is the defining difference between AA and The PERFECT Program_. This is the place where The PERFECT Program most clearly and meaningfully diverges from the dysfunctional, defeatist model that has been pushed on you and so many others as the American approach to addiction. After you and fellow AA members \"admitted we were powerless over alcohol\" (or whatever you're addicted to: shopping, food, sex, gambling, painkillers), you must then have \"Made a moral inventory\" of your failures (step 4), \"Admitted to God,\" yourself, and others these failures (step 5), made yourself \"ready to have God remove all these defects of character\" (step 6), begged \"Him to remove our shortcomings\" (step 7), and then have \"Made a list of all persons we had harmed\" (step 8).\n\nFeeling uplifted and ready to recover about now? The research indicates not. What's worse, conventional recovery's fixation on character defects appeals to the powerful impulse we have to believe the worst about ourselves. But recovery thus motivated is not compatible with a fully realized sense of yourself. Think of an anorexic or bulimic who has to overcome her sense of worthlessness, along with her belief that she is ugly. Is the path to achieving peace of mind for girls and others with these feelings to constantly examine and apologize for their various imperfections, many unnoticeable or irrelevant or not their fault, like those just about every other human being has? In fact, thinking that way is the problem! It's impossible to expect a person to achieve wellness by focusing on his or her faults and mistakes. Perhaps this is why conventional recovery asserts that people must remain \"in recovery\" forever and continue to identify themselves as addicts, no matter how long they are sober. It is the AA worldview itself that actually makes your recovery so tenuous by imposing a _perpetual state of spiritual dysmorphia_.\n\n* * *\n\n**CASE:** Alexis was, at twenty-eight, a tall, willowy model. And she had developed a terribly damaging case of anorexia. While this condition could be laid at the feet of the modeling business, it was also true that she had never seen herself as attractive\u2014a habit of mind that continued now even as she graced the covers of leading fashion magazines around the world.\n\nAs a child, Alexis was regarded as tall and gawky. Asked to name her chief characteristic today, Alexis would note her elongated nose, near-sightedness (she wore glasses at home), and the very slenderness that was her stock-in-trade\u2014\"I wish I were more feminine,\" she sighed. As a result, she rarely went to social events, where she never felt she fit the role of glamorous model she was expected to fill.\n\nAlexis was also an extremely caring person. She clucked after the younger models (many of whom were still in their teens) like a mother hen. When she became involved in a charity to help feed African children, the organization's representative remarked with amazement, \"She really cares!\" rather than simply supporting the charity because her publicity agent told her she should. Particularly noticeable was her affinity for\u2014love of\u2014injured and mutilated children she met, whom she hugged as if they were her own.\n\nIf you asked Alexis, someone with a debilitating case of body dysmorphia, whether anyone else\u2014like the starving and bruised children she encountered\u2014deserved the kind of abuse she inflicted upon herself\u2014like withholding nourishment and mocking their appearance\u2014she would have turned on you like a tigress. Her whole being was devoted to making them feel accepted and loved. Her irate reaction would be similar if you asked her the question, \"Should people with blemishes hide themselves?\"\n\n* * *\n\nAlexis would loudly protest that the idea that people should be preoccupied with their physical imperfections is preposterous, degrading, and completely unhelpful for these children and for society. So why does she hide herself, obsessed with her own flaws, believing that she alone, among all imperfect people on earth, deserves to be judged harshly? It's clear that her torment is caused by her inability to view herself through a lens of compassion, like the one through which she is able to see distressed children. Framed this way, it is apparent how warped her perspective towards herself is. In fact, Alexis's greatest need is to overcome this self-loathing in order to cure her addictive eating disorder, as young women often do as they mature, since eating disorders appear primarily in teens and young adults.\n\nThe distorted perspective an anorexic has on her outward physical appearance is like the one you may train on your inner being when you conclude that you are so innately, irredeemably damaged or abnormal that you can never engage in life as everyone else does. Think of Alexis, in whom this prejudice against herself is so obvious. Alexis could never see herself as being as beautiful, engaging, popular, and accomplished as other people saw her to be. So she rejected the compliments\u2014\"you've really been there for so many younger models\"; \"you've created communities for yourself in modeling and around the world that should make you proud\"; \"you are a beautiful person, inside and out, Alexis\"\u2014as she gazed at herself in the mirror with disappointment and even repugnance.\n\nAccentuating the Positive\n\n_Recover!_ 's approach to overcoming addiction requires a radical shift away from the self-degrading examination of yourself and your life in order to enumerate all of your horrible traits and despicable acts. For instance, your recovery program may tell you that you are naturally self-centered and dishonest, that if you are left to your own devices you will always make poor choices, and that you are obligated to focus constantly on such \"character defects\" and misdeeds, then hold them up for public examination. The PERFECT Program replaces this demeaning practice, one that reinforces what may be your already irresistible impulse to pathologize and reject yourself. Instead, _Recover!_ asks you to embrace yourself as already worthy, whole, and wise. Above all, you should realize, _addiction is not a core identity any more than is a flabby thigh or a crooked nose_. They are all superficial characteristics, not foundations on which to build your identity.\n\n* * *\n\n**CASE:** Letter from a man who relapsed after attending AA\n\nI sincerely want to change my habits. I am totally aware that what I am doing is self-destructive.\n\nHowever, as a person who has survived severe emotional and physical childhood abuse, I cannot or will not ever again admit I am powerless. In spite of it all I am a medical professional who devotes each day to ensuring that my severely disabled patients enjoy the highest quality of life. I also respect their right to choose what is the best course for them.\n\nI have failed AA because I am unable to confess I am powerless. I have been told that since I am unwilling to surrender I may as well give up on being sober, that this is my addicted brain talking. I feel that they're telling me I have no worth. Saying I'm powerless and going to 90 meetings in 90 days only reinforces my feelings that I am a failure. In all honesty I feel bad enough about myself as is. If I give up on me, who is left to carry on?\n\nAA veterans have told me this is denial. Am I in denial? I know I drink too much; that is why I came to AA. I do know that when I am happy and doing meaningful work I don't care about drinking at all. And I know that telling myself how rotten I am won't change anything for me. In fact, it makes things worse. Which may be why I bought and consumed a bottle of wine after my last meeting.\n\nIs what I am being told right? Right now I am lost and miserable.\n\n* * *\n\nWhile AA certainly helps some people, this man is far from unique. Ken Anderson noted, \"I have also seen many people whose drinking got worse while attending AA. I am one such person: During my time in AA, I nearly died of alcohol withdrawal.\"\n\nThis man needs not to have his wavering self-image further undermined, but to have his strengths and positive life instincts encouraged, reinforced, and extended. Indeed, we all need that. Consider the last time someone gave you a heartfelt compliment. Did you reflexively deny it or brush it off, as if it would be dishonest or presumptuous to accept it? It seemingly takes an act of will to acknowledge as true an attribute, skill, or good act of yours. The impulse to view your positive qualities with some modesty is reasonable. But, then, you should be just as measured when it comes to your demons. Let someone point out some deep personality flaw that you have\u2014meanness, insecurity, bad faith, fear\u2014and you will likely burrow into your cave and reflect on that insult endlessly. You almost certainly take it much more to heart than you would any praise that someone offers you. Why should insults affect you so much more than compliments? Regardless of the reasons behind this disparity, _your task for overcoming addiction is to find a way of perceiving in yourself what is right and good at least as readily as you reflect on your flaws and errors_. When you identify these positive qualities, you can't rule them out as insignificant exceptions (as Alexis did her charity work and generosity) while regarding your negative ones as being the real, permanent you. Maintaining some balance is only fair!\n\n* * *\n\n**CASE:** Have you ever noticed how hard it is for people to accept compliments?\n\nAt forty, Jack had never settled into a niche in life. Then he began working at a dog grooming service, making appointments, looking after dogs before their owners arrived, and taking payments. Jack had found Nirvana! He was great with customers, loved animals and had a gift for handling them, and was as reliable and punctual as his boss had ever found an employee to be. As a result, she gave Jack more and more responsibility managing the business.\n\nSusan, who brought her dog for grooming regularly, appreciated Jack's care, skill, and attention with her pet and with her. \"Jack, I just so like bringing my dog here. You really seem to love your job!\"\n\n\"That's because Elaine is the best boss I've ever had,\" Jack enthused. \"She changed my life.\"\n\nAs it happened, Elaine was in the shop at the time. \"That's because you don't see me at home, where I'm a real ______.\"\n\nSusan had seen people deflect compliments hundreds, thousands of times. (She did so herself, she later reflected.) But this time, the phenomenon struck her. \"Elaine,\" she blurted out, \"Jack just said you changed his life, and you slough off his feelings as though they meant nothing!\"\n\n* * *\n\nExercise 1, Part 1\n\nBefore you read further, open your journal and make three columns. Title the first column, \"I want to overcome my addiction because. . . .\" Underneath that heading, list as many answers to that question as you can. Then continue reading. You'll find Part 2 of this exercise on page 111.\n\nThe shift in perspective The PERFECT Program requires is not simply from being all-out negative to uncritically positive. Believing the worst about yourself is unrealistic\u2014but it's not any more realistic (or possible) simply to believe only the best about yourself and that everything is hunky dory. Balance requires avoiding _both_ a microscopic scrutiny of your personal defects _and its opposite_ , a silly Stuart Smalley self-affirmation (\"I'm good enough; I'm smart enough; and doggone it, people like me\"). A balanced view of yourself sees you as a complete, fundamentally sound person, one with both positive and negative aspects, neither of which define, support, or detract from your fundamental worth as a human being. It's like the difference in perspective between trying to make out the dirty pattern on the linoleum of an aged kitchen floor and looking at the whole planet from space. Self-acceptance is looking at yourself from the more complete, and therefore more forgiving, perspective of space.\n\nIn the previous \"Pause\" chapter, we introduced you to the practice of bringing your full awareness into the present moment. Mindfulness is a simple and powerful anti-addiction tool that serves you in several ways: It hones your ability to listen to your inner voice, your sound instincts. Mindfulness teaches you to distinguish between your life force and the temporary feelings, cravings, desires, and compulsions of addiction. It gives you the mental distance and room to note and explore where these uncomfortable feelings are coming from without having to act on them. It helps you develop the skill of sitting out these onrushing feelings without being swept away by them. In short, mindfulness is full presence and clarity. But mindfulness alone is not enough to free you from addiction. Self-acceptance\u2014compassion for yourself as well as others\u2014is an equal partner in this endeavor.\n\nIn the last chapter I promised to address the pessimism and discouragement you may feel about your ability to overcome addiction. You may believe, for instance:\n\n\u2022 I am different from normal people. I don't have what it takes to beat my addiction. I have no identity outside of my addiction. My addiction is worse than anyone else's.\n\n\u2022 I am _incapable_ of creating a meaningful or fulfilling life. I am inherently deficient. I can't learn new skills or how to change.\n\n\u2022 I do not _deserve_ a meaningful or fulfilling life.\n\n\u2022 I don't know how to act properly. No one has treated others as badly as I have. I have committed worse acts (sins) than everyone else.\n\n\u2022 The good things in life are for other people.\n\nBeliefs like these hurt you because you can feel right, and even noble, thinking the worst of yourself, as if you were simply being realistic about your limitations\u2014that you are facing the cold facts. Since no one knows you like you do, hearing from strangers like me that you're not as bad as you think you are won't persuade you. The most difficult part of your journey to wellness will be loosening the grip these beliefs have on you and replacing them with positive, self-accepting ones.\n\nExercise 1, Part 2\n\nRevisit your answers to the question, \"I want to recover from addiction because . . .\" and see if you can recognize the extent of your negative critiques of yourself. For example, \"I want to recover from addiction because I am a terrible parent.\"\n\nWhat's Really Wrong with You?\n\nFeeling that you are off the grid in some way is common not only for addicts, but for everyone, even those who seem to have it all. But addicts have an added blanket of self-contempt to contend with, because addiction often goes hand-in-hand with estrangement, deception, inner conflict, and shame. To take one example, you will typically hear addicts despair of their discomfort and lack of confidence in new social situations, as if their awkwardness is unique to them as addicts (this may be a feeling you know well yourself). Many explain they used drugs or drank initially in order to relax in social situations.\n\nIt's true that addicts and alcoholics can feel out of place in social situations. But only the rare social butterfly doesn't feel uncomfortable around new people\u2014put another way, nearly everyone feels more comfortable in familiar settings with people they know. True, if you have spent a lifetime quelling your social anxiety with an addiction, you may have built quite a structure on this common insecurity, because you haven't had the opportunity to develop healthier ways of coping. But these experiences nonetheless fall well within the normal spectrum of human experience. They are not unique to you and other addicts, and it isn't true that you can _never_ remedy these feelings. You _can_ change such responses by exposing yourself to new social environments in new ways.\n\nEven the most progressive addiction experts in the field, those who reject the destructive aspects of recovery culture, seem unable to shake the habit of searching for underlying pathologies common to addicts. The fact that the field can't settle on what your real problem is should give you pause: Is it childhood trauma? Or has your brain chemistry gone haywire? Or maybe you lack the inherited chemical means to process alcohol (this is one that may strike entire races!). You can find a whole laundry list of root causes. Perhaps you were abandoned as a child. Perhaps you were overly attached to your mother. Could be you have no impulse control or an inability to delay gratification. Maybe you can't process sugar or white bread or are deficient in amino acids. The list is endless, especially when these experts start mixing and matching. There's no doubt you can find one or more of these theories that apply to you.\n\nWhat makes this approach so compelling is that it homes in on addicts' urges to embrace any evidence supporting their deeply held belief that there is something fundamentally wrong with them. Now, at last, you have an explanation for your problems; you have a place to rest, however negative this perch is. There is a certain satisfaction, a seeming solidity that comes with discovering your \"real problem.\" Now fixing yourself becomes an entirely straightforward proposition: Heal your inner child; rewire your brain; take a medication; relive your trauma; quit sugar; find groups of fellow sufferers to rehash your experiences with. However, you may know from personal experience that none of these approaches will remedy your addiction. Instead, defining yourself as damaged and deciding you are spiritually or physically impaired can reinforce your worst behaviors.\n\nThe causes and manifestations of addiction are infinitely complex. Searching for a single cause\u2014and, by extension, a single cure\u2014is simplistic, unnecessary, distracting, and obviously counterproductive. Say, for example, you trust the expert who tells you that your addiction stems from childhood trauma. Of course, there will be evidence to support this explanation because we all have bad memories with which to fill in those blanks. But, what if you cannot recall anything life-altering? What if this explanation doesn't sit right with you? Do you embark on the program anyway, believing that you cannot trust your own mind?\n\n* * *\n\n**CASE:** We met Suzanna in Chapter 2. Suzanna was actually an alcoholism researcher herself, in her late twenties. She was popular, but nonetheless a bit of a loner. She had had boyfriends, but nothing lasting. Moreover, she felt her work unsatisfying\u2014that others determined the direction of the research she worked on, while she carried out the grunt work. This despite her sterling academic record, her reliability, and her desire to make a contribution. Moreover, bad feelings regularly surfaced for her, as a result of which she drank steadily, needing alcohol to feel okay. Suzanna was one of three children. Her home had not been a happy one. She never saw her parents embrace, or really talk kindly or considerately to each other. Then, shockingly, when Suzanna was eight, her mother disappeared from her life.\n\nOne day, her mother no longer lived with the family. Her father and an unmarried aunt who moved in with her and her siblings explained that she had to leave for important reasons Suzanna couldn't grasp. Only years later, as a teenager, did Suzanna learn that her mother had gone to live with another man\u2014first in their same city, and then moving some distance away.\n\nAlthough her mother did contact the children\u2014and even visited with them, taking them shopping and to shows from time to time\u2014Suzanna always understood these were to be short outings. At first, Suzanna would cling to her mother throughout these times together, as though she could make them permanent by never letting her mother out of her grasp. But as a teenager, Suzanna came to have a very jaundiced view of such get-togethers and barely showed any interest in them. Nonetheless, she constantly asked herself, \"Why did my mother desert me?\" She was torn between feelings of inadequacy about herself and anger at her mother. Her older brother seemed untroubled by such feelings. Her sister, close to her age, was even more devastated by the experience than she was. Years later, her sister died in a drug incident.\n\nSuzanna never felt privileged, protected, prized not only as a child, but also as a student and young professional. Nonetheless, she was independent and capable. She threw herself into her studies, wrapping her life around them, achieving success upon success. In pursuing her academic career, she never allowed another person to become a permanent part of her life. She didn't feel she could trust anyone. After gaining a Ph.D., Suzanna became a post-doctoral researcher in a prestigious alcoholism research program. But she never sought out a senior mentor, and her career stagnated.\n\n* * *\n\nSeeking to right her emotional state and thus not to require alcohol as an emotional crutch, Suzanna began attending a group of trauma survivors. The leader of the group, a great believer in physically locating the traumas group members had experienced, provided diagrams of the inescapable ways such events damaged the midbrain and limbic system. Suzanna didn't identify completely with this scenario, because it wasn't necessarily the specific moment her mother left that depressed her, so much as the cumulative experiences of her upbringing and dealings with her parents.\n\nWhat if we replace \"childhood trauma\" with \"powerlessness\" or \"impulsiveness\" or any number of universal human experiences or characteristics that could just as easily (or not) be the root cause of addiction? The only people who are truly helped by zeroing in on a single problem are the experts, who are sure to touch a nerve and can then build their program on that single premise. That's not to say that these negative elements aren't important and worth your attention. This was critically true in Suzanna's case. There is no denying or ignoring the enormity of losing one's mother or father, particularly when they desert a child and the family.\n\nYou may have suffered deeply as a child, with serious emotional effects\u2014even as others who underwent comparable experiences did not or, perhaps, had even worse consequences. These experiences may have searing effects on your life, and you may have done self-destructive things in their wake. But there is a difference between accepting these things as one part of you, on the one hand, and using them to explain and determine the rest of your life, on the other.\n\n* * *\n\n**CASE:** Beth was a successful lawyer who drank heavily at times. As the years went by, she found that she just didn't have the stamina she used to. Hangovers began to interfere with her work and sense of well-being. This feeling that she was not the master of her life was foreign and unsettling to her. She sought help from an expensive, private addiction specialist, an ardent follower of the Adult Children of Alcoholics (ACoA) movement.\n\nDuring their first session together, the two discussed Beth's childhood, which Beth did not consider particularly traumatic. Her parents loved her. She appreciated them and knew they had done their best. \"On the weekends,\" Beth told her therapist, \"Mom and Dad would drink steadily, starting with Manhattans on Friday after work and ending with an all-day Sunday hangover.\" Indeed, this pattern was fairly common in their upscale social milieu at the time. It may seem odd, but Beth remembered these rituals almost fondly. There had never been incidences of abuse, and Hangover Sunday was actually a pretty cozy day, with the family lounging around together, having dinner on TV trays in front of _60 Minutes_.\n\nBeth's therapist had a completely different perspective on her memories. Gently, but very assuredly, she pronounced that Beth was not only an alcoholic, but also an Adult Child of Alcoholics. Beth accepted her therapist's assessment, even if it didn't sit right with her. But she assumed that was her resistance operating and wanted to trust the therapist, who was charging her a hefty fee.\n\nBeth quit drinking altogether as the best policy for her. But she maintained deep misgivings about what she was learning. At the same time, she accepted that her mind was warped and would try to deceive her. She was afraid _not_ to believe that. Beth began to view everything she had worked for in her life as nothing more than a symptom of child-of-alcoholics pathology. She became almost ashamed of the things that used to bring her pride and a sense of purpose and meaning.\n\nBut all this wasn't helping Beth feel any better about herself. She wondered if this proved she was deeply in denial. Out of the blue, she consulted a therapy directory and found Mike. When she entered his office, Beth felt a whole different aura. Mike was cheerful; even his handshake was encouraging\u2014\"We're going to do good work together,\" he enthused.\n\nAlmost instantly, Mike strived to get beyond Beth's rehashing whether her parents were alcoholics and she an ACoA. \"Let's review all of your accomplishments. Your success at work, and especially your success in rearing your daughter.\" Beth was married with an adult daughter. Her daughter also had a good career and a sound marriage. Moreover, her daughter was a _moderate_ drinker.\n\nMike's approach was novel for Beth. You mean therapy wasn't about ferreting out your deepest, innermost, never-to-be-resolved problem? \"Can you tell me how you were able to help your daughter learn to drink moderately?\" Mike questioned Beth. \"I drank carefully in front of her . . . You know, I actually asked her that recently. She said, 'Mom, how could I have done anything else when you loved me so much?'\"\n\n* * *\n\nLet's return to the values assessment you completed in Chapter 4, this time answering only the second half, which focuses on your skills, gifts, and accomplishments.\n\nVALUES QUESTIONNAIRE\n\n6. What key skills or talents do you have?\n\n7. What are your most positive qualities?\n\n8. Name at least two accomplishments or events that you are proud of: Did you help someone? Did you win a competition? Did you build or create something? Did you stand up for something you believe in?\n\n9. Who are the most important people in your life, either people you really care about, or people you can really count on, or both?\n\n10. Which three human values do you elevate most, such as kindness, generosity, friendship, honesty, hard work, creativity, independence, integrity?\n\nImagine the things Beth might enter in response to this survey: Her brilliance as a lawyer. The skills and thinking that gained her respect. Her professional colleagues. Her family (how _did_ she produce a moderate-drinking daughter?). Like Beth, you have successes and accomplishments. You have strong areas of your life, skills, and other assets, including your own values. You're not a blank slate for somebody or something to imprint _their_ mark on. Your answers tell you a lot about who you already are. Nonetheless, the function of this exercise is to recognize the as yet unleashed power of your personal resources, ones you have neglected, quarantined, or not given the time and place to develop more fully.\n\nWhat Is Self-Acceptance?\n\nSelf-acceptance is a fundamental concept in contemporary psychology. Think, first, of all the girls who have negative self-images because of how they look at their bodies, of Alexis and other anorexics and bulimics. Self-acceptance is also, in the form of the concept of \"loving kindness,\" a precept of Buddhist philosophy. Self-acceptance and loving kindness are compassion for yourself and the belief that you, like everyone else, are entitled to fulfillment and joy. In her book _Radical Acceptance_ , Buddhist psychologist Tara Brach describes the two sides of self-acceptance: \"seeing clearly, and holding our experience with compassion.\" Mindfulness is the essence of seeing clearly. And now we must bring compassion to our clarity. Compassion, as Brach describes, \"is our capacity to relate in a tender and sympathetic way to what we perceive,\" including our vision of ourselves. Self-acceptance is grasping emotionally and intellectually that there is nothing so different or wrong with you that you are disqualified from being a part of humanity and claiming what life offers you. When you address your addiction, you realize that, yes, you have made mistakes; no, your life is not a mistake in the universe.\n\nPut yourself in the position of a parent of a child whose physical features do not meet the cultural ideal. Let's say she has a large nose. Of course, you believe\u2014and strive to make clear to the child\u2014that she or he is not defined by her nose, that she is not disqualified from any activity by her nose, and that kids with less prominent noses all harbor their own individual quirks. One may have an ideal nose, but happen to be carrying some extra weight. Another might have a developmental disability. While yet another might have infinite freckles. The parent is not primarily oriented to noting other children's deficiencies, of course. Instead, she wants to convey to her daughter what a beloved, talented, appealing human being _she_ is.\n\nThe truth here is that all these children\u2014each of whom falls short of perfection\u2014deserve to participate in a joyous adventure together, no matter what their peculiarities. Perhaps you can see where this is going and can follow this analogy to its logical conclusion for you, as a child of nature. And it is a _logical_ conclusion.\n\nReflection: Self-Compassion\n\nWhen you view another person through the panoramic lens of compassion\u2014as you would for any child born on this planet\u2014superficial standards of perfection are irrelevant. Compassion is not blindness to negativity. It is perspective. It's the ability to see both flaws and ideals as incidental to the whole, which is abiding. Everyone, including you, deserves to participate fully in life. Your positive qualities don't entitle you to fulfillment, but neither do your negative qualities disqualify you. Surely you, like everyone else, have areas that need attention\u2014areas that hinder you from honoring the things you value. Addiction\u2014among other things\u2014is one significant such hindrance. And these negative attributes of yours can never excuse your not honoring what matters most, or prevent you from doing so. If you feel some resistance to viewing yourself compassionately, remind yourself that this is the most rational and healthy perspective, the way you would treat any child, any young person, any fellow human being. Reread and _think about this_.\n\nExercise 2: Self-Compassion\n\nMake a list of the negative traits that you believe you are saddled with. Next to each trait, record how it makes you feel to believe this about yourself. (Don't worry\u2014we'll complete Exercise 1, Part 3 shortly!)\n\n\u2022 How did you come to believe this about yourself? Did you hear it from someone?\n\n\u2022 Now, can you think of a time when you behaved in a way that emphasized the opposite characteristic? For instance, if you listed that you are selfish, remember when you behaved generously and write about that experience. Now, think of another time. How does it make you feel to remember this\/these experience\/s?\n\n\u2022 How realistic is it for you to believe that you are defined by that negative trait? Put that negative quality in a more realistic perspective in terms of your whole life.\n\n\u2022 Imagine that you are speaking to a beloved friend with the same negative characteristic. What would you tell him or her if they said they were overwhelmed by their own worst trait?\n\nSelf-Acceptance in The PERFECT Program\n\nTrue recovery is built on self-acceptance, which begins with embracing a view of yourself as someone who deserves a normal, fulfilling life. You cannot start down a path that will lead you toward wellness and peace of mind if you do not believe that the best life has to offer is for you, too. Taking action to overcome addiction is, after all, an act of self-care. So, instead of beginning your journey by looking for something that's wrong with you, let's start by embracing what's already right and then building on that. As well as your deserving the best, the people and things (values, connections, accomplishments) you care about deserve your best.\n\nExercise 1, Part 3\n\nRevisit your original answers to the question, \"I want to recover from addiction because . . .\" and your reflections about how negative your view of yourself is. Focusing on negative pronouncements, shift your perspective to one of compassion and objectivity, and see if your earlier statement still makes sense. For instance, maybe you can see that you are not a terrible parent, but a loving parent who has behaved in ways that you would not if you were free of your addiction. In the second column, write down these more realistic observations.\n\nBy this point, even if you see that self-acceptance is the rational, healthy approach, it still takes real effort to apply it to yourself. Habits of mind are hard to break, and that's why _self-acceptance, or loving kindness, is a practice_ , in exactly the same way that mindfulness is a practice, and not an instant revelation. What's more, self-acceptance is a more challenging practice, because it tends to confront and even activate our fears about ourselves, causing us to respond defensively. For instance, deliberately working to accept the idea that you are not a social misfit can actually feel frivolous and embarrassingly self-indulgent. Imagine how it would feel to repeat the phrase, \"I love you, [your name here],\" out loud to yourself. Just thinking about this scenario\u2014let alone actually doing it\u2014probably makes you cringe.\n\nDon't worry\u2014I won't ask you to do that one. It's pretty advanced! Instead, the exercises will introduce you to a meditation that has its roots in the Buddhist practice of loving kindness. That is, the deliberate cultivation of compassion, which goes hand-in-hand with mindfulness. Clarity and self-acceptance are the cornerstones of your reclaimed life, ones that you will reinforce in creating new habits of mind. In referencing Buddhist practices here, I am not encouraging you to adopt a religion. (I _will_ note that Buddhism does not have a higher-power, God concept, which has led courts to rule that it is unconstitutional to force Buddhist practitioners to participate in AA.) As I've said throughout, this thousands-year-old practice replicates important contemporary psychological and therapeutic concepts. And even the idea of \"practice\" strongly suggests the modern cognitive-behavioral principle underlying _Recover!_ \u2014that you do best and most readily that which you have rehearsed doing until it becomes a natural response for you.\n\nExercise 1, Part 4\n\nAfter having listed your reasons for wishing to escape addiction in the first column, then assessing how negative they can be and recasting these in positive ways in column two, now move to the third column and reframe your answers to \"I want to overcome addiction because . . .\" based on your middle-column revisions. For example, you might replace \"I am a terrible parent,\" with \"So I can be present and involved in my children's lives every day.\" The point of this exercise is to help you internalize the positive, life-affirming reasons for beating your addiction. If you can think of any more ways that living addiction-free will have a positive impact on your world, please list them here, too.\n\nForgiveness\n\nAddicts are known for excusing all sorts of misdeeds toward others and society. But there appears to be little difference between such shallow notions of self-forgiveness and sociopathy\u2014whatever I do for myself is fine, is justified. So how is it possible for you to \"let go\" of the guilt you may carry for destroyed relationships, broken promises, deteriorating health\u2014even instances of betrayal and violence? How (like Rose) do you forgive yourself for letting down a child or squandering your dreams? It's quite impossible, if we believe that forgiveness means absolution from responsibility or simply moving on as if nothing had happened. _And, yet, a crucial ingredient of self-acceptance is forgiveness of self and, in an act of sister compassion, forgiveness of others._ Just as mindfulness meditation affects addictive behavior and brain centers, compassion can also be learned.\n\nForgiveness is both a critical element in and a natural result of self-acceptance. Self-deprecation and guilt for past misconduct do not lead to better behavior, as we saw earlier in relation to relapse after feeling shame. Self-control research has discovered that self-criticism _reduces_ self-control. Rather, self-acceptance and forgiveness\u2014especially in the face of stress and failure\u2014 _enhance_ people's capacity for changing negative behaviors. Consider a study of students who procrastinate, then beat themselves up for having done so. The very act of self-recrimination for procrastinating makes it _more_ likely that they will do so again before future exams _. The harder the students were on themselves, the greater this effect._ Thus, \"forgiveness, not guilt, increases accountability . . . taking a self-compassionate point of view on a personal failure makes people more likely to take personal responsibility for the failure than when they take a self-critical point of view. They also are more willing to receive feedback and advice from others, and more likely to learn from the experience.\"\n\nThe seeming paradox that being kinder to yourself makes you more ready to accept negative feedback follows from Freudian psychology as well. The energy spent defending your ego\u2014like that used for patchwork on your addicted self\u2014diverts you from the essential changes you need to make. And, so, the opposite of self-forgiveness is as likely to be self-protective defensiveness as it is to be self-abuse. Both end up at the same place\u2014maintaining your self-defeating behavior.\n\n* * *\n\n**CASE:** George and Melissa's child, Sam, was having behavioral problems at school. When presented with his parenting deficiencies, George immediately became defensive: \"So, I'm a bad parent!\" The only alternatives for George were, first, to blame his own father and mother for their poor parenting; second, unfortunately, to offset the negative feelings he had about his own parenting by labeling Sam with this or that condition to excuse his misbehavior. This then contributed to George's remonstrating and punishing Sam, which sometimes dominated their interactions.\n\nInstead of having the therapy be about saying that he was a bad parent, the family therapist emphasized, they were all in the business of allowing George to interact more constructively with Sam: for instance, by distracting Sam with positive activities when he acted out, by praising him, and by causing him to be mindful (as age-appropriate!) about his acting out. \"Sam, I wonder how you were feeling when you hit that boy at school. How did you feel afterwards, and when the teacher sent you home?\" As George relaxed within himself over the course of therapy, his self-forgiveness created a chain reaction of his showing greater tolerance for Sam's behavior while Sam in turn became more self-accepting and, as a result, better behaved.\n\n* * *\n\nNow let's define the alternative to self-protective defensiveness as forgiveness of a type that reflects compassion and realism. Even if you are not ready or able to completely release the emotional pain, you can strive not to be guilt-ridden. It may feel to you, at this moment, that you don't deserve to live without guilt: You willingly take on the painful burden of self-reproach as penance. That is normal, but I hope you will accept this insight along with your pain: Grasping for pain by ruminating on and reliving your worst moments will keep you stuck in pain\u2014 _and pain begets further pain._ Anything you have done to harm or betray yourself or others was done from a place of pain. So, your journey to true recovery is not simply a selfish gift to yourself, but a genuine act of atonement to the family and friends you may have hurt or betrayed. Lifting yourself out of the painful frame of mind and heart that would allow you to perpetuate destructive behavior begins with forgiving yourself.\n\nReflection: Self-Forgiveness\n\nForgiveness is not an event. It is a _process_ of releasing paralyzing emotional pain by focusing compassionate and understanding attention on your memories and feelings of remorse or grief. Reread and _think about this_.\n\n* * *\n\n**CASE:** Harry abandoned his girlfriend and their young daughter, Anne. He had no interest in family life or the responsibility involved. He tried here and there, but the hit to his freedom made him seethe. He had a regular barstool at the local pub, and it missed him keenly when he was elsewhere. That felt more like home to him than his apartment with his girlfriend and daughter. So, he just dropped out of their lives and became a deadbeat dad\u2014missing child support payments, missing birthdays, going months without a phone call. Sometimes he felt like a heel, when he thought about it. But more often, he cynically used his estrangement from his daughter\u2014blaming it on the girlfriend\u2014to garner sympathy from women at the bar, going on and on, drink in hand, about how he missed Anne, wished he could see her grow up.\n\nGrow up Anne did. And Harry missed it. As a teenager in high school, Anne treated him like a distant relative, which he was. But now, as a middle-aged man with less interest in barstools and barflies, Harry was overwhelmed with regret. There are no do-overs in situations like this. Harry had blown it. His guilt grew into a persistent self-loathing, the pain of which he still alleviated at the bar, albeit during briefer periods spent there. The change was superficial; Harry was still indulging the same behaviors that had brought him to this point. He missed his daughter's graduation\u2014not simply because he'd rather be partying, but because he now felt that he didn't deserve to celebrate her accomplishments with her.\n\nFor her part, despite the fact that she was used to his missing her milestones, Anne was nonetheless hopeful that Harry would show himself, and then disappointed when he didn't show, a pattern that never failed to dismay her.\n\n* * *\n\nHarry's profound remorse kept him paralyzed, stuck in a life that perpetuated and deepened his own and his daughter's pain. It's true that he can never make up for the lost time and can never undo the damage his abandonment did to his relationship with his daughter, nor can he fix the hurt he had caused. Perhaps he deserves a life of loneliness and regret for the choices that he made. However, wouldn't it be better for everyone whose lives Harry touches if he could influence his social sphere in a positive way? It might be satisfying\u2014to observers and to Harry himself\u2014to know that he is suffering. But as long as he is consumed with self-loathing, he will continue to hurt the people around him, including his daughter.\n\nShifting perspective to one of compassion for Harry, we can provide a context of understanding for his behavior. Harry had been emotionally abandoned himself as a child. His parents were divorced, his father was a deadbeat dad, and his mother raised Harry along with three other children. So he came into fatherhood having no experience of it as a child or a man, believing that he was incapable and unworthy of it. Now, understanding what happened and why is not the same as absolving Harry of responsibility for his behavior. He has to live with it. What he does have, however, is the opportunity to influence future outcomes: to become a healthy, positive influence on his daughter's life from here on. To do that, he must begin the process of self-forgiveness.\n\nThe 12-step practice of \"making amends\" (step 8) involves going to all of the people you have harmed in your life, acknowledging to them that you have hurt them, and telling them that you're sorry. It sounds like the correct thing to do. However, in AA, amends is an event, like confession, and once you have made your apology, you are absolved and need never revisit your misdeeds. This is in keeping with AA's \"keep your own side of the street clean\" philosophy and its essentially selfish\u2014\"look after yourself\"\u2014program. \"Amends\" plays out the idea that one makes amends for oneself\u2014to support one's own sobriety\u2014not to establish an understanding with the people one has harmed, or even to develop a new aspect of one's own personality, view of life, and actions. Thus, amends-makers are told that it is none of their business whether the recipient of their amends is receptive or not. You've done your job when you apologize.\n\nGranted, you cannot control whether or not others forgive you or choose to reinstate you within their community. But to believe that you have done your part by apologizing and that it is \"their problem\" if they don't accept your contrition lacks the depth and maturity of genuine compassion and accountability. Harry has apologized to his daughter more times than he can count, and has even felt sorry for himself when his overtures have not resulted in her immediately embracing him and all his faults. For Harry, forgiveness requires an interwoven three-part journey, one that requires him to forgive himself, to seek forgiveness from his daughter, and to forgive his own parents\u2014each part influencing and supporting the others. Let's examine each one separately.\n\nIn order to forgive himself, Harry must start by taking a broader view of his behavior, opening with the understanding that he is not, at his core, a selfish, irresponsible, irredeemable human being. He has behaved in ways that he is ashamed of, but the very fact that he can feel shame and remorse indicates that there is a wise heart alive within him, just as your recognition of your flaws and mistakes shows your own wise heart. Broadening his perspective on his inner landscape to include his wise heart will allow Harry to bring the lenses of compassion and understanding to bear on his interpretation of his past behavior. Where he once saw nothing but coldness, he might now recognize fear. Where he once saw selfishness, he might now see the floundering of an abandoned child. And where he once saw intractable negative qualities, he might now see a path opening into possibility, even redemption. At the point where he can see that transformation through self-forgiveness is possible for him, Harry confronts a straightforward choice, but one difficult to make. He can choose to live in guilty pain, or to release it.\n\nHarry's potential act of self-forgiveness may provide cold comfort to his daughter, and, indeed, she may never forgive him no matter how profound his transformation. Continuing down the path illuminated by his wise heart, regardless of her acknowledgment\u2014respecting her boundaries without expectation and without believing that her rejection or resentment is \"her own problem\"\u2014is one way Harry can honor the pain he has caused her and genuinely change the situation and the people involved in it. Whether or not his daughter chooses to forgive him, Harry can still live a life infused with compassion and understanding for her, allowing him to cease making decisions that cause her more grief. Even should Anne forgive her father, she might choose to maintain her distance from this virtual stranger, whom she has known to be toxic and who has brought such disappointment. Her own wise heart prevents her from continuing to put herself in harm's way.\n\nHarry may include his own parents on his journey to forgiveness. Again, he has the choice to continue ruminating on the wrongs done to him and the devastating effects they have had on his life, to feel sorry for himself and bitter. Or he can view these things with forgiveness in order to release his own feelings of abandonment. He may be able to see that his mother was tired and overwhelmed when she neglected him\u2014that she simply was not able to be a nurturing caretaker. Perhaps now he might see that she was doing the best she could. Harry can acknowledge the heartache his mother's withholding caused him as a child. But extending compassion to her now allows him to begin down the path of healing as an adult. And being able to see that her behavior was an indictment not of his lovableness, but of her capacity to express love, reinforces Harry's ability to love himself. In other words, Harry's choice to forgive others is bound to his ability to forgive himself, which in turn gives him the ability to seek forgiveness from and make genuine amends to Anne and others he has harmed.\n\nIt is a common platitude to say that forgiveness is a gift we give ourselves. The underlying message in that aphorism is that we don't forgive people who harmed us to let them off the hook; we do it so that _we_ are off the hook, so that we can move on with life and be better ourselves. While it's true that we forgive for our own well-being, our well-being has an impact on everyone and every situation we come into contact with\u2014past, present, and future. To expand on the notion that it is a gift we give to ourselves, bear in mind that self-forgiveness is essential to true recovery. Releasing your pain of remorse or self-loathing is no easy thing. But doing so is freeing.\n\nReflection: Harm Reduction and Forgiveness\n\nIn Chapter 3, I introduced the concept of harm reduction\u2014the idea of curtailing the addiction script of \"in for a penny, in for a dollar.\" That is, the idea that you've already made a mistake, so why not make it a doozy\u2014if you've had a drink, go all out and expose yourself to the worst dangers possible. We will see the reversal of this script again in the practice of \"relapse prevention,\" in which you pull up short on your incipient bender. The same pattern and its opposite apply to your deteriorating relationship with someone you care about.\n\nNotice how Harry's guilt caused him to continue to turn away from his daughter, exacerbating his alienation from her. This is typical of addictive patterns, where one bad feeling begets others, until your whole attitude cascades into a total abandonment of the situation\u2014and often consciousness\u2014at the cost of further failure and bad feelings. Can you find an example where this has occurred in your life, where your initial overreaction led to bad feelings between you and a loved one that fed off each other? As painful as reimagining such a situation can be, think now how you might have practiced forgiveness at the outset and avoided such bad consequences including, perhaps, the end of the relationship? Think how the other person involved in the situation might have responded differently, more positively, and your life would be richer today.\n\nPerhaps now you are prepared to make forgiveness your practice the next time you face such a situation. Or perhaps you are not quite ready to stop ruminating over something you did or something someone did to you, or beating yourself up over something you may continue to do. In those cases, you can begin planting the seeds of forgiveness by simply allowing for the possibility of release. Be aware of the trap you may set for yourself by heaping more reproach on yourself for your resistance to change. Just like recovery, mindfulness, and self-acceptance, forgiveness\u2014as I said\u2014is a process. If you are struggling with self-forgiveness because you find it difficult to accept the harm you have caused yourself or others, or because others have wounded you in a way that keeps you in a state of heartache, you can start the process of forgiveness\u2014make room for it in your heart\u2014now.\n\nWhich brings us back to Suzanna, the twenty-something alcoholic alcoholism researcher. Suzanna, of course, is in a role similar to Anne's or Harry's with respect to their parents. Moreover, she drinks to mask her pain, the pain of abandonment she always felt from a mother who endangered her by her own selfishness and inadequacy, by leaving her to her father\u2014and to fate. That time has gone. Suzanna is an extremely accomplished and talented survivor, and her mother is still alive and active and wants a relationship with her daughter. Yet, in her late seventies, she is not really in a position to fully acknowledge her forgone sins and her role in Suzanna's problems. In fact, she is not that different from the person she was when she left her family, although she is in a different situation now, living alone, having divorced the man she left them for.\n\nHere is how Suzanna thinks:\n\n\"I don't mean to attempt to relinquish personal responsibility for my actions\u2014that's pointless. But I guess there is some comfort in the thought that maybe I'm not actually weaker than other people on a fundamental level, maybe I'm just still trying to overcome a deep pain, and maybe I'm doing okay. I've always had a strong drive towards personal integrity, had a deep desire to be good, and that includes taking care of my body and my mind. I feel deeply ashamed that I have wasted time, energy, and brain cells on a never-ending quest to feel better. But it's not feeling better that I crave, it's feeling okay, like maybe this life is at least a little bit more than a burden to be suffered through.\n\n\"These are the things that plague me when I don't drink. Drinking makes me happy in the short term, yes. But more importantly, I think, is that it has a sustained effect of dulling negative feelings and quelling intrusive thoughts. And in that way it is the best medication that I have found so far\u2014better than antidepressants!\u2014and I don't know if I'll ever really be able to give it up. And I don't mean drinking a healthy amount either.\"\n\nAs to Suzanna's mother:\n\n\"I am not willing to let go of the emotional pain yet. It serves a purpose, just like drinking does. We learn lessons from pain. I can decide to not beat myself up about it, but I refuse to let it go. I know that my previous experiences of hurt cause me to be wary of strong feelings towards other human beings. Only time will convince me that it is really safe to have such feelings. It may take a long time.\"\n\nSuzanna, like all of us, is a work in progress. So, what should Suzanna do? Remember, the problems we are concerned with are Suzanna's, and not just forgiveness for forgiveness's sake. What will make her whole within herself, allow her to avoid drinking to self-medicate, and enable her to accept and love herself and enter the world of trusting and intimate relationships? As with Harry, for Suzanna, too, the answer may be forgiveness\u2014or at least acceptance.\n\nJeannette Walls was asked about her mother, whom she described as selfish and neglectful in her powerful memoir, _The Glass Castle_ (Scribner, 2005). For years, Walls avoided her mother, even as the older woman was homeless in New York where Walls was a member of the glitterati. Now Walls's mother lives in a separate residence on her farm. Walls says, \"So many people ask, 'How could you forgive your mother for the way you were raised?' It's really not forgiveness in my opinion. It's acceptance. She's never going to be the sort of mother who wants to take care of me.\"\n\nMoving Forward\n\nAll of these decisions and efforts\u2014to strive to forgive, to get beyond pain and negativity\u2014are motivated by larger values you hold: to want to love, to be at one with your family, to be at peace, to be free to accomplish larger goals, to be a good person, and to benefit others and humanity. In the following chapter, we will turn our focus to the elements of your life that are most valuable to you\u2014rediscovering meaning and beginning the process of infusing your life with purpose.\n\nExercises and Meditations\n\n_Meditation: Loving kindness_\n\nLoving kindness practice is meant to cultivate compassion by making it a familiar state\u2014a habit of mind. It challenges you to direct compassion toward yourself and to extend it to others. Often, one will begin with a template of sorts\u2014a list of wishes you might have for someone you love unconditionally. For instance:\n\nMay ____ be healthy and whole.\n\nMay ____ be safe from danger.\n\nMay ____ be content and at peace.\n\nMay ____ love and be loved.\n\nNow, please consider someone you love without reservation, and in your Personal Journal make your own list of well-wishes for them. Feel free to use the ones we provided, write your own list, or mix and match.\n\nEvery day\u2014when you wake up, when you're walking the dog, before your daily meditation\u2014repeat your list of well-wishes, focusing at first on one or more people you love. Normally, one would use one's self as the first object of the loving kindness meditation, but if you have a difficult time conjuring these feelings for yourself, it will help to start with someone for whom you already feel a more spontaneous sense of compassion. This will allow you to become accustomed to holding compassion in your heart. You are going to keep extending these well-wishes, in this order:\n\n1. Someone you love (or all the people you love)\n\n2. Yourself\n\n3. Someone you are neutral about (perhaps someone you see every day, but don't know well)\n\n4. All of humanity\n\n5. Someone you dislike or harbor difficult feelings about (perhaps a bully)\n\nRepeat your list of wishes at least three times for each object of your compassion, then move on to the next. If this is a lot to take on at once, feel free to approach this practice in small steps over time. Take the time you need to feel comfortable doing this\u2014and making it part of your routine\u2014before extending your practice. You might start by directing your wishes only toward your beloved and to yourself. When that begins to feel natural, extend your practice\u2014you should always feel challenged as you push your boundaries.\n\nThere are many variations and approaches to loving kindness. You can explore and find others. All have the same kernel\u2014an idea, a spirit, an approach to life to which you have now been introduced, and that you can continue to explore while reading _Recover!_ , while embarked on the rest of The PERFECT Program, and throughout your life.\n\n_Journal exercise_\n\nThis is an exercise with three components, paralleling Harry's\u2014and Suzanna's related\u2014path to forgiveness. This is a detailed writing project\u2014one that may be emotionally difficult\u2014so allow yourself ample time to complete it, even if that means working on it over the course of a few days.\n\nBegin by writing down in your PERFECT Journal all of the things about you, or things you have done to yourself, some of which you may still be involved in, that you feel are unforgivable or undeserving of compassion. For instance, have you damaged your health or finances through your involvement with addiction?\n\nNext, write down the things you have done to others, or negative situations you believe you are to blame for (which, again, may still be ongoing) that you feel are unforgivable. For instance, have you behaved neglectfully, carelessly, selfishly? Recklessly or violently?\n\nFinally, write down all of the harmful things that have been done to you by others, things you feel you cannot forgive.\n\nOnce you have made your lists, review them with the intention of seeing each of these events as the result of some fear, hurt, incapacity, or void in your life or in someone else's. Even if you have believed that your behavior (or someone else's) was due to your own (or someone else's) fundamentally weak or evil nature, make your best guess about what could have allowed for such behavior. Coming up with a reason does not mean that you must immediately extend forgiveness. Rather, this exercise is broadening your understanding enough to allow for the possibility of forgiveness. It opens the door.\n\n_Mindfulness meditation:_\n\n_Forgiveness of others along with oneself_\n\nSit comfortably in your meditation spot and bring to mind an event or a personal characteristic for which you cannot forgive yourself or someone else. Remember it in as much detail as possible, and pay particularly close attention to the feelings the memory arouses in you. Bring your mindful attention to those feelings and the physical sensations they produce. Then name these feelings, both emotional and physical, as precisely as possible. For instance, if you feel shame or hopelessness, call them what they are. If those feelings register physically as restlessness, burning scalp, or weakness, name those sensations as well.\n\nHold those feelings at the front of your mind\u2014tolerating the discomfort if you can\u2014but, as you hold them, imagine expanding the physical space you occupy and the emotional space around those feelings. For instance, imagine that you have expanded into the space around you by six inches. Allow these feelings to exist as they are, but visualize making more room for them. This may take some practice, but when you are able to do this and to hold that open space, shift your perspective into the neutral space and reexplore these hurtful feelings with a compassionate eye. You can do this meditation focusing on self-forgiveness or forgiveness of another.\n\nLike the loving kindness meditation above, the following is a direct meditation to address forgiveness.\n\n_The PERFECT Program version of_\n\n_Buddhist forgiveness practice_\n\n_To those whom I may have caused harm, knowingly or unknowingly, through my thoughts, words, and actions, I ask your forgiveness._\n\n_To those who may have caused me harm, knowingly or unknowingly, through their thoughts, words, and actions, I offer my forgiveness as best I am able._\n\n_For any harm I may have caused myself, knowingly or unknowingly, through my thoughts, words, and actions, I offer my forgiveness as best I am able._\n\nCHAPTER 6\n\n_Rediscover_\n\nIntegrity\u2014Finding and following your true self\n\n* * *\n\n**CHAPTER GOALS**\n\n\u2022 To develop your focus on your true core values and sense of purpose\n\n**Starting by:**\n\n\u2022 Creating realistic expectations for yourself\n\n\u2022 Understanding the flow and change in your ability to follow your purpose\n\n\u2022 Putting into play a plan to reconnect with your values\n\n**Purpose:** Keeping your eye on the prize\u2014escaping addiction\u2014is difficult when you're unclear about why you want to pursue that goal. Addiction blurs and distorts the horizons of your life, preoccupying you with its immediate and superficial gratification, so that your true center has become obscured and confused. Even _after_ you loosen your addiction's grip, you may still not be able to hew to your true center. So how do you stay the course to wellness, when you find yourself overwhelmed with endless possibilities and frustrating setbacks? Your task is to sharpen your purpose\u2014your _reason_ for quitting and steering forward\u2014one that is personally clear and meaningful to you. In this chapter, you will reconnect with what you value most in life, what brings you joy and fulfillment, and begin the process of transforming those values into clear goals, including especially a non-addicted, fulfilling life.\n\n* * *\n\nDon't Change, Become\n\n_Why your resolve fails_\n\nOne of the great mysteries of human nature is that we ever feel tempted to continue in\u2014and often fall back into\u2014behaviors that we _know_ make us unhappy. You've probably experienced this phenomenon yourself: You want to quit your addiction and enthusiastically adopt a new lifestyle\u2014you even begin down that path, perhaps proceeding a good distance. You look great, feel great, and even get a little evangelical about it all. You can't believe you ever chose the barroom over the family dinner table, or smoking over breathing, or sugar over whole foods. And then you find at some point that you are right back where you were before you seemingly pulled it together. Why is it so easy to give up something new that makes you feel fantastic and revert to a lifestyle that you know full well will make you miserable? How does this happen?\n\nWe have already seen, in Chapter 2, that _addiction makes complete psychological sense. It's a natural human response to unmanageable life circumstances, one through which people mistakenly attempt to find purpose and a sense of well-being._ You gain important \"benefits\" from the addiction, rewards that sustain the addiction and, for a time, sustain you as well. As I noted:\n\nAddicted people seek refuge in any powerful, consuming experience that allows them to cope with a life that feels meaningless or out of control\u2014a feeling that is both worsened and relieved by their addiction. The addiction further fills countless hours beyond those eaten up in altered states of consciousness or compulsions. Think of all the mental and emotional energy an addiction wastes: days planned around purchasing and consuming the substance or practicing the activity; fielding negative fallout (like angry co-workers, family members, and friends; mounting bills; health problems); making solemn promises to stop; remorse and guilt. Yet, as painful and self-defeating as these feelings are, their predictability sustains addicts and even lends a bizarre sense of purpose to their lives.\n\nSo, freeing yourself from an addiction takes some effort. Obviously, keeping off drugs or alcohol or away from another addiction involves something akin to willpower. Recently, researchers and human potential writers have reinvigorated the concept. Experimental psychologist Roy Baumeister found both that willpower can be practiced and exercised (for example, by standing straight, not buying Doritos, and solving difficult puzzles) and that it can be exhausted by overuse (students forced to use willpower in order to resist a snack when hungry, track a boring display, or control their emotions during a tear-jerking movie immediately afterward showed less self-control). All of this is a bit like you might expect, were it not for intervening messages you have received, like the 12-step doctrine ridiculing and dismissing willpower as a tool in recovery.\n\nBaumeister's findings don't add up to easy answers for the withdrawing or sober addict. They suggest both that exercising willpower in many areas enhances your resistance to your addiction and that, having freshly quit an addiction, your willpower is being strained and shouldn't be taxed. Indeed, conceiving that you are exercising willpower (as in dieting or thinking that you can never use a substance again) can actually weaken your resistance. The PERFECT Program reframes self-control so that you see yourself as becoming, rather than as resisting temptation or even as changing. For example, you can view quitting smoking not in terms of overcoming your addiction, but as embracing and perfecting your true core self. Used in this way, willpower research informs my recommendations throughout _Recover!._\n\nThese issues\u2014what can be called motivation\u2014appear in all phases in releasing an addiction, as we shall see both in regard to initial quitting and later in avoiding relapse. To begin, there may be a certain element of disillusionment that accompanies positive life changes. Consider, for example, the longtime restaurant server who opens her own restaurant, after years of fantasizing about being her own boss. She dreams of independence, success, but mostly of serving uniquely delicious food to a packed house of satisfied customers. She has a solid background in food service, has done all the research, and feels that she is ready for, and realistic about, the incredible amount of work it will entail. She dives in, head first. But, after the initial burst of excitement wears off, this new venture becomes her real life. The twelve-hour days become a routine: bookkeeping, managing her staff, fixing appliances. . . . It's no longer a thrill to see the distributors show up to stock the kitchen\u2014those are costly items she must use up quickly by inducing customers to consume them.\n\nThere's a bit of a catch-22 in play here, because if she had factored waning enthusiasm and drudgery into her bright plans for the future, she might never have mustered the enthusiasm and energy required to get the ball rolling. But, then, she's not as prepared for the inevitable reality that work is still work, and she is still herself\u2014only now, her responsibilities are more serious and there is more at stake. It is at this point that keeping focused on her sense of purpose is vital. This new restaurant owner can face a crossroads. Feeling overworked and out of her depth could discourage her, causing her to throw in the towel literally, by closing her doors, or figuratively, by carrying on resentfully and martyring herself to her business as it fails. Or, with her eye on the values that inspired her in the first place (independence, creativity, passion for food, love of people)\u2014she could see the drudgery as one element of the big picture that motivates her to succeed.\n\nOvercoming addiction is similar. You may have fantasies about who you would be and what life would be like if you were not held back by your addiction. Those fantasies can give you the inspiration you need to get started, which is a good thing. But, ultimately, you are going to need a reason to keep pursuing your goal when it becomes clear to you that straightening up will not result in instant realization of all your dreams. Here is another restaurant analogy for you: People who are learning to carry trays of food and drinks to tables are taught to keep their head up and their eyes forward, focused on the direction in which they are going. If they look at their feet or at the tray they are carrying, they are prone to lose their balance, and food and drink will inevitably start sloshing around, perhaps hitting the floor. When you embark down the path toward wellness\u2014freedom from addiction\u2014you must employ a similar technique: Keep your focus on your goal. This is easy enough to do when you're carrying a tray full of drinks and you know where you're going with it. It can be much more difficult when you're headed down an unfamiliar, metaphorical path with no clear goal in sight\u2014perhaps some vague destination called _recovery_ or _spiritual enlightenment_ \u2014which is how you may feel now.\n\nExercise 1, Part 1\n\nIn your Personal Journal, indulge your fantasies. Write down everything you imagine you would be, or would do, were it not for your addiction. Relationships, work, travel, home life, wellness\u2014the whole shebang!\n\nWhen you're in the thick of addiction, it's easy to conjure up fantasies of the person you could be, in the same way that it's easy to see only booming success and personal satisfaction before embarking on a new business venture. As I said, these fantasies can be very useful and motivating, but they are not sustainable. Not only that, but\u2014as usual\u2014addiction can bring even more confounding obstacles to this common scenario, aside from disillusionment.\n\n* * *\n\n**CASE:** Graham is a plumber, an independent contractor with a spotty reputation. He has a big and charming personality and does solid, high-end work. That is, when he's on his game. But, he's a binge drinker. His weekend benders have become legendary around town, and, although people think he's a great guy who gets the job done right\u2014and even on schedule\u2014he has been losing contracts because customers are wary of hiring him. Graham has never been just a social drinker, a scotch-with-friends or wine-with-dinner kind of guy. Once he starts drinking, the switch is flipped: His sound judgment is replaced with an insatiable appetite for more. _He knows this about himself._\n\nDespite the single-minded self-obliteration he indulges in, and its resulting blistering, days-long hangover, Graham still manages to stop partying when he has a job to get to. He pulls himself together, full of excruciating regret, believing in his heart that now he will quit for good and all. He never, ever wants to put himself through this again. He also has a family: a wife and two kids. He may not miss work, but he has missed family weekends and date-nights with his wife, among other wholesome personal obligations. So, how is it that, after a couple of weeks or even months off the sauce, when he's feeling good, physically and mentally, Graham is able to talk himself into that \"one drink\" he knows will lead to another lost weekend? How does he convince himself that enjoying a drink after work will not go the way it always goes? This is a man who never in his life has had the experience of enjoying a single drink\u2014what disconnect from reality allows him to believe he ever will? Why does Graham make such an irrational decision, given his reality, after he has been sober for a period of time? Shouldn't he be stronger and sharper\u2014better able to stand up to temptations\u2014when he escapes the gravitational force of his addiction?\n\n* * *\n\nWhy is it so easy for some people to change for just a short time, then go off the wagon and give in to temptation? Put more positively, what is the secret to making changes stick? If you have quit an addiction in the past, and wondered how on earth you could ever have lived so self-destructively, only to find yourself right back in the thick of addiction, then Graham's story should ring a bell for you. It is a common experience, and it is baffling. Quitting an addiction can be almost like waking up from a vivid nightmare: The memory of a horrible dream might linger for days, the same way the pain of a particularly brutal hangover or the sting of a mortifyingly shameful episode might linger for a time. The sharp memories of the aftermath of addiction might keep you determined to stay on the wagon. But the immediacy of those memories begins to fade, the same way a nightmare does, leaving you with hazy impressions of what it was really like (\"It wasn't _that_ bad, was it?\u2014sort of fun, really\u2014none of these daily concerns and worries.\").\n\nIn other words, focusing on the horrible downsides of the past might _in the short term_ start you on the recovery path, as it does episodically for Graham. When you're keenly aware of the misery you are avoiding by quitting your addiction, it is easier to combat challenges to your resolve with the fear of reliving those horrible feelings. This may tie in with the stage you are at in leaving your addiction, as we will see. But, as the memories fade\u2014as they will do\u2014you will have to find other, more sustaining goals and motivations.\n\nReflection: Self-Forgiveness Versus Self-Excusing\n\nWe spent some time in the last chapter talking about forgiving yourself. Keep in mind that ignoring or dismissing the pain you have inflicted on yourself is not the same thing as self-forgiveness. Self-forgiveness springs from mindfulness\u2014or clarity of perception\u2014while forgetting springs from mental sloth, or obliviousness. Self-forgiveness doesn't say, \"Oh, that wasn't so bad,\" when it really was. It says, \"That was bad, but it does not define me.\" Can you reconcile recognizing the negatives of what you have done, sometimes the horror of it, with respecting and loving yourself? Review the answers you gave in Exercise 2 (page 118) and in Exercise 1, Part 4 (page 120), in Chapter 5.\n\nRemember that addiction is a consuming, destructive involvement that captures your time, your mental and emotional energy, your focus. So much of your life as an addicted person revolves around indulging in and recovering from addiction\u2014interspersed perhaps with fantasies of your non-addicted life. But the dreams of who you could be without addiction fade as quickly as do the nightmare visions of the past. In the stark daylight, you find yourself feeling lost in the world, not knowing how to fill your time, even feeling that you don't know who you are anymore without your addiction. Everything does not automatically fall into place once you clean up\u2014in fact, your responsibilities, your burdens, increase. As Rose (in Chapter 1) found, the first realization upon quitting is a recognition of the many neglected things you _must_ do\u2014family obligations, work and school, healthy behaviors\u2014along with avoiding your addiction. Like the new business owner, you now have to cope with the challenges of everyday life, and you have to do it without an escape hatch. Like Graham, who believed he could have one drink (while knowing he wouldn't), you might fantasize about taking a quick respite from your addiction. But, for you, early in recovery, this may be a quick respite that doesn't exist.\n\n_Finding your true self_\n\nIt may be helpful to think about this seemingly inexplicable but universal experience of reverting to self-destructive behavior this way: You simply cannot carry out a charade for very long. One-size-fits-all programs that promise quick\u2014but superficial\u2014transformations or spiritual awakenings are impossible for most people to maintain very long, let alone over a lifetime. For you to succeed in recovering from your addiction, you instead want to make meaningful changes that bring your behavior into harmony with what's truly important to you\u2014not by transforming who you are, but by _becoming_ who you are, or who you want to be. As a result you grow into your sense of purpose in life, or your true self.\n\nExercise 1, Part 2\n\nFollow through on those indulged fantasies about who you could be and what you could accomplish once you are free of your addiction. Imagine that these fantasies are reality, and consider what such a life\u2014in all of its corners\u2014would look and feel like. How would you spend your time? Who would you be with? What activities and people would be forever gone\u2014or at least kept at a distance? What feelings\u2014good and bad\u2014would you need to leave behind? What will make you happy, keep you content? Flesh out fully this vision of your future self.\n\nWhat do you think of it? Are you ready for it?\n\nWhen memories and dreams fade, and when disillusionment sets in, what you're left with is just you. Who you are. What will satisfy you and bring meaning to your life?\n\n* * *\n\n**CASE:** Rodney is a good-looking and talented young man. He is technically skilled and maintains a good-paying computer job. He also is perpetually stoned on marijuana and flits in and out of relationships, often going from one woman to another on successive weekends.\n\nWhen he is with each woman, he pays attention to her needs. He is concerned, and the woman feels cared for. But just as quickly, Rodney disappears, often not to surface again for a month or more. If she tries to reach him, Rodney doesn't even answer his cell phone.\n\nOne of Rodney's girlfriends moved in with him at one point. He generally came home from work, went into the bedroom, and got stoned. They might eat dinner together, but gradually, as the woman saw Rodney's mind was elsewhere, she moved on to some other activity\u2014reading, watching TV, going out with a girlfriend. Eventually, she moved on entirely.\n\nRodney is also part of a close-knit nuclear family. His parents have been married for a long time. His sister, like Rodney, has nerdy technical skills. But she settled down young, with a man who was probably her first lover, and had two children\u2014taking an extended leave of absence from her job during her kids' early years.\n\nWhen Rodney looks at his sister's life, he both envies and rejects it for himself. He wants children himself and often plays with his niece and nephew. Yet he can never imagine actually living his sister's life. He wonders if his brother-in-law really is satisfied, even as he is sure his parents are with their long marriage.\n\n* * *\n\nThere are two possibilities for Rodney. The first is that his habitual lifestyle is the best expression of who he is. Not everyone is made for family life, and more and more people live alone. We shouldn't assume that settling down should be everyone's ultimate goal in life and that doing so will bring fulfillment. What brings Rodney satisfaction may be his freedom. Perhaps he is conflicted because he feels he should want the benefits of a stable family life and can see how they make other people happy, but he doesn't want them for himself. He might just be another completely self-oriented person\u2014now often termed \"narcissistic\"\u2014who never really connects with another person.\n\nBut, in fact, this turned out not to be true for Rodney.\n\n* * *\n\n**RODNEY** did find someone with whom he wanted to live, Alyssa, who accepted him as he was while encouraging him to advance in his career. Whereas previously he had been content to jog along and maintain his footloose lifestyle, Rodney applied to return to graduate school in information technology.\n\nBut Rodney was still not his family's\u2014nor perhaps anyone else's\u2014model of a settled person. Six months into his relationship with Alyssa, Rodney had to move to another city in order to attend the program that accepted him.\n\nRodney regularly texted and spoke with Alyssa. But he didn't return her expressions of longing to be together. As he put it, \"I haven't had any 'withdrawal' from Alyssa. Often my girlfriends\u2014including Alyssa\u2014think I am kind of cold because I don't miss them. I just don't yearn to see them if I know we will see each other in a month or two. That's fine for me.\n\n\"I do enjoy living with Alyssa, but I like living by myself also. However, I know I'm more directed and use my time much more efficiently\u2014and smoke a lot less pot\u2014with Alyssa around!\"\n\n* * *\n\nRodney has seen and pursued a different option for himself, one that holds out the promise of really fulfilling himself and growing up even though he remains outside of the traditional lifestyle. Whether this means that he will remain permanently off the standard marital and family grid can't be judged as yet\u2014along with what his ultimate use of marijuana will be. But he is nonetheless exploring the realm of true recovery.\n\nReflection: To Accept, To Change, To Wait\n\nMany people\u2014in some ways everyone\u2014face Rodney's two possibilities. One is to accept some things about himself as probably permanently different from most other people, but not bad or unworthy on that account, and to carve out a different path for himself. The other is to accept himself as he is at the present time: \"This is what I am now, and that's okay, but I may not always be this way.\" You may not be able to determine this about yourself right now. Think about your lifestyle, how you live, in addition to and beyond what may be your addiction. Name three things about it you would most like to change. Do you really want to change them? Do you predict that you will change them? Why will you or might you not?\n\nStages of Change\n\nGraham and Rodney are people in different stages relative to their purposes in life, and to their substance dependence. Rodney has begun making changes\u2014but he's still figuring out who he's supposed to be. Graham has decided he wants to change in line with an idea he has about who he is, a professional and family man, but he can't stay the course. They are at two different places in relation to their life purposes, or true selves.\n\nYou may have heard of a model called \"Stages of Change,\" which proposes that people who are in the process of quitting an addiction\u2014or we might also say are transforming their lives or finding and following their true selves\u2014follow a certain path, as shown in Figure 6.1.\n\nFIGURE 6.1\n\nThe Precontemplation stage represents a phase in which people are just beginning to tune into their impulse to make a change, but do not yet feel that it is possible. Contemplation is the phase in which change seems like a definite possibility. The Preparation stage is when people are beginning to make plans. And Action is when the plans begin to take effect. Maintenance is the phase where you focus on staying on track. People find this model helpful, in that many do experience some of these phases, and it is perhaps the most referenced addiction change tool.\n\nBut I take issue with it in some ways, since the proposed trajectory does not represent a universal reality. Many people's actual experience differs, as common sense and research tell us. People simply do not as a rule follow this exact pattern\u2014they skip steps, reverse direction, spend years in one stage and moments in another. There is no single path to change. Furthermore, the Stages Model does not take into account that the natural maturation process changes people's priorities. Consider Graham's case, for instance: He jumps back and forth between \"contemplation\" and \"action\" a couple of times every month. Or, consider Rodney, who was\u2014and to some degree remains in\u2014a prolonged state of precontemplation. Can a person be permanently precontemplative, at least for the majority of their adult life, or are they likely to move beyond that stage? All such possibilities and permutations occur. And, often, when people contemplate parenthood\u2014or become parents\u2014they leap through many stages in a single bound!\n\nThe Stages Model can be useful to you, however, if you put a more holistic spin on it by focusing on your identity and true self. Understand that change is not a step-by-step process and that you may experience one or more of these phases at any given time. Furthermore, different areas of your life may go through different stages, just as Graham is mature at work and poorly evolved in his family life. Instead of looking at these stages as a progression that you should pass through in order, look at them as representing different facets of transformation, which do not exist on a hierarchy, but work more like a gyroscope that is continually revolving, sometimes seemingly up, other times seemingly down.\n\nPerhaps the model loses its usefulness if we take away its forward trajectory. What's the point of recognizing these phases if we can't pinpoint where we are on the path, or if we can't use it to get a handle on our progress and look forward to the next step? On the contrary, we can find information and insight that are all the more useful when we apply the model in this real-life way. Let's translate each of the stages into what it means for finding your life purpose, the theme of this chapter, using Rose's story as an illustration. Envision yourself proceeding through each phase yourself, and what that might really look like, in what order and with what timing. Of course, this is just rumination, and your actual experience when embarked on your recovery path may be quite different and may shift as you go along.\n\n_Precontemplation:_ The sense that something is not right. Something doesn't jibe with your principles. But, in terms of purpose, you have not yet solidified what your primary goals are (see Rodney), where you want to be\u2014or head towards\u2014in life. Remember when Rose had first turned to meth and sent her daughter to live with her mother? Of course, she knew something wasn't right. But what, and what to do about it? \"Rose's regret loomed in the background. She wished for a do-over; she promised herself that she was going to stop as soon as she finished the drugs she had on hand. Or next week.\"\n\n_Contemplation:_ You have acknowledged that something is not right and must be changed\u2014but you're not sure how you can realign your life. Here, you may identify important values and a purpose, but you can't yet see how to proceed toward these. Rose, recall, had an epiphany: \"Missing her daughter's birthday party had a special impact for Rose, and her thoughts constantly returned to it. It made clear to Rose, as nothing else could, that the costs of her drug use outweighed any benefits that remained from it\u2014even as this would have been obvious all along to anyone with an outside perspective.\"\n\n_Preparation:_ You now identify how you can bring your values into alignment with your behavior and imagine what these initial steps will be. Rose had to get off a powerful drug, deal with her withdrawal, and reconnect with her real, meaningful life. \"When Rose felt that the worst of it (coming off meth) had passed, she called her mother. . . . Her mom came over with a homemade meal. Together they came up with a plan for Rose to reestablish her life, placing what was important at its center.\"\n\n_Action:_ Taking action, both in the narrow sense of quitting your addiction and in the larger sense of advancing your life\u2014like going to school, dealing with psychological issues, taking control of critical parts of your life. As Rose did:\n\nWith what she was struggling to achieve firmly reestablished in her mind, Rose moved back into her parents' house, rejoining her daughter's daily life. Rose returned to school and found a part-time job at a dentist's office (which was good, because she required considerable dental work). Although she had given up quite a bit of freedom, Rose now shared child-care responsibilities while living with her parents, and that support took enough of the burden off her that she could pursue her studies while sustaining her recovery from addiction.\n\nWe turn to your taking these steps in the next chapter.\n\n_Maintenance:_ In PERFECT, maintenance is living a value-driven life, one where you constantly steer according to your purpose and goals, while using relapse-prevention techniques that keep your goals in focus\u2014which I turn to in succeeding chapters. Once again, for Rose:\n\nMost important was that Rose was able to see the positive results of her changed life and to savor being clean. She was living in harmony with the goals that had been eluding her even before she became addicted. Rose was able to fit both play and quality time with her child into her schedule, as well as spending time with her family. Given where she was coming from, the situation seemed like a dream come true. Beyond this, Rose made space to run and do yoga. Her new circumstances honored the vision she had been working so hard for before her addiction. Now every facet of her life reflected her heart and brought her sense of purpose into sharper focus. She was using her values as a guide to create a place in the world for herself that she had dreamed of.\n\n* * *\n\n**CASE:** Sarah was an investment banker. Although tremendously successful academically and professionally, she was bad at relationships. Instead, she would have periodic alcohol- and drug-fueled intense interactions with men\u2014sometimes lasting a weekend, sometimes a few months.\n\nIn her early thirties, Sarah became involved with a man who was far less successful than she was. Of course, that wasn't uncommon for Sarah, and Ron was reliable and capable\u2014he ran the shipping department of a large company.\n\nRon admired Sarah tremendously and promised her a lifetime of devotion and emotional support. Tired and worried about remaining alone forever, Sarah accepted Ron's suggestion that they marry, and they lived together contentedly, even if Sarah felt the absence of true passion that she had once dreamed of (an experience she shares with many, if you recall the discussion of sex addiction in Chapter 2).\n\nSarah traveled for her job. During these trips, she began returning to her substance-stimulated affairs. Sarah felt guilty about these and worried that she might be addicted to sex and alcohol. On the other hand, she always returned home to Ron. Indeed, she realized that maintaining her marriage was necessary for her to keep a steady course as an elite financial professional.\n\nOnce, as Sarah was considering these things, she was asked to write her bio for a company brochure. As she did so, she recalled how much her work meant to her and how directed she had been in pursuing such a position, a direction she wished ardently to continue. In fact, writing her bio was a values-and-purpose exercise, one that clarified what really motivated her.\n\n* * *\n\nBy returning to the home base of her true purpose\u2014that of a high-level, skilled, and motivated financial professional\u2014Sarah was able to correct course, both eliminating her affairs and cutting back her drinking (which she had often used as a way to facilitate her sexual interactions). She had assessed her purpose, her true self, and concluded that these steps were a matter of fulfilling her destiny. Of course, Rose made a very similar choice, or refocusing, which neither Rodney nor Graham has yet done. Compared with Sarah, Rose had gone much farther in the course of her addiction, suffering far worse consequences. Would both Rose and Sarah be expected go through the same stages of change, then? They both navigated their true selves in a way that worked for each of them. The method each used wasn't chiseled in stone and delivered to them by God or psychiatry, just as it isn't true that they both went through the same stages of change\u2014or really _any_ stages, other than leaving addiction behind. But their successful resolutions were for both a matter of focusing on what was most meaningful in their lives and sticking to that direction and purpose.\n\nYour Values Assessment\n\nIn Chapter 3 you filled out your \"Values Questionnaire.\" You returned to it in Chapter 5. The second time you filled it out to assess and appreciate your skills and resources, focusing on the last five items. This time, refocus on the first five and the last two items to locate your true self and purpose.\n\nVALUES QUESTIONNAIRE\n\n1. Name three things that are important to you, whether or not you are actively honoring them right now.\n\n2. What activities would you be pursuing if you were not so occupied with your addiction?\n\n3. Have you abandoned any dreams because of your addiction? If so, name these.\n\n4. What are some things you value that you could lose in the future due to your addiction?\n\n5. What do you hold close to your heart that most opposes your addiction (religious faith, parenthood, political activism, health, self-respect, regard for others, etc.)?\n\n. . .\n\n9. Who are the most important people in your life, people you really care about, or people you can really count on, or both?\n\n10 Which three human values do you elevate most, such as kindness, generosity, friendship, honesty, hard work, creativity, independence, integrity?\n\nHerein, you will find the signposts to your true self. These are the key elements of your life that you may have been ignoring or giving short shrift. The longer you have been living with addiction, the more overwhelmed you may feel by looking at your answers. Let's tackle this list the way a professional organizer or productivity expert would approach a chaotic household or office. You're going to process and sort through your underlying values, what you ultimately care most about, so that you can begin the process of setting goals for yourself that are meaningful to you, that will give your journey a sense of true purpose. This endeavor is like sorting a pile of papers that has accumulated on your desk to the point where you have no place to work, or like cleaning a kitchen that is so out of control that the only appliance you use is your microwave. To accomplish this task, you need a plan of attack.\n\nOrganization and efficiency experts will tell you that every stray, homeless item contributes to the chaos in your household and in your life. Anything you see that isn't where it should be or reminds you of something you're supposed to do saps your energy, whether you know it or not. Every unpaid bill, moldy Tupperware container, or unframed picture is like a person staring at you, hoping you'll make eye contact. These things are not accidental, but they are also not necessarily essential to your life. Wherever they fall in your life hierarchy, they s _till_ represent unkept promises or contribute to a chaotic living situation for you and your family. And they represent a lack of attention to your values. If inanimate objects can have this kind of power, imagine the weight you are bearing under the imploring stare of the values and purpose that are most precious to you, but that you are ignoring.\n\nWhen you are approaching the daunting task of organizing a physical space full of stuff, you begin by handling each item with the intention of making a few decisions about it: Do you keep it or toss it? Does it need immediate attention? Can it be put off? Is it sentimental? Where does it belong? If you are working with an organization expert, he or she will withhold judgment about what is of value to you. That is up to you to determine. You are going to follow the same principle here, using your answers from your values questionnaire. Reviewing your list might inspire some self-recrimination or feelings of shame for time or dreams lost. If so, summon your foundational mindfulness and self-acceptance practices to guide you here. Like the professional organizer, do not judge yourself; rather, focus on holding yourself and your difficult feelings with mindfulness and compassion.\n\nExercise: Sorting Your Values\n\nIn your PERFECT Journal, process each of your answers to the Values Questionnaire, 1\u20135, 9 and 10, into one of the following categories\u2014it's okay if they overlap. And feel free to add your own categories.\n\nThings that bring you joy:\n\nThings you believe in:\n\nPeople you cherish:\n\nDreams and goals:\n\nStrengths and positive qualities you possess:\n\nThis exercise shows you that you do have a true north. These categories represent the important areas of your life\u2014your values\u2014where you will find inspiration, meaning, and purpose. These are your reasons for pursuing freedom from addiction. Feel free to add more items to your list. You can place it where you will see it regularly, like over your desk or by your bed.\n\nMoving Forward\n\nTo find the values and purpose that allow you to take\u2014and keep\u2014an addiction out of your life, you need to explore what's important to you and sort through competing demands. In the next chapter, you will begin mapping your way toward actualizing your visions for the future\u2014making your visions real through concrete plans and actions.\n\nFurther Exercises\n\n_Personal Journal_\n\nCarve out some private time before bed, every evening, and review how you spent your day. In your Personal Journal, identify the things you did and the choices you made that reflect your values. For instance, if you decided to cook a healthy dinner instead of ordering take-out or if you did a favor for a friend, record that event and make note of what personal value or values you supported. You might be able to name just one, or more than one.\n\n_Exercise_\n\nMake a date with yourself and put it on your calendar when you do the values exercise, or as soon as you can after you have done your basic sorting. On that date review your list of values and list one activity you have undertaken in that interim that honors each value. Perhaps you made time to watch a movie you have always loved or spent time alone on another favorite activity, did a favor for a friend, read up on something you have been wanting to pursue, planted some flowers . . . you know the things you value and consider important. Write about how you feel about those things you've done. Make special note of any values not pursued in this time, and list those values for the next review date you set going forward.\n\n_Meditation_\n\nEnvision a time when you have been fully engaged in an activity that has nothing to do with your addiction. You might have to think back to childhood, when imaginative games could feel so important, satisfying, and creative. It might be when you play a sport. Or when you swim at the beach. Or when you see a scary or adventure movie. Do your best to remember what it has felt like to be so fully engaged in something that you don't have to think about what it is that you want; you are just doing it. Bring your mindfulness skills to this meditation and focus on the sensations you experience when remembering this time: What feelings does this memory conjure up? Does it recall certain smells or textures or vistas or people? Do you actually feel different _physically_? Spend as much time as you can exploring in your mind\u2014occupying\u2014this event.\n\nCHAPTER 7\n\n_Fortify_\n\nCoping\u2014Learning the skills for life management\n\n* * *\n\n**CHAPTER GOALS**\n\n\u2022 To assess your strengths and weaknesses\n\n\u2022 To implement new life skills\n\n\u2022 To discover resources for effective living\n\n\u2022 To address mental health issues\n\n**Purpose:** This chapter focuses on the essential skills and practices that will help you navigate the world freely, non-addictively, and effectively. These are broad subjects, each touched on in a variety of ways. They include practical ideas about skills that will enable you to connect to the world\u2014such as listening, anger management, accepting others, and decision making\u2014combined with brief introductions to cognitive-behavioral techniques such as social network therapy, reciprocity marital counseling, problem solving, assertiveness, the community reinforcement approach (CRA) and family training (CRAFT), and motivational interviewing. You will also contemplate setting and respecting boundaries\u2014your own and others'\u2014and consider the crucial question of boundaries in therapy, and especially in addiction treatment.\n\n* * *\n\nLiving with addiction, every day you encounter the same scenarios, navigate the same problems, meet the same demands\u2014all centered around your addiction. By remaining focused on this infinite loop of addiction, you neglect important areas of your life. Your home, family life, or finances may be in disarray. You may not know how to cope maturely with stressful situations, hiding in addictive behaviors rather than facing and handling whatever life throws your way. Freedom from addiction allows you to embark on life's adventure, a forward path with goals to set and meet. But living out your true self requires coping skills that you failed to develop on your circular path, making it difficult for you to handle the twists and turns\u2014and sometimes tedium\u2014present in even the most productive and fruitful lives. This chapter is dedicated to providing you with resources and tools for effective living.\n\nDefining \"Life Skills\"\n\nDo you know people who seem to manage their lives with uncanny effectiveness? They're able to meet the demands of family life, work, and community, and still have time for leisure activities. They don't seem burdened by endless problems that defeat their goals and happiness. In fact, they have learned how to prioritize and to concentrate: to determine what's important and to navigate a path through life focusing on activities in a way that reflects what is most meaningful to them. These highly effective people at the same time deal with stress\u2014conflicting demands, family and personal dynamics, unexpected problems, and even trauma. They aren't people without troubles. They are people who keep these problems in perspective and deal with them without losing track of their larger goals.\n\nIn the previous chapter, you took the initial step toward effective living by establishing your priorities\u2014determining what is of ultimate value to you\u2014and setting your course. Now, you will turn your attention toward developing the practical skills you need to follow the course you set for yourself. People may acquire these skills as a matter of course on their way to adulthood. The myopia and all-consuming nature of addiction, however, can hinder you in these key areas, even bring you to a complete halt, making the demands of everyday living seem overwhelming and unmanageable.\n\nIf you have always coped with stressful situations by getting high or running outside to smoke a cigarette or stomping out of the house to get drunk, how will you respond to stress once your addictive behavior is off the table? If you have allowed yourself to go into deep debt and have dealt with creditors by refusing to answer the phone and letting the mail pile up unopened while you continue, single-mindedly, looping around your circular addiction path, what do you do about your financial improvidence now that you can see clearly? Do you know how to budget? Or, say you dream of going back to school, but when you start to do the research, you find yourself stymied by all the requirements and options. How do you pursue this goal effectively?\n\nThe range of life skills that allow you to live up to the standards of your priorities is very broad, and you may not need help in every area that I am going to cover in this chapter, which is like a crash course in adulthood. One abiding truth about the nature of recovery from addiction is that a large majority of people who experience addiction will \"mature out\" of it. Many do this on their own, through the natural process of shifting priorities that goes hand in hand with growing up. But, for others, who find themselves blinking into the light after years of addiction, it doesn't come quite so naturally. And the thing they most lack for completing this process is the skills required for coping. These skills cover a lot of ground, so let's break them down into categories.\n\n\u2022 Anti-addiction skills\n\n\u2022 Decision making\n\n\u2022 Goal setting\n\n\u2022 Coping skills\n\n\u2022 Communication skills: Listening\n\n\u2022 Emotional skills\n\n\u2022 Boundary setting\n\n\u2022 Boundaries and addiction treatment\n\n\u2022 Effective therapies: CRAFT and motivational interviewing\n\nEach of these categories encompasses a dense set of subcategories\u2014a chapter could be devoted to each one. And, indeed, in my previous books\u2014like _The Truth About Addiction and Recovery_ and _7 Tools to Beat Addiction_ \u2014I have put together whole sections of detailed coping skills (like problem solving, anger management, communications, etc.). These have been developed by psychologists who have observed closely the deficiencies that people with addictions often display. I won't be repeating\u2014but only alluding to\u2014these in _Recover!._ The information in this chapter will provide guidelines in these areas, and you can find more detailed descriptions of each as needed in my earlier works.\n\nPeople can develop severe, life-disturbing problems in any\u2014or all\u2014of these areas. And no one of them stands out as causing addiction. Not everyone will need support with every skill. For instance, you may be very high functioning despite your addiction and need help with only a few. Or, you may need guidance in all of them. With that in mind, I will offer an exploration of these categories and provide you with exercises, resources, and direction so that you can continue your development in the areas with which you feel you need the most help. In fact, discovering and using resources is an important life skill itself. In reading this, you are already beginning to practice that critical skill.\n\nAnti-Addiction Skills\n\n_Recover!_ is all about overcoming addiction, so an anti-addiction section might seem redundant. Following The PERFECT Program, you are approaching your addiction holistically\u2014from all areas of your life. You are realizing a new overall perspective and establishing a completely different foundation for living. But, in doing so, you will face daily challenges to your resolve and will struggle with addictive compulsions and urges. Anti-addiction skills are those practical, systematic ways of dealing with these addictive urges before\u2014or as soon as\u2014they arise.\n\nAddicted people have different triggers\u2014situations that instigate a pull toward destructive behaviors. These might include stress, boredom, depression, just plain habit (like grabbing a cigarette when you're talking on the phone or a bag of potato chips when your favorite TV program is on), or returning to a familiar environment where, or seeing people with whom, you previously engaged in your addiction. Oddly, it is also common\u2014as Alan Marlatt and his colleagues indicate in _Relapse Prevention_\u2014for people to be drawn back to addictions when they are feeling elated or triumphant. As one young female alcoholic athlete described her drinking career: \"When was I driven to drink? Whenever we had a big victory, I celebrated. Oh, of course, whenever we suffered a tough loss, I drank to drown my disappointment and depression.\" And, as I discussed in the last chapter, the tendency to relapse may even occur for some when they are most positive and confident about their recovery.\n\nSometimes, a gentle urge to get high or binge will present itself seemingly out of the blue. You may dismiss it, but find that what started as an innocuous, stray thought morphs for you into inevitability. Let's explore some of these scenarios and practical ways of dealing with them.\n\nExercise: Addictive Triggers\n\n_What are your addictive triggers?_ For some, simply waking up in the morning is enough: you might open your eyes and reach for your pack of cigarettes or for your computer to check in on your online game, or obsess over whether your last date or hoped-for love has e-mailed you. Or maybe it's at night when you have finished with your work schedule or other daily obligations. It could also be a place you pass or find yourself in, like a bar, or a group of people\u2014like those you usually drink or get high with. Or it could be a mood\u2014such as boredom or stress or anxiety\u2014that compels you to go to the refrigerator or out for a snack.\n\n_When are your cravings the strongest_? If you are not sure what triggers you, spend a week keeping track in your PERFECT Journal on a page earmarked \"triggers.\" Make note of the time of day when addictive urges are strongest, what you are doing at the time, what your mood is, and whether or not you are able to overcome them each time.\n\n_Have a plan in place_\n\nWhen a craving arises, or when you anticipate that an urge will arise in a certain situation, be prepared for it. Have a few ideas for activities you can engage in when cravings or urges appear, relying on the things that are important to you. Make a list, both in your Journal and to be kept handy, because you may not be able to recall these things when you're in the throes of a desire to indulge. These could be short-term\u2014but enjoyable or satisfying\u2014distractions, like taking a walk, playing catch or doing some other activity with your child, composing an e-mail, weeding a garden, calling your mother or a friend. If you are headed someplace where you know you may face triggering opportunities, have other destinations available to which you can divert your path\u2014the library, grocery store, a coffee-only caf\u00e9, a friend's house, the gym.\n\nOther times, you will be triggered by your daily routines. If, for instance, your usual habit has been to get high as soon as you come home from work, simply walking in the door will be a powerful trigger. You might plan instead on taking a shower as soon as you get home and then starting dinner right away. The idea, obviously, is not to leave things to chance\u2014plan exactly where you will be going within the house and what you will do there. Mindfully locate yourself in time and place\u2014see the place, then follow through on your plan.\n\n_Keep your reasons for quitting close_\n\nMake a list\u2014or even write a paragraph\u2014of the most important reasons you have for overcoming your addiction. Write it in your Journal and keep it on hand. You can also attach a picture to it, say, of a loved one or a child or of a fitter, healthier you. When an overwhelming urge hits, it will try to push out thoughts of anything else. Having a reminder of your priorities where you can readily access it is a powerful way to put addictive cravings into perspective.\n\n_S.P.O.T. exercise_\n\nYou will find this in Chapter 4, \"Pause,\" on page 95, which describes being in the here and now so that you can identify and overcome addictive urges and cravings.\n\n_Meditate on your discomfort_\n\nMindfulness meditation is a powerful, long-term anti-addiction practice, one that you have been working on throughout _Recover!._ It's also a terrific tool for combating urges as they arise, as I previewed in Chapter 3 on getting ready. There I discussed focusing your daily meditations on your breath or other ordinary parts of your existence. But you can also focus on more urgent feelings, like pain or discomfort. Craving is such a difficult feeling, one that can make you restless, agitated, even angry. One thing mindfulness teaches us is that feelings are not reality; they're not permanent. They're like clouds passing quickly across the sky.\n\nMindfulness Meditation: Suppressing Cravings\n\nWhen you are in a suitable place to meditate and are relaxed, focus your attention on your craving and the feelings it creates for you: agitation, discomfort, longing, even emotional pain. As you focus your attention on these feelings, name them to yourself. You might say, \"This is restlessness\" or \"This is frustration.\" And try to describe the quality of those feelings, how they present themselves in you\u2014say you feel empty inside or, instead, a burning in your stomach. Notice, for instance, if you are fidgeting. You don't want to make these feelings go away, or to stop fidgeting. Just acknowledge that these things are present and real. Say to yourself, \"This is how craving (or discomfort, or longing, etc.) feels right now.\" Concentrate on the feeling; notice how it shifts and mutates, how it is not always the same from one minute to the next. View this with a sense of curiosity, or with wonder.\n\n**Variation 1:** Imagine your craving as a physical presence\u2014ground undulating beneath you, or a wave that you are riding or surfing. Note that it varies in intensity. Ride up and down with the craving\u2014note its high points and then how it declines.\n\n**Variation 2:** Explore your body, and see if you notice any area that feels good or right\u2014even if it is your nose or your feet. Focus your attention on that area, in the same way you would focus on your breath.\n\n**Variation 3:** If you are feeling claustrophobic in your own skin\u2014if you feel too agitated to relax at all\u2014imagine expanding the space your body occupies, say, five inches all around you, and place your attention in that \"free\" space. Meditate in and from this place.\n\n**Variation 4:** What is the happiest place you can imagine? Think about being there. Think of every sensory detail\u2014see, hear, smell, taste, and touch these.\n\n**Variation 5:** Imagine a ray gun. Visualize your craving as a robot or a monster. Then atomize it with your weapon. Imagine the robot or monster disintegrating, its pieces spraying all over the surrounding space, until it no longer has any substance. Or imagine the craving as an alien space ship that you're shooting at in a computer game with the same result.\n\n_Change your routine_\n\nShake things up a bit! As it is, your life's routines are often structured around your addiction. Addiction _is_ routine. You smoke, or eat, or drink, or use, or shop, or play games in the same places and times. So, do different things every day\u2014or add things to your routine\u2014that don't accommodate your addiction. Take a different route home from work, spend more time outside, talk to new people. Add a new thing every day or week.\n\n_What's the logical conclusion?_\n\nAs I mentioned, addictive urges can overwhelm your ability to think clearly in the moment. When that little voice whispers to you that you could really use a [fill in the blank], it's difficult to see beyond the immediate gratification. Grab your PERFECT Journal and, in a section earmarked \"cravings,\" work through the scenario: write down how it would feel to indulge your craving at this moment, but then follow this scenario through to its logical conclusion. If you start now, where will you be in a few hours? Will you feel bad and guilty almost immediately? Will you feel out of sorts, and tired, and sick in the morning? What are all the potential consequences? Be as detailed, as graphic, as possible.\n\n_Variation:_ If you find yourself actually experiencing the logical conclusion\u2014say, you have just awakened with a mighty hangover\u2014take the opportunity to write down everything you are feeling at the moment. Keep this record somewhere where you can easily refer to it.\n\n_Give yourself permission\u2014for later_\n\nThis technique might seem counterintuitive. But, white-knuckling your abstaining from your addiction, telling yourself that you will never, ever do it again, can be demoralizing in that it tends to increase your feelings of deprivation and hopelessness. In the last chapter I reviewed Roy Baumeister's research on willpower. Your efforts at willpower can be exhausting and can get exhausted\u2014it simply doesn't pay to bite off too much at once\u2014or to intimidate yourself with what seem like insurmountable tasks ahead of you. Telling yourself that you're not going to do it now, but maybe another time, can release pressure. It's like a mental hack. It actually makes it less likely that you will indulge later. It works by giving you the feeling that you are in control, that you are making the decisions, thereby reinforcing your free will. The choice not to use is yours, and when you feel that it is a matter of choice, your priorities have a stronger voice, now and in the future.\n\nOf course, AA tells people to focus \"one day at a time.\" The essential difference with the mindfulness PERFECT Program approach is that AA actually means \"forever.\" In PERFECT, you simply don't determine, don't limit who you are and will be forever. As we noted in Chapter 3, late in his life, the great Irish actor Richard Harris\u2014after a major-league addictive history and a just-as-frequently recounted recovery\u2014started having a Guinness stout or two at his local pub. As a grandfather in his seventies, Harris wasn't as driven to excess as he had been. AA and the disease theory, in having us view ourselves as permanently addicted, take advantage of a strange wrinkle in human thinking. We all recognize how much we have changed from the past to our present situation. Yet, when we project into the future, we imagine ourselves being very much the same as we are now. In fact, we are just as likely to change throughout our lives (that is, very likely), although we fail to recognize this future likelihood.\n\n_Don't beat yourself up if you give in_\n\nIn my discussions of conventional addiction treatment, harm reduction, and self-acceptance, I have emphasized that perfection is impossible and simple abstinence is not the gold standard. Believing that you are a lost cause simply because you fell off the wagon or are having a hard time getting on the wagon is unrealistic and self-destructive. If you have gone off the rails, treat yourself compassionately, learn from your experience as best you can, clean up the messes you've made, and\u2014look forward. Your path is your own. No matter where you happen to be at the moment, you always have the choice and the chance to move forward.\n\n_Arrange social situations mindfully_\n\nSome people are more likely to be triggered by being alone, impelled by feelings of loneliness and boredom and resulting depression. For them, finding social outlets involving non-addicted others is crucial. But other addicts are set off when they are around other people. Quitting your addiction can feel more daunting when you are out with friends, or around people who are using when you are not\u2014or trying not to.\n\nFirst, let's get one boogeyman out of the way: Many people who are quitting an addiction worry about being conspicuous\u2014calling undue attention to themselves\u2014if they don't indulge. The truth is that most people don't notice and won't give it a second thought if you're not doing something. If you pass on a joint that's going around the room, they'll go on to the next person. If you don't have a cocktail in your hand, they won't ask you why. You don't owe anyone an explanation, and most people won't ask for one. Saying \"no thanks\" will usually garner a shrug. If you encounter some inappropriate outlier who lacks the good grace to ignore your abstinence, you can tell them that you're driving, training for a marathon, or pregnant (men\u2014don't try this last one), and find someone else to talk to. There's no one you have to answer to about your choices.\n\nNow, let's talk about more difficult situations\u2014say you are with close friends who use your addictive object in a situation that you would normally spend indulging your addiction with them. If you are accustomed to or have often enjoyed doing something when you are with others, temptation can almost be irresistible when everyone else is partaking. Seeing other people do something that you might feel like doing can also make doing it seem less destructive. If they can do it, why can't you?\n\nThis is when your mindfulness skills and your clarity about your sense of purpose are key. Ask yourself whether and how your social circle supports your life values. It may be that your friends' only real connection to one another and to you is based on addiction. If you have nothing in common with a set of people aside from addiction, you might consider bowing out of that group and finding new friends. If people who have shared your addiction remain valuable to you, you can work on developing a deeper connection to some of them in situations that involve doing other things. Something as straightforward as deciding whom you will hang out with actually comprises an evidence-based therapy\u2014one more often used in Great Britain than the United States\u2014called \"social behaviour and network therapy.\"\n\nIt is not simply that friends and acquaintances of yours tend to be users themselves who tempt you to use\u2014they may actually try to undermine your resolve to quit. Perhaps they miss their playmate or feel that your new direction is an indictment of their choices. It might even occur that someone close to you, who has been begging you to deal with your addiction, resents your quitting. So much of their life has been intertwined with your addiction\u2014even simply through asking you to stop\u2014that they find your abstinence intolerable! Or, it may be that they just don't trust you. You may also find people who don't believe that you can change your life if you are not in AA or NA and will not accept any other approach. Whatever the reason, you may find it difficult to gain support among your friends and family.\n\nMore basic relationships\u2014such as within your family\u2014can be the most challenging. Working through family relationships into sobriety will require your self-acceptance and compassion because those closest to you find it so difficult to trust and accommodate your change. They may respond to your new way of life with inexplicable anger\u2014or even by discouraging or sabotaging you\u2014often without recognizing what they are doing. For example, they may express pessimism that you can succeed, or they may even present triggers that they know set you off.\n\n* * *\n\n**CASE:** William's wife, Sabrina, was a stay-at-home mother who started drinking in the early afternoon. She was able to care for the household and the children, but was usually in bed by 9 p.m.\u2014passed out. William was disgusted by her drinking and found the \"wino housewife\" routine so clich\u00e9. It was just not how he had envisioned his life with her when he proposed marriage. Sabrina had made many promises to William to stop, and tried several times. But, every time she tried, she would make it only a few days before William would start looking at her cynically, asking whether she had begun sneaking drinks again, or suggesting that she soon would be. With this lack of encouragement\u2014actually, suspicion and cynicism\u2014Sabrina's shaky willpower didn't last long.\n\n* * *\n\nSo why would William undercut the very change he insists Sabrina needs to make by quitting drinking? While William is unhappy with his wife's lifestyle and its impact for him, he's also so used to it that he almost doesn't know who he is when he isn't martyring himself to Sabrina's addiction. Furthermore, he has built up reserves of resentment and distrust that are always ready to burst out of him. Putting down and doubting any gains Sabrina might claim she has made make him feel virtuous for all of his past suffering, and in an odd way give him control over the situation\u2014which Sabrina's drinking likewise does. As long as she is drinking, he knows what to expect. When she stops, he does not, and that makes William deeply uncomfortable.\n\nLet's say, however, that Sabrina has decided to end her destructive drinking, is clear about her reasons for doing so, and has shored up her inner resources and priorities. Of course, this is Sabrina's mission\u2014she is the freewill protagonist in the terms of this book. But being married to and living with someone is a very challenging matter, on the one hand, and one that offers a great deal of potential support, on the other. William should be able to reinforce Sabrina's resolve, reward her efforts, and encourage her to go forward. He can be made aware (perhaps by reading this!) that he is undermining her instead. If he can clarify his purpose and goals\u2014keeping them in line with Sabrina's, as they should be\u2014he can be a very helpful resource for her quitting. And in doing so, he will be extending a welcome sense of compassion\u2014including forgiveness for her past behavior that has hurt him\u2014to the woman he loves. Because they should recognize that their marriage is the top priority for _both_ of them, they should coordinate their efforts to make them both happier in a household without recrimination, belittling, and guilt. When each partner accepts that the other's efforts are genuine, together they can form a powerful team that will strengthen the two of them. William can then stop waiting for the other shoe to drop, or even trying to instigate Sabrina's failure.\n\n_Reciprocity marital counseling_\n\nThroughout this book I have emphasized the connection between the needs of an addict and his or her loved ones. Here is a place where the spouses' efforts need to be coordinated. The skills required for overcoming addiction are reciprocal ones. One important alcoholism therapy that has repeatedly been shown to be among the most effective is called the community reinforcement approach, or CRA, which integrates changes throughout a person's work, recreational, and home life to reinforce sobriety. One component of CRA is reciprocity marital counseling, in which two partners are led through a series of exercises where they share the importance of different aspects of their lives together (e.g., sexual, financial, child rearing) and how well these are being fulfilled. A counselor then assists the partners to see how their interlocking needs can be best satisfied by working cooperatively and by noting and rewarding positive changes each partner makes in the other's direction.\n\nOne of these areas, of course, is the addictive behavior. While couples sometimes find it awkward to engage in this counseling, they soon realize how positive the shifts can be for each of them and begin to \"catch\" and to appreciate their spouses doing good things for them\u2014which itself puts their relationship on a new, positive footing.\n\n_Find professional help_\n\nOf course, CRA and reciprocity marital counseling are therapies that you'd have a hard time carrying out on your own. You can ask a competent marital counselor or therapist if they practice that type of treatment and undergo several sessions, always being clear when scheduling your next session that you expect it to add value, and ceasing when that isn't true. Likewise, addiction counseling by a sensible therapist or counselor can be a valuable aid. In keeping with the ideas underlying The PERFECT Program, you would seek out either a cognitive-behavioral therapist or a Buddhist psychologist, someone who is knowledgeable in mindfulness techniques. If you can't afford therapy, you can find free non-12-step groups such as SMART Recovery. (For links, see Chapter 10.) But you may also enlist a friend or family member you can rely on to help you with accountability.\n\n_Ask your friends for help_\n\nAs you work toward achieving your life's vision, you may come up short when approaching certain arenas. Say you require babysitting so that you can attend a class, or maybe you need help organizing, learning to drive, using your computer, or cooking healthy meals. Ask your trusted friends and family for help. If, by chance, anyone declines your request, try not to take it personally or to consider it a rejection. They may have time constraints or other pressing obligations. But it is far more likely that they will be thrilled to share their knowledge or time with you, because they care about you, want to connect with you, and are proud to know they have something of value to offer toward your success.\n\nTrusting that the people closest to you among your friends and family are willing to help you is difficult. It's hard to admit vulnerability to people you respect and to let people you care about really see the extent of your problems. It's possible you have been rebuffing them, or maybe you have imposed on or hurt them through your addiction. Furthermore, asking for help implies accountability to the people who are extending themselves for you. You might be afraid to disappoint them. But it is a sign of seriousness when you open yourself to this accountability by calling on your friends and family to ask for their help. And asking for and accepting their help allows them to show their love for you.\n\nOne word of caution: you may encounter people who will present you with ultimatums, or make intrusive or meddlesome demands of you in return for their help. This is a difficult scenario, especially when you are short on resources and feeling vulnerable. If you're presented with such a situation, you can shift your perspective to their point of view: Have you burned them in the past, and are they simply taking precautions? For example, if you request child care so that you can attend a class, and someone asks to see your registration or receipt first, rather than taking offense, see this as an opportunity to regain their trust. On the other hand, they may insist that you register for a program that they recommend, but that doesn't suit you, in return for their help. Hear them out, but make clear that in seeking their assistance you aren't turning your will and decision making over to them, or to anyone else.\n\nDecision Making\n\nFreedom from addiction is all about making choices, including individual daily decisions, dealing with problems, and global life planning. Effective decision making, problem solving, and goal setting require mindfulness, self-acceptance, and an awareness of your values, priorities, and purpose. As I discussed in the last chapter, it's easy to embark on\u2014or fantasize about\u2014an exciting new venture, but maintaining your drive is hard if you don't have a realistic vision of your strengths and what's actually possible for you, or the resources to support you when the going gets tough. Similarly, it's easy to make a self-destructive decision, in the moment, if your foundation is weak. If you have been following The PERFECT Program to this point, you should be in a better position than ever before to trust the choices you make for your future\u2014you also have the skills you need to reassess your decisions and to rechart your course as needed. Finally, problem-solving techniques are learnable skills.\n\nPerhaps you\u2014like many people\u2014are overwhelmed when you're confronted with situations requiring decisions. You may not trust yourself to make a good decision or don't believe that you are in a position to make decisions; perhaps you don't feel qualified or feel so stuck in your current circumstances that you don't have the freedom to _make_ decisions. Such indecisiveness sometimes occurs because you believe your decision carries much more significance than it actually does and that tragic results can befall you no matter _which_ way you decide. You may worry that your choices will expose something you want to hide. Consider the innocuous everyday example of a group of friends trying to decide where to go for lunch: No one wants to choose a place that will be disappointing, and so you'll hear a lot of, \"Anywhere's fine! You decide.\" Or take a much more important decision, like \"Should I ask for a divorce?\" Making a decision is, essentially, taking a stand, asserting yourself and your will in line with your purpose, which can be nerve-wracking.\n\nHaving an addiction can make it much more difficult to make decisions, both because you have avoided making choices previously and because your addiction takes a lot of options off the table. As I have said, you adopt your addiction in good part as protection against the angst of decision making\u2014you can _know_ where you are headed without the effort or the pain of having to choose. Of course, the best way to develop the skill of choosing\u2014like all skills\u2014is practice. And every moment presents you with opportunities for choices. If you bring your mindful awareness to each opportunity, you will hone your ability to recognize when you have decisions to make and to choose directions that support your values, even in situations that trigger addictive urges.\n\n* * *\n\n**CASE:** Ralph was a partner in a seasonal business\u2014it peaked when the school terms began, in September, January, and sometimes for summer school. During these periods, Ralph was under such intense pressure he could barely breathe. And what breaths he took were generally chemically infused. He took tranquilizers to stay calm, drank heavily after work, broke out into cigarette smoking, and got high on recreational drugs on the weekends. Yet, when each such period was over, he relaxed, sometimes at a beach home he enjoyed with his wife and kids. During these retreats, Ralph cut out virtually all his substance use (except for drinking wine after the kids were in bed). Yet he never used such reprieves to figure out new hires or how to rearrange responsibilities with his partners to fend off the wall of stress he inevitably faced around the corner, when he would once again succumb to all the pressures that caused his substance abuse.\n\n* * *\n\nBy not addressing his work issues when he had a chance to, and by avoiding critical work-related decisions, Ralph was committing himself to perpetuating the unhealthy\u2014dangerous\u2014stress in his life and his resulting addictive behavior. And Ralph was a highly seasoned, successful professional.\n\n**JOURNAL :** Write down decisions you have made in the last couple of days: decisions about people, at school or at work, etc. How many can you come up with? Did any of these decisions make you anxious? What insight do you have into why those decisions are more difficult than others? Then extend the scope of your deliberate, mindful decision making by identifying larger decisions over which you are hesitating, but that are important for you to make or that you will benefit from by making.\n\n_Problem solving_\n\nProblems are special events\u2014often urgent\u2014requiring your best decision making and coping. Your addiction is an example of faulty problem solving\u2014of attempting to remove the pain or the awareness of a problem by using artificial means to mask it or to divert your attention. This process can involve either large problems (of the kind Rose faced in Chapter 1, where basic aspects of her life weren't working), persistent problems in one area (like Ralph's business tensions or a person's problems within a relationship or finding intimacy at all), or specific traumas or emergencies (such as failure of a relationship, or a financial or housing crisis, or an illness, or with a family member, like a child, and on down to smaller crises that can occur, sometimes several at once).\n\nYou may view life as a never-ending cascade of problems you must face off and deal with. This viewpoint can be excruciating, since it makes life so negative as to undermine the simple pleasures it offers, like taking time-outs, finding positive outlets, and enjoying people, activities, and the world. And such negativity often underlies the need to seek addictive escapes. On the other hand, the ability to cope with problems is an essential life skill, one that addicts as a group unfortunately often lack. Cognitive-behavioral psychologists teach people how to deal with problems directly, rather than turning to their addictions. The indexes of my earlier works, _Truth_ and _Tools_ , both point to sections that focus on this skill. The process involves five stages:\n\n\u2022 **Recognize** you have a problem, that something is uncomfortable or hurting you.\n\n\u2022 **Don't panic** but size up the matter, or slice it into manageable bits.\n\n\u2022 **Seek information and inputs** from various sources, including solutions others have used.\n\n\u2022 **Try out** one or several likely-seeming approaches.\n\n\u2022 **Pause** after you have given an approach a fair shot, judge how well this effort has gone, and decide whether to continue in this mode or to try another approach.\n\nThe key to this process is to realize that problems occur, that you are not a special victim, and that you have the essential grasp, strength, and confidence to meet the challenge and emerge whole at the end. Life will go on, as will you.\n\nGoal Setting\n\nYour goals reflect what is important to you. Having goals keeps you on track, allows you to measure your progress, and infuses you with self-confidence and motivation, while driving you closer to your ultimate vision for yourself. Establishing realistic goals\u2014meaning that they are achievable, that they are what you genuinely want, and that they jibe with your strengths and values\u2014is an art that requires you to set priorities based on your values and a true understanding of yourself and your capacities. In Chapter 3, you completed the Goals Worksheet. For your convenience, I present the worksheet again. Please review your earlier answers and update them as you see fit. You'll notice that the worksheet follows a certain outline, beginning with a grand vision for yourself and ending with a manageable to-do list of things you can accomplish right away to get the ball rolling.\n\nGOALS WORKSHEET\n\n**1. Long-Term Goals**\n\na. Visualize your ideal life and write about it in as much detail as possible. You might describe what a typical day of freedom looks like, for example.\n\n**2. Short-Term Goals**\n\na. On one line, name three areas of your life that are suffering because of your addiction and, under each one, list some possible changes you can make right now to spark improvement in those areas.\n\nb. Read over your options\u2014some of them will be ambitious and some will be practical. Choose the one change from each list that seems most doable to you. For instance, if you are sedentary and concerned about your health, choosing to train for a 5K might sound inspiring, but a more realistic goal might be to start walking three times a week.\n\nc. Now, under each of your choices, make note of things that will help you achieve these goals. To continue with the example above, what would you need to begin walking? A pair of sturdy but comfortable shoes? Some motivating music queued up on your MP3 player? A walking schedule? A walking buddy? A dog (you can always borrow a neighbor's, and your neighbor will thank you)? Begin gathering your resources.\n\nd. Set a day to start implementing each of these changes, and set up a tracking system. You can use a calendar, a daily checklist, or your PERFECT Journal. There are even websites out there (like ) that help you set goals, track your progress, and connect with others who share your goals. A free online calendar, like Google or Yahoo, will allow you to send reminders to yourself.\n\ne. Remember that making these changes points you in the direction of true recovery. You are aligning yourself with your values. If you miss a day or slack off, just pick the ball back up. Every moment is an opportunity to make a positive choice.\n\n**3. Mid-Range Goals**\n\na. Consider the journal entry you wrote on your vision for yourself, and make a list of goals you will need to meet to actualize your vision. For example, if you see yourself earning a degree, you will need to begin researching programs and requirements. Do you have to earn your GED or take the GRE?\n\nb Are there things you can do right now to begin preparing? If not, when would be a realistic time to begin? Write down that date.\n\n**4. Addiction Goals**\n\nTaking all your answers into consideration, and recalling from Chapter 3\u2014perhaps rereading the various options presented there\u2014what is your ultimate goal in regard to the substance or behavior you are addicted to? What is the best way for you to achieve that? For instance, if you are aiming for abstinence, is it more realistic _for you_ to taper off, to implement harm reduction methods, or to go cold turkey? If you are aiming for moderation, is that a long-term goal that you expect you will fall short of sometimes in the present? If so, how will you handle your addiction while protecting yourself in the meantime? Compose a plan for yourself now, listing your addiction goals and the avenue you want to take there. Be as cooly realistic as you can be. Remember, you can always go back and revise your plan as you gain clarity about yourself and your values.\n\nCoping Skills\n\nNow, let's drill down even farther into the specific areas of your life that may have been neglected or dissolved into overwhelming disarray as you were absorbed in addiction. As we mature, we tend to learn life skills organically, through observation and practice, trial and error. We develop habits and systems\u2014and, depending on our personalities, we may be adept in some areas while we struggle through others. Someone may be a wizard of efficiency at work, but completely disorganized at home. That's normal. When you're emerging from addiction, however, you might find yourself completely stymied by all of it, not having developed global skills or resources (remember how many aspects of her life Rose, in Chapter 1, had to tackle at one time?). Let's bring your self-acceptance, the self-awareness you have gathered, and the basics of goal setting and decision making to the following arenas and get started putting things in order.\n\nRemember that you will be more inspired and adept in some areas, while others will seem more tedious and unimportant. That's okay. It's the rare person who can maintain a perfect sense of balance. Even Martha Stewart couldn't keep her financial life in order. So, be gentle with yourself. Since an entire book could be written on each of these subjects (and they have been), I will offer you an overview and, in Chapters 8 and , will provide further ideas and resources. This is a starting place. Begin by completing your Goals Worksheet, 1 through 3, for each area. You may find that your goals have become clearer or better developed since you filled out the worksheet in Chapter 3.\n\nCommunication Skills: Listening\n\nPaying attention to others is difficult when your mind is focused elsewhere\u2014like on your addiction or what's next on your to-do list. Or, let's be honest, when the subject doesn't interest you because it isn't about you. Genuinely listening when someone is talking to you takes effort and a certain generosity of spirit that improves with practice. It may seem obvious that listening is a good thing to do, but be clear about why that is: First of all, when someone feels that you are honestly paying attention to what they're saying, it makes them feel important. Sometimes, listening to someone is more about establishing and reinforcing the foundation of your relationship than about what they are saying at that moment. It doesn't matter if you're riveted by the subject matter. Second, it inspires a feeling of trust and goodwill toward you\u2014people will continue to seek out your company. Third, listening is a good way to practice your mindfulness skills. Bringing your attention to someone else\u2014even when you're not fascinated\u2014is the essence of mindfulness. Fourth, you might learn something about your conversation partner or about yourself if you are listening rather than simply waiting for them to stop talking so that you can start. You may feel that you are not being interesting enough if you aren't constantly talking, but the truth is that people will feel that _you_ are interesting when you make _them_ feel interesting.\n\nListening is the single most important skill for therapists to cultivate. Some common ways of developing _your_ listening skills (some of which you may already be familiar with) are these: Sometimes simply repeating what the other person has said will reassure them that you are attentive and concerned. \"Mirroring\" means rephrasing or interpreting what you have just heard and offering it back to your companion so they can elaborate. For example, if someone is sharing something personal with you, you can say, \"It must have been shocking to learn that your mother has been keeping such a dark secret.\" Here you are reflecting the emotions the situation created for your friend.\n\nYou might also expand and interpret something he or she has said. \"It seems to me that what your mother did has really been upsetting to you even today, all these years later!\" You can see the big difference between such reflective comments and saying, \"My cousin's mother had a secret, too.\" Other listening techniques include thinking of questions you can ask to move the conversation along. Ask for more detail; ask about how the person felt about an event; ask them what insights they gathered from it. These are essential methods used in the cognitive-behavioral technique called _motivational interviewing_ or _motivational enhancement_ , which I discuss below, in which the therapist constantly turns the interaction back to the individual seeking help to allow them to develop their insights and to spark and focus their motivation to change something that is causing them difficulty.\n\nEmotional Skills\n\n_Patience and choosing your battles_\n\nOf course, listening requires patience. But sometimes you may find that certain people or social situations aggravate you. For instance, suppose you are in a hurry at the grocery store and end up in line behind a customer who doesn't speak English, doesn't understand the payment system, or can't find her money. It's taking forever. You might want to throw a body-language tantrum by tapping your foot, sighing, looking at your watch. You might even want to grab her wallet out of her hand and get her money out for her. You then fume about it all the way home. Life throws us curve balls all the time, usually in the form of other people. We have to wait for them, wait on them, accommodate them, drive behind them, work for them, answer their phone calls, and deal with their idiosyncrasies and ignorance. That's what it means to get along in this world. And, in no small way, life is an accumulation of such moments, as is your overall mood. Allowing for this human truth will make your life much more peaceful. Consider that, in pursuing your addiction, you may have tried people's patience yourself!\n\nMaintaining your perspective is the key to patience, starting with the Buddhist or universalist insight that we are all part of a large, moving universe, human and otherwise. Try to keep in mind that a lot is going on at all times outside of your small realm. Not everyone is on your schedule; not everyone knows the things you know; people make mistakes in traffic (including you). Say you're back in that grocery line, waiting for your turn behind the frustrating customer who is taking a lifetime at the counter. Be aware that, no matter how long it takes her to figure it out, you will surely have your turn within mere minutes. Imagine, as well, her own frustration or embarrassment, especially if she is not fluent in the language\u2014going shopping takes some guts! Take into account that, if you are in a rush, you might have managed your time better. And finally, what is the absolute worst that will happen if she takes another five minutes to count out her bills? Losing your patience is something you can control (a topic for the next chapter).\n\n**JOURNAL:** Write down some of the scenarios that you know cause you to lose your patience: Having to explain something more than once? Seeing the toilet paper turned the wrong way on the roll? Friends who are always late? Drivers who don't use their turn signal? When you examine this list, can you decide which items are irrelevant and which ones you might find ways to mitigate? Are there some over which you have no control, but others that you can't\u2014or shouldn't\u2014tolerate? Are there situations you contribute to or condone by not speaking up? We often lose our patience about things we could exert some control over. Take, for example, the perpetually late friend. He is always twenty minutes late. This is a battle worth picking, because your schedule is as important as his. Think about realistically changing _that_. Seething silently or lashing out with passive-aggressive barbs instead is not effective, and the scenario will simply repeat itself.\n\nMindfulness: Curing Road Rage\n\nConsider what you are doing when you get angry at some stranger for some misdeed\u2014or imagined misdeed\u2014on the highway or the street before you. You are deciding that this person\u2014idiot, miscreant, or innocent that he or she is\u2014can affect your nervous system and brain and significantly alter your view of the universe and mood for the day. My, that's a big consequence to your life from someone's not signaling a turn! How does that unsignaled turn stack up against your precarious financial position, wayward child, or conflicted marriage or intimate relationship, let alone global warming, the national debt, and our troops fighting and dying around the world? I'm sorry to bring all of those up! But you get the point\u2014what this bad driver did is **nothing**.\n\nIf there's one thing you can count on, it's that every day you will be presented with opportunities to navigate obstacles: Your kids will break something; there will be road construction at rush hour; there will be yet another form to fill out; customer service will give you the runaround. Not allowing these things to bug you isn't always easy, and sometimes you just have to stomp around about it. But you don't want to be the type of person who comes unglued at the slightest hitch in things. _Because these are peak moments for resorting to\u2014or else, relapsing back into\u2014an addiction._\n\nThere are some things you can't anticipate, but can use your loving kindness skills and mindfulness to achieve perspective about. Some things you can anticipate: put your Ming vase in the cupboard until the kids are grown; leave home earlier and bring a good audiobook for the ride; read the directions carefully and ask questions; ask to speak with a more helpful representative. Finally, bring your self-knowledge and priorities to bear in cases that require you to negotiate with other people.\n\n_Know\u2014and be true to\u2014yourself_\n\nIt might seem that having social skills means being popular, having a lot of friends, holding court, being witty and attractive. And that a quiet person who avoids crowds, prefers the company of close friends, or would rather engage in solitary activities is lacking in social skills. Neither is true. Social skills are simply your ability to navigate as a worthy person among people in your life in a way that is true to you, so that you and others can coexist peacefully and develop productive and satisfying relationships. And most of us fall somewhere in the range between introvert and extrovert. _When you consider your vision for your life, ask yourself if it matches what you know to be true about yourself_. Do you imagine yourself having a packed social calendar, when in fact you may really enjoy having a cup of coffee with a friend once in a while? Or, do you imagine yourself living a life of quiet contemplation, gardening or knitting or meditating on a mountaintop, when you really love to be around other people, at least periodically? Do you find yourself feeling drained after an outwardly enjoyable event with other people? Or do such situations energize you? Would you rather play a team sport or a sport in which you are competing only with yourself?\n\n**EXERCISE:** Contemplate your idea of social life. Do you see yourself engaging with people in a way that you are currently not doing? For instance, if you are mostly solitary, do you envision a life surrounded by friends? If you are overly involved with people, do you see yourself spending more time alone? Keeping in mind that it is not better to be either an extrovert or an introvert (can you think of an objective reason why one is preferable?), which do you think describes you best? If you enjoy a lot of company, but would like to spend more time alone, can you think of activities you can engage in that will introduce more solitude into your life without abandoning your social life? For instance, you might consider taking up a new activity with one other person, or choosing something you can do on your own. If you spend most of your time alone, but would like to be more involved socially, can you think of activities that will bring you around people, but that will not be overwhelming? You might join a walking group, for instance, or take a class.\n\nBeing comfortable in your own skin is one of life's greatest challenges, and rewards\u2014as Chapter 5, on self-acceptance, describes. As in other areas, your mindfulness skills will help you achieve a clear perspective to guide you in assessing and navigating your social life. Being able to recognize when you are expecting the impossible from yourself or beating yourself up for not meeting arbitrary standards is a skill you can develop. And, of course, being true to yourself does not mean hurting other people in order to satisfy your newly realized emotions. Just because you have decided it is time to assert yourself does not justify offloading against friends, relatives, or the smoothie clerk (as Steve Jobs often did).\n\n_Appreciating others' successes_\n\nWhen Warren was in the first grade, he started taking Kung Fu with a group of other kids his age. A few times a year some members of the class who excelled at a particular level would be elevated a rank, in the company of their classmates, who would then shake hands and bow to the kids who had received this honor. Warren was always thrilled when he was up for a new rank, but felt destroyed and despondent when other kids would elevate. He couldn't see that other kids' elevation was not a personal insult directed at him or a put-down of his abilities. Whenever he came sulking out of class after watching his classmates earn a new stripe on their belts, Warren's mother would ask him how he would feel if the other kids responded as grudgingly when it was his turn to elevate. \"Do you want them to be happy for you or mad at you?\" After continuing in his Kung Fu for a few more years, Warren's perspective gradually changed. Watching his peers progress according to their skills, while he continued to move up as well, allowed him to genuinely appreciate being part of the celebration\u2014part of his community of classmates\u2014no matter who was receiving the honor. It taught him to recognize that his pace is his own, but also allowed him to view his friends' successes as inspiration and motivation.\n\nFeeling genuine joy for others' accomplishments in life is not natural to everyone\u2014maybe not to most people. Do you know the term _schadenfreude_? For many\u2014or most\u2014of us, taking delight in others' misfortunes makes us feel better about ourselves, since we judge ourselves by comparing our fates with others'. This is more true the less secure our own footing is. It takes an effort of will and a deliberate shift in perspective to turn your focus away from yourself and toward someone else in a positive way. One of our national pastimes is to invade celebrities' lives, following them around with a microscope, picking their lives apart in minute detail: their wardrobe choices, their bodies, their relationships. Clearly, this satisfies some collective urge to bring others low, even if they have no relationship to us. It's also something we do to each other on a personal level, as when we direct resentment or spread gossip about people who seem to have something we don't, or feel jealousy rather than joy at a co-worker's wedding announcement or promotion.\n\nNot only do these practices diminish your sense of well-being and integrity, they also shift your attention from your accomplishments and strengths. On the one hand, worrying about other people's successes and failures really has no consequences for\u2014and may actually impede\u2014getting into the swing of your own life. Furthermore, being able to celebrate and respect others for what they have or what they are doing\u2014or, alternately, feeling compassion when they fail\u2014connects you to people in a positive way. Anything that enhances your feeling of community, of belonging, is good for you. Just as they did for young Warren, others' accomplishments can inspire and motivate you.\n\nBoundary Setting\n\n_Respecting boundaries\u2014yours and others'_\n\nThe notion of maintaining one's boundaries hit the mainstream a long time ago, but its meaning can be vague and self-serving. For some, it means taking an uncompromising stand or putting yourself first in all circumstances; for others, it means learning to say \"no\"\u2014important, but still just one part of the picture. Respecting boundaries requires you to know your own limits, and also to know whether it's appropriate to be flexible or to stand firm. It also means recognizing and respecting others' boundaries, without taking their limits as personal affronts. You deserve to be treated respectfully, whatever your quirks, and it is your job\u2014no one else's\u2014to make sure others don't demean or discount you. The converse requires that you don't pressure others to act outside their comfort zone\u2014even when you believe it may be best for them. Here are a few basic elements in respecting boundaries:\n\n\u2022 **Defining your boundaries:** What lines won't you cross? For example, will you never drink or smoke or take drugs in front of your parents or your child? Equally important in setting boundaries is what you will refuse to allow others to do to you, or even in your presence. Actions, activities, or behaviors that make you uncomfortable or that you will not tolerate from other people because they compromise your values or detract from your quality of life form such boundaries. If you have friends who indulge in malicious gossip about other members of your circle, perhaps you think they are behaving badly. But you can get caught up in the moment and listen or participate, despite your unease. Setting your boundaries in cases like this can be difficult because you fear rejection from your friends, perhaps becoming the next topic of conversation. How might you draw a line so as not to violate your values in a situation like this?\n\n\u2022 **Knowing how to be flexible without violating your values:** Can you make exceptions to your rules, if, for instance, it would serve a higher purpose? Can you do so without feeling undermined? Other types of boundaries include how you respond to requests (or demands) from others. Suppose you have a family member whom you love, but who has consistently taken advantage of you, and lately you have steadfastly denied her requests. She is currently in need of help. You have values in conflict: On one hand, you want to avoid feeling used; yet you feel her suffering. Can you think of ways you might help her without compromising your integrity, perhaps by imposing clear limits on, or conditions for, your help?\n\n\u2022 **Effectively and respectfully communicating your boundaries:** Are you able to tell people directly when their behavior violates your boundaries? Can you do so before you are feeling helpless or angry? Are you afraid of what will happen if you draw a line in the sand? What if a friend ignores crosswalks and sends pedestrians scurrying while you, as a bicyclist, are hypersensitive about respecting people who aren't in cars and trucks? Are you sure to mention to your friend that you feel they are doing something wrong? How sternly should you make your point? Should you refuse to drive with them if they keep it up; to stop dealing with them altogether? What if a friend talks to counter servers\u2014or to his or her children, for that matter\u2014in a disrespectful way? Will you bring it up to your friend? If so, immediately or later? How will you introduce the topic?\n\n\u2022 **Being clear about the consequences of violating your boundaries:** Clearly communicating your boundaries is part of the broader question: How will you respond if someone violates your boundaries? Are you clear with yourself and others about those consequences? Will you follow through? Children are perhaps the most skillful boundary pushers on earth: Say you are at the store with your child, who is making your shopping trip impossible by begging and crying for toys and candy. And you respond by alternately pleading for cooperation, issuing threats, and giving in. Now, imagine telling your child, before you enter the store, that if they begin whining and pleading, you will pick them up, walk out of the store, and give them a time-out at home. And imagine actually doing so, matter-of-factly, without losing your cool. You know that if you are consistent with your response, your child will learn quickly. Are there other areas of your life where this approach will serve you well? One that we discuss below, with CRAFT, involves children or spouses who violate the sanctity of the family or household through their drug use or drinking.\n\n\u2022 **Learning to reassess or redefine your boundaries based on experience:** What if you realize that a boundary you have been protecting is no longer relevant to you? Can you change or discard that boundary? Sometimes, for example, you feel that you must cut off contact with a person who has hurt you in the past, especially if you are vulnerable to being hurt by them again. A lot of healing and growth can happen over time (per Chapter 5, about children who come to or are considering forgiveness of parents who have neglected or abused them). You might find that, while there was a time when a certain person held some negative power over you, they no longer do. Whether or not they have changed or are remorseful, _you_ are no longer vulnerable to being hurt by them, or you have forgiven them. It might be time to reconsider your boundary, especially if you genuinely care about them or have other reasons to reconnect.\n\n\u2022 **Understanding that others deserve the same rights:** How do you respond when someone denies your request for help? In the first place, what are reasonable requests for you to make of your friends and family? When someone denies your request, your feelings will almost surely be hurt. However, can you also take a perspective that allows you to accept such decisions as not being a comment on your value to those you know and love, but more one based on their personal circumstances? In other words, can you remove yourself as the presumed primary factor in others' personal choices?\n\n_Standing up for yourself_\n\nThe best known, most often used method for respecting boundaries is assertiveness training, which teaches people to express their needs and preferences calmly, firmly, and respectfully. At one extreme is complete passivity and submissiveness, where a person makes no effort to be clear about his or her values or wishes. At the other extreme is open aggressiveness, where people impose their values and requirements on others with no regard for others' feelings, values, or needs. Assertiveness takes a constructive stance between these extremes.\n\nAssertiveness includes being able to give and receive feedback. When you feel that your boundaries are being violated, both in terms of your basic values and in your addictive areas, you need tools to allow you to tell others where your boundaries are and how they may be overstepping them. In doing so, you need to rely on communication\u2014or feedback\u2014skills. Here are key elements of giving people feedback about your boundaries:\n\n\u2022 Be specific about what you don't like and explain why you don't like it: that is, how it violates your boundaries or values.\n\n\u2022 Don't express anger or dislike toward the person\/people, but only at the behavior or the message of which you disapprove.\n\n\u2022 Reinforce your liking or love of the person or people (if this is true) to whom you are giving the feedback.\n\n\u2022 Describe what you need to take place in order to continue in the interaction\/relationship.\n\nOne further element in the feedback process is that you need to be able to accept and respond in the same vein to feedback others give you when you violate their values or overstep their boundaries. Suffice it to say, you want to be as open to their sincere expression of their concerns as you hope they will be to yours.\n\nBoundaries and Addiction Treatment\n\n_Helping others_\n\nBoundary maintenance is important when giving as well as receiving feedback. What if people don't respond to the wisdom you offer them? Can you respect that their expectations and desires may simply be different from yours? Or that they simply are not prepared to make changes, even when you may be right that these would be good for them? Of course, addiction often drives a person's relatives and friends around the bend, causing them to become more and more forceful in their demands, to the point of constraining the addict's options and behaviors. In the law, this is permissible when the person becomes a danger to themselves and\/or others. But in any but extreme circumstances, taking control of someone else's life out of their hands has serious implications, some of which you may never be able to reverse.\n\n_Boundary violations in addiction treatment_\n\nThe belief that addiction means that a person cannot control themselves, and that addictive behavior inevitably leads to decline, collapse, and ultimately death, has been used to justify all sorts of unwanted intrusions into people's lives. Taking this approach more often than not backfires and doesn't produce positive results. The hectoring that goes on in 12-step circles is considered sacred because its practitioners claim, \"We know what you are better than you do\" (remember that Rose, in Chapter 1, had this experience). Violating someone else's personal space and autonomy includes taking away their right to their own self-conception. After all, when people say, \"I don't believe I am a lifelong addict,\" they are far more often right than wrong\u2014especially when they are young. Yet young people are those most likely to receive such unrestrained\u2014even vicious\u2014attacks on their own self-definitions and wills. Tough Love is one example of unrestrained boundaries in the addiction treatment industry that has been shown to do much more harm than good, both with adolescents and with adults.\n\n_Accepting those close to you_\n\nWhen someone close to you is self-destructive, you naturally want to help. Presenting people you love with ultimatums or cutting them out of your life completely can go against your most life-affirming instincts. That is not to say that there are not times when you must do so. As we have seen, people are often acting in some sense of their own interest by pursuing addictive gratifications and, for some, this may be the best they are capable of at the time. Ultimately, most become clear about better ways to find satisfaction and get what they need from life. In the meantime, whether or not you decide to close the door on a relationship requires you to prioritize your values and to know yourself and what you can live with. It is an extreme scenario, one that requires you to maintain your boundaries\u2014say, with a child or a spouse\u2014in day-to-day life, as described above. This means:\n\n\u2022 Accepting the people and situations into your life that bring you fulfillment and satisfaction, even if they are difficult or challenging.\n\n\u2022 Excluding the people and situations that detract from or compromise your priorities, or that do you or your loved ones actual harm.\n\n\u2022 When there is no simple answer, moderating or accommodating your demands, but withdrawing as required at particular moments, in a way that allows you to maintain your integrity.\n\nEffective Therapies\n\n_Community reinforcement and family training (CRAFT)_\n\n_Recover!_ tells you that you can get over an addiction on your own, as most people do. It offers you information in a non-technical form that you can use yourself and in the service of others. Yet, some people don't get better, or at least at the pace you need them to in order for you to be content in your own life and on their behalf. What do you do when a family member's or loved one's addiction is disturbing, disrupting, or hurting you and the rest of the family? The alternatives include trying to be as helpful as you can be or, if you're in a position to do so, to help or encourage the person to find an effective treatment.\n\nI have interspersed in this chapter references to cognitive-behavioral therapy techniques. One such resource is called Community Reinforcement and Family Training, or CRAFT, which is an extension of the Community Reinforcement Approach (CRA) described above. As with other such techniques, I review CRAFT in _Truth_ and _Tools_. Here I describe its basic concepts. CRAFT is a way of applying behavioral reinforcement techniques within a family context. It aims to teach spouses and parents how to (1) protect themselves and other family members, particularly children, and (2) encourage addicted family members to seek needed help for themselves. CRAFT's elements are simply extensions of the boundary principles already discussed:\n\n\u2022 Be clear on your own boundaries, needs, and self-protection. Make these limits crystal clear to an addicted family member, and allow them to participate in the family so long as they observe these boundaries.\n\n\u2022 Be prepared to expel the family member\u2014either temporarily or for a longer duration\u2014when they refuse, or fail, to honor the boundaries.\n\n\u2022 Access and make the family member aware of help they can seek (for example, therapy) in order to help themselves and potentially reenter the family context.\n\nOne form of addiction treatment you may be aware of from television is interventions, in which severely addicted people are confronted with an absolute need to seek treatment\u2014which they are then forced into. Judging from the great successes TV portrays, you might wonder why every addict in the world isn't simply coerced to attend treatment as these fortunate souls were. Well, aside from the violations of personal integrity and potential legal violations I have discussed, these interventions simply don't work well (which is often apparent even in the shows that promote them). One of the best known of these, _Celebrity Rehab_ , administered by Dr. Drew Pinsky, attracted a lot of negative attention when Mindy McCready became the fifth of the show's alumni to die. Most people don't end up succeeding when they're forced into treatment (nearly always 12-step, of course). In fact, most don't even end up going. CRAFT is an alternative that has been shown superior for helping the addicted family member, whether or not treatment is ultimately involved.\n\n* * *\n\n**CASE:** Riva's boyfriend Glenn abused alcohol, and it often made him unreliable and ugly. They had a young child together. Riva's constant fear was that the boy would see\u2014or just sense\u2014Glenn's problem drinking, and that it would affect the boy both directly and indirectly. Yet she was reluctant to throw Glenn out of the home. For one thing, as the father of her child, she couldn't ever completely get rid of him.\n\nRiva went to a therapist who she heard was good in such situations. Together, they made a list of behaviors that Riva simply would no longer tolerate\u2014and she would lock Glenn out of the house when he did these\u2014getting a restraining order if necessary to do so.\n\nOn the other hand, Riva wanted to offer Glenn every chance to reenter their home and participate fully so long as he wasn't drinking (or drinking in an ugly manner). She and the therapist she saw also drew up a list of likely resources\u2014support groups, from AA to SMART Recovery, as well as potential counselors, men's groups, anger management classes, etc.\u2014for Glenn to access, if he thought these would help him meet the mark that Riva was now setting for him.\n\n* * *\n\n_Motivational interviewing_\n\nPerhaps the single most difficult skill discussed here is learning how to assist people without telling them what they should do. The first skill I trained all my counselors at my residential treatment center to use was a listening technique called \"motivational interviewing\" or \"motivational enhancement,\" as developed by William Miller and his colleagues. People don't respond when you instruct them on how to act\u2014even when they ask you to tell them exactly that. Instead, addiction clients\u2014like everybody\u2014react defensively when given such instructions, which, of course, people take to be criticisms. People argue back, even counterattack, thinking: \"They just don't understand me and my situation.\"\n\nAnd people\u2014you\u2014are right. No one can understand your needs, goals, and situation as you can; nor can you understand any other person's as well as they can. Therefore, as Miller and other researchers have shown, the best way to encourage the motivation to change\u2014and actual changes\u2014is to help people come to grips with their problems through their own thinking and motivational processes. You enable others to do this\u2014as I have discussed above\u2014by listening and with sympathetic, genuinely inquisitive questioning, a process called motivational interviewing (MI). MI is currently the most popular therapy technique in addiction circles. Just about every program claims to use it, even when it is the last thing counselors and the program believe in. As Anne Fletcher demonstrated in her book _Inside Rehab_ (Viking, 2013), addiction counselors and programs actually rarely use effective approaches like MI. Most such programs and counselors instead follow a top-down, dictatorial model. If they did use MI, they would have to permit the addict to pursue whichever path he or she feels is likely to work best, including moderation or harm reduction, as long as that is their preferred route (which they are therefore going to pursue anyhow).\n\nThe Questioning Exercise\n\nThe next time someone\u2014a friend or family member\u2014asks you for advice, tell them that before you can offer them any inputs, you first need to clarify their situation for yourself. Then question them. Some key elements you might cover are:\n\n\u2022 Information about the person: their backgrounds, experiences, current situation (job, family, emotional).\n\n\u2022 Only after establishing these personal foundations\u2014including your willingness and ability to listen sympathetically\u2014ask them to flesh out the problem that concerns them, whether addictive or otherwise.\n\n\u2022 During the course of the above, ask the person what is most important to them (family, work, health, self-determination, religion, whatever) and how this affects the problem\u2014and, specifically, why it makes them want to change (remember the case of Ozzie in Chapter 2, who decided to quit smoking when someone made him realize it directly opposed his union allegiance).\n\n\u2022 Without ever presenting your own views directly, work as best you can through your questioning to explore the person's expressed reasons for changing and the consequences they have experienced from their problem (addictive or otherwise), allowing them to make as many and as vivid connections as they can between what is important to them and the need for change.\n\nThis is the therapy that has most demonstrated its effectiveness in the case of addiction, and much else.\n\nMoving Forward\n\nThis chapter has given you a lot to digest. Take a moment to pause, reflect, meditate. When you're ready, we will move on and devote the next chapter to putting your skills and values into action and to achieving balance in your life through self-awareness and reframing your perspective on failure.\n\nCHAPTER 8\n\n_Embark_\n\nEquilibrium\u2014Proceeding on an even keel\n\n* * *\n\n**CHAPTER GOALS**\n\n\u2022 To develop a foundation of self-knowledge\n\n\u2022 To decide what to change and what to do now\n\n\u2022 To take first steps into your new life\n\n\u2022 To understand and prevent relapse\n\n**Purpose:** Preparing for a journey, while necessary, is a lot of work: charting your course, honing your skills, gathering your resources, anticipating challenges and troubled waters. It's possible to spend a lifetime planning and arranging and waiting for the perfect moment to shove off. Ultimately, there is no perfect time, and no amount of preparation can be as valuable to you as the lessons you learn and the skills you develop by actually doing. This chapter is devoted to encouraging you to set sail and guiding you through some of the early demands on you and rough patches that may shake your resolve. Above all, you want to keep your forward motion, which requires\u2014and also helps you maintain\u2014your balance. This requires sharpening your self-knowledge or awareness, so that you can make deliberate choices based on your priorities; acting decisively on the decisions you make; and being able to maintain your larger perspective through failure and relapse by treating them as information to learn from.\n\n* * *\n\nSelf-Knowledge and Personal Choice\n\nLearning about yourself\u2014developing insights into who you are, what you want, how you function\u2014is self-knowledge (or self-awareness). Self-knowledge is a critical skill in fighting addiction. There is no one approach to overcoming addiction, and The PERFECT Program is designed to help you discover a path that honors your heart, values, and personal choices. Your goal is not simply to quit your addiction, but to make addiction impossible by replacing it with a path of your own design that is true to you. Knowing yourself, your strengths and passions as well as your vulnerabilities and areas of self-deception, is essential both for making on-the-spot decisions and for completing your long-term goals. Self-knowledge is the engine of free will; it allows you to understand your motivations and then to make decisions consciously and deliberately, with your purpose in mind. Addiction generates a massive blind spot, preventing you from seeing beyond its own immediate satisfaction. Whether or not you have been addicted to anything, you surely have witnessed the results of this blind spot in other people. Perhaps you have even expressed frustration and incredulity over their unwillingness to see what is so clear to everyone else: \"Why doesn't she leave him?\" \"What was he thinking when he did that?\" \"How could she leave her kids alone?\" \"Who does such a thing?\" And, maybe you offer a concession to your own blind spot, \"I have my moments, but I'd _never_ go that far.\" You probably _wouldn't_ go that far, and you know yourself well enough to make that assertion.\n\n* * *\n\n**CASE:** Liam is strikingly handsome\u2014compelling in a rakish, movie-star kind of way. He is also a long-term alcoholic. His friends (of whom there are few) and acquaintances commonly refer to him as \"a drunk\"\u2014if not worse. \"Drunk\" is a harsh term, but the images it conjures are apt for this person. Liam is, it seems to everyone, a lost cause. Insufferable and obnoxious, he blows the fuse on everyone's last nerve and has been banned from almost every bar in town. He wears out his welcome almost instantly by telling racist and sexist jokes, making rude observations about other patrons, and\u2014like the classic drunk\u2014spilling his drinks and falling off his stool.\n\nAlthough Liam seemingly has no limits and no restraint, there are two things he will not do no matter how impaired he is: He will not drive drunk, and he will not cheat on his girlfriend (surprisingly, Liam does indeed have a longtime girlfriend).\n\n* * *\n\nLiam's personal taboos\u2014few in number as they may be\u2014are deeply ingrained in him. They spring from genuine values: his sense of loyalty to his companion and his unwillingness to chance hurting or killing someone. No matter how wasted he may be and no matter how many bridges he burns or people he offends, he is incapable of giving himself permission to cross those certain lines. The converse of Liam's case is also true. Excusing poor behavior by blaming it on addiction is one of the ways that addiction blinds\u2014or deludes\u2014us. After reading Liam's story, you might say, for instance, \"Okay, so maybe I drive occasionally when I'm high, but I'd never tell a racist or sexist joke no matter how messed up I get.\" If you had a similar thought, ask yourself this question: \"How is it that, no matter how impaired I am, I will never do one thing, but can still find an excuse to do the other?\" It's really rather remarkable, when you think about it.\n\nConsider, for example, someone who is prone to flying into rages. He's unpredictable, and people walk on eggshells around him, never sure what will set him off or when he will throw a tantrum. When this guy loses it, he screams obscenities, slams doors, stomps around, menacing and invading others' personal space. He might throw something across the room or turn over a piece of furniture or put his fist into the wall. When it's all over with, he always feels ashamed of himself and excuses his behavior by saying that he was so angry that he lost control. If you were brave, you could ask him at this point, \"If you're so out of control, how come you haven't killed anyone yet?\" Think about it like this: even when this loose cannon is in a blind rage, he is always able to prevent himself from taking his behavior to the point of no return. From where does that self-control and will come?\n\nThis example and Liam's case are both extreme and disturbing scenarios. I have included them here to demonstrate that everyone\u2014no matter how far gone\u2014has standards and lines they will not cross. The taboos they have established for themselves spring directly from their personal priorities. But the converse is also true. Say you do things that you feel violate your true value system as a result of your addiction, such as cheat on your partner while drunk, gamble away your children's college fund, or skip work to play World of Warcraft. It's a difficult pill to swallow\u2014but you would not do these things if you did not give yourself permission to.\n\nSelf-knowledge is a lifelong process of discovery. Shedding light on your motivations requires you to bring your self-acceptance practice to bear on everything you learn about yourself. You might find that you have certain positive priorities that you always honor. Say, for instance, you haven't yet quit smoking, but you never smoke in the house or in front of children. Or, although you have a serious drinking problem, you never drink too much while with your parents. Clearly, your commitment to your family is key and inviolable. But you may find that other values you hold dear are more easily shunted to the wayside\u2014your own health, for instance.\n\nTo continue with the example of the smoker, let's say there are a couple of value systems in conflict within you. Smoking provides you with some alone time, helps you focus on your work, and makes you feel productive. At the same time, you know that you're putting your health at risk through your smoking and thereby endangering your family's well-being. How do you reconcile this? When you allow yourself to see that you have a conflict of values, you are in a position to make some decisions, to act on your primary motivations. Rage-aholics who are able to control their behavior despite being consumed by anger seem to do so in unplanned ways. That is, they don't deliberate about which acts of violence they will commit. They're acting on autopilot. Self-knowledge allows you to shine light on the motivations behind these choices, hidden somewhere within you, so that you can make your decisions intentional ones.\n\nHere are exercises and practices that will help you become more self-aware:\n\n**BE PRESENT:** As I discussed in Chapter 4, we all experience moments of grace, in which we hear from our inner self. Rather than waiting for these moments to arise spontaneously, call them forth deliberately. Whenever it occurs to you\u2014perhaps set a chime on your cell phone as a reminder a few times a day or choose a regular time every day, say, when you're in the shower\u2014to stop what you're doing for a couple of minutes and bring your attention into the present moment and to all your senses. What are you doing at the moment? How is your posture? What is the quality of light in the room or outside? What are the objects that surround you? What do you hear? Smell? Do you have any aches or pains? What is your mood? You don't have to write anything down. Just notice, and bring yourself as fully into the present as possible.\n\n**MOVE:** If you are a physically active person, employ the same \"Being present\" exercise when you are engaged in an activity. Bring your full attention to your body's movements. Alternately, find a physical activity that you are unfamiliar with\u2014say, learn a new dance or take a yoga class\u2014and as you're learning new, awkward-feeling moves, take a moment to bring your attention to these unfamiliar physical sensations. If you are not physically active, carve out some time during your day to walk or stretch or swim. When you are engaged in the activity you choose, focus your awareness on your body and movements. If you are walking, for example, pay attention to your steps\u2014how the ground feels under your feet, how your muscles feel when moving.\n\n**LISTEN:** When you are engaged in a conversation with another person, practice intentional curiosity. Take the time to focus your attention on what your companion is saying and respond only with relevant questions or with acknowledgment that you have heard\u2014put your own input and desire to express opinions on the back burner (remember motivational enhancement?). This is especially powerful when you converse with a child and focus on his or her mind and world. Do you notice any discomfort in forcing yourself to listen? If so, can you describe what that feels like? How does it feel to keep your opinions to yourself? Why do you think you experience this discomfort?\n\n**HOW DO OTHERS SEE YOU?:** Choose three people in your life. They don't all have to be close to you. You might choose your spouse, a close friend, your boss or employees, your neighbor, your roommate, your mother. In your Personal Journal, compose a picture of yourself through each of their eyes. Do you believe they see you accurately? Do different facets of your character present themselves depending on whom you're with? Keep in mind that this is fine: It's usual that you treat different people differently\u2014like your spouse and your parent. If, for instance, you find yourself patient with one person but short and irritated with another, remember that these are simply facets of yourself. You are not being dishonest or fake just because you behave differently with different people. Self-acceptance (Chapter 5) is key here. On the other hand, when you bring this difference into mindful self-awareness, you might ask whether you want it to persist. _Should_ you be as patient with one person with whom you are short-tempered as another with whom you display greater tolerance? This is a trait you obviously are capable of expressing\u2014should you use it more readily?\n\n**WHAT ARE YOUR STRENGTHS AND VULNERABILITIES?** In your journal, make a list of the areas of your life in which you excel or have excelled in the past. Then make a list of areas of your life where you feel vulnerable. If you have trouble making this list, ask for help from someone you trust. In fact, even if you don't have trouble, you might benefit from doing this exercise with someone you trust. They may provide a more realistic, objective perspective on your answers. If you choose to do this exercise with a companion, note the areas of disagreement.\n\nShoving Off\n\nThe overarching goal of The PERFECT Program is to reach the point where you can lift your sails, free from addiction, and embark on your real life's journey. The skills you have been learning will help you achieve the balance necessary to head off into the sunset, rather than to keep you moored to a program, a label, or a prescribed way of life\u2014whether that be \"addiction\" or \"recovery.\" It's time to take that step, like the tightrope walker Philippe Petit, depicted in the film _Man on Wire_ , taking his first step onto the wire spanning the two World Trade Center towers. (Well, your step is not _quite_ that daring.) After all the work you have done, it's time to put what you've learned into play. Let's start by navigating out of the rocky, sometimes perilous port you've been anchored in.\n\nYou have identified a vision for your life and have defined some goals\u2014it's time to take some decisive steps, make some real moves. In the previous chapters, you gathered and organized everything that is important to you, the things that bring value, purpose, and meaning to your life, and you made some decisions about where you need some life-management support and skills training. Now, you can bring these elements into present actions. You have thought about life changes you want to make: some monumental or frightening, like leaving a relationship or tackling your debts, and some more gentle and exciting, like starting a garden or going back to college. Regardless of whether your current goals are difficult or simple to activate, getting started\u2014taking that first step off your secure mooring\u2014can be daunting.\n\nWe have a tendency to think there is some magic moment in the future when we will be the person we think we should be. Everything must be right in some mystical, undefined way before we can fully exist, as if a square on the calendar held some transformative power: We'll start on Monday. We'll wait until after the holidays. We will wake up a completely different person on New Year's Day. Of course, it can be helpful to pick a date to start making significant changes or to create a new project. If you find that works for you, by all means, get out your calendar and mark it off. At the same time, there is nothing stopping you from making smaller corrections to your course, based on the goals you have set for yourself, this day\u2014this hour. You are here, now, and you can start right where you stand.\n\nBegin by deciding and committing to what is immediately doable and essential\u2014that is, what you can and want to introduce into your life _today_ \u2014and beginning to do so. (Exercising regularly, for instance, or doing yoga or meditating.) Next, you will focus on your long-term goals and what you need to do to achieve them. (Going to school, acquiring a new skill, forging intimate relationships with family members, friends, or people as yet unknown.) Finally, you will approach the monumental life changes you want to make and decide on some strategies for setting these in motion. (Moving, forming a partnership, getting divorced, having a child, changing careers.)\n\nYou have identified important goals you want to pursue and have decided how you want to approach overcoming your addiction in a way that works for you, based on your values and preferences and your exposure to the ways people overcome addiction, as described in Chapter 2 and throughout this book. Now let's prioritize your necessary steps, starting with things to be addressed immediately\u2014including, of course, your addiction. You may also need to deal quickly with concerns around your family, health, or work. One way to decide what to do now is to address the things that will create chaos if you wait any longer.\n\nYou may also want to start to do simple things that will enhance your quality of life\u2014like keeping your residence clean and organized. Think of those things also that you'd like to adopt into your life, like exercise or other wholesome activities. In terms of larger goals, consider your education, career, and perhaps social and family life. And, finally, you may have some serious changes to make to your living situation that may require you to shore up your resources (both financial and emotional), to seek legal counsel, or to venture into territory that is overwhelmingly unfamiliar, such as striking out on your own for the first time. Use your Goals Worksheets to help guide you.\n\n**IMMEDIATE:** In your PERFECT Journal, list the changes you intend to make now and describe the consequences for you if you do not. Consider how you will implement these changes\u2014break them down into smaller steps and prioritize them. Then make a commitment to yourself by scheduling these things on your calendar. For instance, if you must see a dentist because you are in pain, commit to a time to make the phone call and set the appointment. Similarly, if you plan to go cold turkey on your addiction, commit to it on your calendar. If you are delinquent on your bills and risk being shut off or going to collections, contact your creditors. Get started now, and keep close track of whatever you do to further your goals. Do not forget to make note of how it makes you feel to tick these tasks off your list. If you find yourself overwhelmed by the number of tasks you have set for yourself, go back and reprioritize.\n\n**INTERMEDIATE:** List in your PERFECT Journal those things you want to bring into your life, and begin setting a sensible schedule for implementing them. You may need to do some research to accomplish this. If so, schedule time for that work. As you did with your immediate plans, make commitments, follow through, and check off their accomplishment. Keep track of your activities and how it makes you feel to pursue these things. In your Personal Journal, if you find that you have lost interest, or that something you have included on your list doesn't live up to your expectations, explore those feelings and ask yourself whether your plans were true to you, why you were wrong in thinking they were, or if there is another reason you have abandoned them.\n\n**MAJOR CHANGES:** If you are experiencing impending or current major upheavals in your life, you may have a lot of planning to do and hard decisions to make. It could be that making a major change is imperative; it must take top priority and so also becomes an immediate need, albeit a potentially life-altering one. If you are in an abusive or destructive domestic situation or, say, your house is in foreclosure or you are in a serious legal bind, you must focus on this right away. In this case, you may need to find some community, therapeutic, or governmental resources to help you take control of your situation and prioritize the tasks required in order to make changes\u2014or simply to cope with your situation. Use your goal-setting tools and begin taking the steps you need to take to see this through. Chapter 10, about triaging, provides you with lists of resources for difficult or unfamiliar situations.\n\nIf the major changes you'd like to make are less emergent\u2014say, a long-coming divorce or a residential move, buying a house, having a child\u2014you can begin to prepare yourself in less dramatic ways. Meanwhile, focus steadily on your addiction and wellness goals so that you are in a stronger position to navigate the inevitable frustrations and surprises that come with tackling your major life goals\u2014put simply, you can't have children or launch a new career while getting drunk daily or having other unaddressed psychological and health issues.\n\nGetting Straight\n\nIn the early stages of leaving an addiction, you may have a lot to put in order\u2014many things to remedy and take care of\u2014before you can feel fairly secure in your recovery. The most prominent single finding from Baumeister's research on willpower is that you develop that muscle\u2014become capable of self-regulation\u2014the more you practice it throughout your life.\n\n_Honoring your commitments_\n\nYou may have to clear up quite a bit of baggage and debris following your emergence from addiction. After dropping a lot of balls and sacrificing much to your addiction, correcting your course is not about making up to particular individuals (see Chapter 5, on forgiveness), but about establishing yourself as a worthwhile, dependable person. Doing what you say you're going to do creates a secure identity, both in your mind and the minds of others, and a feeling of having a firm place in your community and the world. Part of making and keeping legitimate commitments is being able to recognize when you are over-committing or making promises that you simply cannot keep just to maintain some peace in the moment or to make someone feel good. If you generally have trouble following through on your promises, here are a couple of approaches to enhancing this skill and value:\n\n\u2022 Don't make commitments impulsively, even if someone is pressing you for an answer or it sounds like fun. Take the time to see whether it will fit into your schedule, whether it is something you find important, or whether it will compromise other, more important commitments you have made.\n\n\u2022 Practice making and keeping commitments in small ways. Start by, say, scheduling a task and doing it during the time you set for yourself. Find an event that interests you and commit yourself to attending.\n\nHonoring your commitments to yourself is a major value to cultivate\u2014an essential element of mindfulness, self-knowledge, and overall fulfillment.\n\n_Domestic space_\n\nMoving from your existential place in the world to the most physical space you occupy, having a living space that provides comfort and sanctuary will contribute greatly to your peace of mind. You must decide for yourself what that looks and feels like for you. That might entail putting your kitchen in order so that you can cook meals, or it might mean decluttering your entryway. You might like to have a home that could be featured in _Better Homes and Gardens_ , but a more realistic and satisfying target for you may be to avoid a pile of dishes or food rotting in your sink and to sleep on clean sheets. You may be someone who can't rest unless everything is in its place, or you may find that puttering around your house each morning completing small household tasks is calming. Whatever your inclination, start following through on it. Your Goals Worksheet enables you to identify key areas to focus on\u2014begin there. Here are some ideas and resources that may help you get going:\n\n_Getting help and exploring resources:_ You may be in a position to hire a home organization expert or a cleaning service to come in and do a deep clean. Don't be reluctant to do so because you're embarrassed by whatever mess you have. They've seen it all. (Which I, as an addiction therapist, might also say\u2014in case you need to consult someone like me.) You can also enlist a good friend to come in and help (as described in Chapter 7). Another option is to seek out a local co-op group, or start one yourself, of people who all meet at one member's house on the weekend and work together to tackle the domestic chores.\n\n_Accountability:_ Free online resources can provide you with accountability and direction. Here are some websites that you might find useful: Flylady. net is a coaching resource that helps you prioritize your household tasks. Rememberthemilk.com is a task manager, which you can use online or as an app for your phone. Do some exploring; see if you can find other resources with a built-in community of people who are working toward the same goal.\n\nSocial Skills: Creating Community and Intimacy\n\n_Community_\n\nOur communities consist of our families, living mates, neighbors, social networks, co-workers, activity partners, church congregations, towns and cities. Nothing enhances our sense of purpose, of belonging on earth, of meaning, of contentment more than does feeling part of a community. This is fundamental to the human condition, and the general loss of community in modern culture is a severe blow to all our humanity\u2014as well as being a major cause of addiction. Addicted people tend to form pseudo-communities around their addictions (think again of Rose in Chapter 1), and often their fear of losing that pseudo-community is a strong component in maintaining an addiction. That is, people fear they will be lonely if they are deprived of their addiction mates. Conversely, forming positive communities is a strong antidote to addiction and is even used as a form of treatment, social network therapy, as described in Chapter 7. Reconnecting with such non-addiction-focused, real-world groups in meaningful ways will bring you a deeper and more satisfying sense of belonging than addiction ever can.\n\n**EXERCISE:** In your journal, compose a list of the communities you are involved in or touch upon. Acknowledge your connections to the world. Make another list of some others you would like to be part of. Depending on your personality, you may want to limit yourself pretty much to family or a close social circle, and your neighborhood; or you may want to involve yourself in a number of different areas involving special interests you have or want to pursue. Imagine how you would participate in these groups, and then ask yourself if it is realistic to make the commitment. Complete a Goals Worksheet to help you prioritize and decide what steps to take to find and join such communities.\n\n_Making friends_\n\nJoining communities has much in common with making friends\u2014finding compatible and accessible people with whom to spend time, share interests, and perhaps develop deeper feelings and relationships\u2014up to and including love. People\u2014as we discussed in the last chapter\u2014have different degrees of sociability, of skill at and tolerance for interacting with others, of enjoying time alone. But it's fair to say that everybody needs some degree of skill at both being alone and being with others. A free life can't be lived without some version of both traits. If you can never be alone, then you can never be at ease and must always desperately seek out contact\u2014for better or for worse (see the case below). If you can't spend some time with and interact with people, then you can be shut into yourself\u2014sentenced to aloneness that is a kind of addiction.\n\nThe short answer to how to be able to live both parts of yourself is\u2014as with nearly everything in this book\u2014practice. Schedule time to spend by yourself\u2014something you must, of course, do when you are meditating. Reading, listening to music, walking, being with a pet\u2014all of those do count (the PERFECT Program is very open-minded). Watching television counts if you do it purposefully, because you are specifically watching something you enjoy for reasons you know. And schedule time to interact with others. This may mean going to one of the groups you described in the previous section. Or it may mean calling and speaking with, or arranging to visit or meet, an old friend, a relation, or someone you'd like to get to know\u2014for any reason whatsoever. It is a mark of our times\u2014and it is not a good mark\u2014that actual contact with people, even so much as talking by phone, is becoming a relic of the past. Nothing against e-mails and iPads, but we can't do without human contact.\n\n* * *\n\n**CASE:** Isaac had been a good student. But when he arrived at his large, well-regarded high school, he suddenly seemed intimidated. And so, for most of his first semester, he walked around the school as though he were in a penitentiary. Of course, Isaac's parents\u2014Rachel and Bob\u2014were worried. And, so, when he returned home one day with a smile and said he had lunch with a few kids, one of whom he liked especially, his parents were glad.\n\nBut it turned out that this outsider's group was heavily immersed in drugs. Thus followed four years of hell for Isaac's parents, ending when they used a large part of their life savings to send Isaac to a residential treatment program. The program seemed like a good one, although Rachel and Bob questioned some aspects of it. Was it really true that Isaac had inherited a disease and that he could never drink (let alone take drugs) for the rest of his life? After all, he was only nineteen. Moreover, when he graduated the three-month program, he was sent to a residence. But in many ways the kids in this group were a lot like those he was with in high school, only now supposedly recovering.\n\n* * *\n\nBut what most worried Rachel and Bob was that, as they kept up with the parents of the other kids they met in treatment and the group home, nearly all of their children had relapsed. How is that possible, Bob asked Rachel, after they learned so much and did so well interacting with one another in treatment and the halfway house? What had occurred, of course, is that they had simply fit in again with their substance-abusing peer groups as soon as they returned home.\n\nThe crucial issue at every point in Isaac's story is how easily he formed relationships, with whom he did so, and in what direction the friends he made pulled him. Isaac's story is about the centrality of friendship formation and dealing with others in addiction and recovery. Learning social skills like those in the previous chapter in order to meet diverse and healthy individuals is an essential element of an addiction-free life.\n\n_Intimacy, love, and addiction_\n\nLove is one of those large goals that an awful lot of people pursue\u2014and that an awful lot attain in one or more forms (including spouses, friends, and children). But it's no sure thing, and\u2014depending on how far you are starting behind in your life\u2014it may take you some time to acquire and assemble these resources. They then become the building blocks outlined in this chapter and the rest of _Recover!_ for forming truly satisfying relationships. This is because love\u2014as Archie Brodsky and I indicated in _Love and Addiction_ \u2014is built on the exact opposite foundation from an addiction. Addiction stems from the absence of connections to life and substitutes for such connections. Love flourishes best when you have the _most_ points of contact with the world, including other positive relationships. Addictive love relationships are most likely when you are desperately seeking emotional sustenance from other people while you haven't yet created the necessary basis for sharing such intense feelings by having a solid life in place.\n\nPractical Skills: Education, Work, Financial\n\n_Education and work_\n\nDon't assume that you have ruined the connections you have to every part of your life and every person in it because of your addiction. You may have hurt them but, often, many can still be rescued. I have offered several case studies of people who are successful at their jobs despite their addiction (of course, other areas of their lives suffer). So don't reject\u2014in anticipation of being rejected\u2014any parts of your life that have survived your addiction even as you work to improve them. For example, if you haven't been fired, don't quit your job out of guilt.\n\nHowever, for many, keeping a job or pursuing an education has fallen by the wayside. If you're in that category, you may be wondering where to start\u2014and completing your Goals Worksheet leaves you feeling lost. How do you set realistic goals for yourself when you feel so far behind or so far out of your element that you can't even be sure what your real options are? Do you know how to look for and apply for a job, what courses to take at school, how you will pay for these courses, or what degree suits you best?\n\n* * *\n\n**CASE:** Thomas had been smoking pot regularly for so long that all he could do was sell the drug to others as a way of getting by. He had once been a quite capable computer programmer. But he was long past the point of feeling up-to-date with writing code, the Internet, and information technology skills. Whenever he considered quitting smoking grass, he was confronted with the enormity of the barriers separating him from the real work world. How could he _begin_ to reengage?\n\n* * *\n\nOf course, Thomas had once been able to obtain jobs in information technology. As always, getting started\u2014or restarted\u2014is intimidating. You may imagine the barriers as higher than they are. In any case, there is no alternative other than to begin. Thomas began taking online courses, which are readily available and accessible. As he settled into doing course exercises, he saw that his old skills were still relevant; he even compared favorably with others taking the courses, according to the published grade curves. In a short time, he was applying for jobs (albeit having to fashion crafty explanations for the gaps in his resume\u2014fortunately, he had never been arrested). The process wasn't dramatic, and Thomas wasn't where he would have been if he hadn't devoted several years to his drug of choice. But, then, life is a process, always beginning with now.\n\nFor specific practical suggestions for continuing or resuming your education, getting a better job, or starting a business, see Chapter 10, \"Triage.\"\n\n_Financial_\n\nMoney management can be enormously stressful, especially for those in the throes of an addiction who have allowed bills to pile up or who are avoiding calls from creditors or the IRS. Addictions are expensive habits that lead you to spend money you don't have\u2014especially if your addiction is gambling or shopping. Of course, the cost of liquor or cigarettes or street drugs also adds up, as does that for virtually every addiction. You may know about waking up in a panic over money in the middle of the night.\n\nBut no matter how painful it is to contemplate, this is an area you simply must get under control, because it will weigh you down until you do. Dealing with finances can be an unappetizing task if you are in debt or behind on your bills. As anxious as dealing with your finances makes you, however, worrying about your money when you don't have a handle on it is far worse. It is imperative that you know where your ground zero is. In this as in other areas of your life, you are able to address and fix only what you are able to see clearly.\n\nSo let's tackle finances and restore your peace of mind. Whatever the mess you have on your hands involves, you can pull yourself out of it and keep yourself out. Schedule time on your calendar to devote to this. When that time comes, shut off your phone, iPad, and so on, and then break this task down into a series of manageable mini-goals such as those outlined in Chapter 10, \"Triage.\" It's possible that you will have to explore bankruptcy. That's a big topic for which this book is not the right source of advice. But be aware of it as a possibility.\n\nPersonal Skills: Your Health and Well-Being\n\n_Self-care_\n\nSince addiction can cause you to disregard so many aspects of your life, your ability to care for yourself diligently may also have suffered. Personal hygiene is not just something you do to make yourself presentable to the world; it is something you do for you. Showering and brushing your teeth regularly, sleeping and eating well, getting dressed every morning, exercising, visiting the doctor, washing your clothes\u2014all are absolutely important. First, they foster a sense of self-respect and energy and help you develop wholesome habits. They engage you in acts of self-nurturance, which you deserve. They signal that you are ready to participate in your own life. If you have slacked off on your self-care practices, ask yourself how, and begin bringing these good habits back into your life.\n\n_Leisure pursuits_\n\nSince addiction takes up so much time and energy, you may have some time on your hands. Boredom, restlessness, aimlessness, and obsessive, intrusive thoughts can be powerful instigators of relapse, and not knowing what to do with yourself can be emotionally and morally excruciating. Do you remember a time in your life\u2014most likely in your childhood\u2014when you could lose yourself in play and creativity? Perhaps you\u2014alone or with friends\u2014were able to invent an elaborate pretend world, characters, and scenarios that kept you engrossed all day long! Recapturing this part of your life\u2014your creativity and sense of pure, free fun\u2014is as important to your life as it is for you to start bringing order to the chaos. When you have such a sense of joy, everything\u2014reading, walking and hiking, seeing people, being alone\u2014can open up to you. Pull out your Goals Worksheet and fill it in with activities that will spark your interests, sense of play, and feelings of accomplishment. You might include art, volunteering, spending time with your children or grandchildren, cooking, exercising, learning a new skill, taking a class, and on and on.\n\n_Spiritual or humanitarian_\n\nIf you practice a particular belief system or religion, or if you honor your place in the grand scheme of things as a member of the human race, consider giving your spiritual or belief system or humanitarian impulses a bigger place in your life. This investment will contribute greatly to your sense of purpose and community, infusing your life and actions with meaning. You may seek out a congregation that feels like a good fit for you, join a meditation group, or volunteer for a cause that you support, with the intention of building community around this important area of your life. Doing so\u2014especially if you lack family or community support\u2014will broaden your scope and give you a comforting sense of your place in the world.\n\n_Mental health_\n\nAs you begin to drill down into the areas of your life that need attention, you may become aware of underlying mental health issues. Perhaps you have already been diagnosed as having\u2014or believe that you may have\u2014bipolar disorder, anxiety, depression, post-traumatic stress disorder, or some other type of psychiatric condition or disorder. Not to minimize these disorders, it is safe to say that we all have some experience of them and other emotional conditions and trauma. As I described in Chapter 2 on addiction and recovery, emotional problems are both causes of and responses to addiction, while at the same time they are important issues for recovery. The good news is that many of the techniques and practices you are learning in The PERFECT Program are equally useful for combating these emotional problems or disorders. So, feelings that you've been masking with addiction may emerge in full force, but you are also developing positive and powerful ways of coping with them.\n\nHowever, just as with the case of seeking bankruptcy relief, there are matters that go beyond the scope of _Recover!_ 's aims. If you need help with serious emotional problems that haunt your ability not only to escape addiction, but also to live fruitfully, you should seek professional help. My approach is obviously consistent with cognitive-behavioral therapy (CBT) and pragmatically oriented counseling, and so I favor that type of treatment. In America today, it is hard to find such help in psychiatry, which is dominated by pharmaceutical treatments. _Recover!_ and The PERFECT Program don't generally go well with drug treatments, although they don't rule them out or disparage them\u2014as long as the medications are combined with counseling. Of course, the quality of the counseling remains a critical issue, and receiving good\u2014or even safe\u2014treatment is by no means guaranteed. In HMOs and other institutional care settings, the psychiatrist prescribes drugs while a psychologist or social worker provides CBT or supportive therapy. Sometimes\u2014too often\u2014supportive therapy simply permits venting that enables people's complaining and blaming others. Psychiatrists, meanwhile, are becoming less able\u2014both by training and due to economic constraints\u2014to practice any kind of psychotherapy.\n\nWhere therapy is provided\u2014whether by a psychologist, social worker, or other trained counselor or, occasionally, a psychiatrist\u2014the favored type is now CBT on the grounds that it addresses your problems directly and has been shown to be effective. Psychoanalytically oriented (\"talk\") therapy, on the other hand, is increasingly difficult to find or be reimbursed for. Feel free to explain what your perspective is and what you seek in exploring and entering any type of mental health relationship. And there is no way for you to eliminate your own critical decision making in deciding whether your therapy is being helpful.\n\nReframing Failure\n\nOnce you start taking deliberate steps to make things happen in your life and develop healthier habits of mind and action, you will certainly find yourself missing the mark on some of the goals you have set for yourself. In times like this, you might recall Woody Allen's famous dictum: \"Ninety percent of life is just showing up.\" To put this in the context of The PERFECT Program: \"showing up\" means that your conscious presence and awareness _is_ your success. Your engaged participation is all that's required, even if the results don't always measure up. You are now using the skills you've learned in the task of making broad and permanent changes in your life. But the key changes cannot be measured by how flawlessly you succeed at the things you set out to do. What's important is that you _made the decision_ to do them and _pursued your goals mindfully_ \u2014that is, intentionally, investing yourself in the process and keeping track of the results. What you're now doing is living your life.\n\nIncorporating the essential elements of your true self into your life is an exercise of your free will, which may have wilted from neglect. You are training your true self to take over for your addicted self, which will, ultimately, make addiction irrelevant. Developing any weak muscle can be painful and make you hyper-aware of the strength of your addiction. Imagine, for example, trying to write clearly and automatically with your non-dominant, or \"wrong,\" hand. The resulting awkwardness and sloppiness shout out to you that you could so easily switch back and just get it over with, resorting to the muscles (or habits) you relied on before. Embarking on your recovery process will bring similar moments of awkwardness and distress. You will feel tempted to resume familiar but destructive habits when you fail at your new efforts. Whether you do or you don't, you may judge yourself harshly. This self-punishment may feel correct, but ultimately it blocks your forward motion.\n\nFor example, say that one of your modest changes was to bring a new plant into your house, to give your environment a sense of vibrancy. But then your plant died because you didn't water or fertilize it properly. Your reaction might be brutal self-recrimination: \"I am such a loser; I can't even keep a plant alive. What's wrong with me?!\" But it's just going to happen sometimes that your best intentions won't pan out. While recognizing this, you needn't allow yourself to accept failure. Plan for failure and learn to reframe it with compassion: _This is not failure; it's information._ You'll do better the next time. Either that, or you're just not a plant person.\n\nWhen you reframe failure as information (or feedback), you maintain your sense of active engagement, control, and forward movement. If you walk into the gym for the first time and try to match the resistance the last person set on a machine, you probably will be unable to lift it. This could be embarrassing if anyone were looking (although no one is), but in any case it's not the end of the world. You don't leave the gym or give up or throw a tantrum (now _that_ people would notice). You simply get real about your abilities, adjust the weights accordingly, rest a bit, and then begin to become stronger gradually and sensibly. Similarly, if you make an attempt at something life-affirming and find that you are unable to see it through, take the opportunity to gather information about your blind spots and your unreal expectations. But always remain mindful of the purpose behind your attempt.\n\n**EXERCISE:** In your Personal Journal, think of a recent failure and write about it: What were you trying to accomplish? What went wrong? What do you think this says about you? Now, try to look at the scenario more objectively and compassionately: Were you trying to do something that requires habits not yet in your repertoire? Were you attempting to take on more responsibility than you could reasonably handle or fit into your schedule? Did you start at a place that turned out to be over your depth? Were there steps you missed? Situations you avoided? If so, why? If you were allowed a do-over, would you try this again? If not, why not? And if so, what would you do differently?\n\nDetour: Relapse!\n\nSpeaking of reframing failure, the subject of relapse is surely on your mind. It is not inevitable, but it happens. You can prepare for it both by anticipating and avoiding it and by developing techniques for righting your course after it happens. Relapse is a return to addictive behavior\u2014a backslide\u2014which occurs after a period of progress. The impact of relapse can be very demoralizing, making you feel as if you were back at square one, or a hopeless case. What causes it? How does it happen and why?\n\nAlan Marlatt began his research on relapse prevention by investigating what caused smokers, alcoholics, and heroin addicts to relapse. The standard interpretations were that (1) their withdrawal symptoms simply overcame them, or (2) in a conditioned response, people were exposed to stimuli associated with their former use, and this association created irresistible cravings to use. But when Marlatt actually questioned addicts, he found that they were unlikely to relapse when experiencing intense physical urges to use, as occur during the immediate withdrawal period. Rather, relapses were responses to negative emotions and conflicts that the study subjects previously may have used their addiction to address and that exceeded their abilities to manage without their addiction. Or else they relapsed when they entered a setting where they had used or were with people they had used with before.\n\nBased on these findings, Marlatt developed relapse prevention techniques to supplement environmental planning\u2014that is, staying away from \"bad\" places, people, and things. Relapse prevention focuses on people's coping mechanisms for dealing with stress (or even pleasure) in general, and specifically for addressing cravings to use that appear either randomly or in challenging emotional situations. Himself a longtime practitioner of meditation (to which he credited his remission from hypertension), Marlatt was moved to see whether and how meditation could be part of the cornucopia of techniques for combating relapse, including cravings. The results led in the direction we have picked up from Marlatt and other researchers and adapted and expanded for The PERFECT Program. Marlatt's work has always had a sound scientific basis. The value added through The PERFECT Program is to develop and tailor these techniques in ways that are personally and clinically useful, since Alan himself never wrote any popular guides for people to follow.\n\nSimply put, a relapse is triggered by imbalance. The situation at hand or the triggering event overwhelms your ability to cope while you are developing new skills, resources, and perspectives. Recalling the \"dominant hand\" analogy, in which your dominant hand represents your ingrained habits, imagine that you are diligently practicing handling all your daily tasks with your weaker hand. Despite the awkwardness, you are becoming more adept all the time. But one day, without warning, someone pitches a ball directly at your head. You instinctively reach out to grab the ball with your dominant hand.* That is just about how relapse works, and there are several scenarios and life events that might trigger it:\n\n\u2022 Stressful situations\n\n\u2022 Major or milestone events\n\n\u2022 Strong emotions, including anger and even joy\n\n\u2022 Unexpectedly powerful triggers that seem to arise out of the blue\n\n\u2022 Loneliness, boredom, anxiety, restlessness, hopelessness, or any other painful or difficult feelings\n\n\u2022 Being around people who undermine your goals\n\n\u2022 Romanticized memories of the benefits of using, while forgetting or downplaying the consequences\n\n\u2022 Unaddressed mental health concerns, such as depression, that require attention.\n\nCan you think of other relapse triggers?\n\n**EXERCISE:** In your PERFECT Journal, in the \"Triggers\" section (page 155), write down any situations that might trigger a relapse\u2014or that have in the past. Can you identify exactly how your skills, resources, and perspective were outmatched by the situation? What action could you have taken to prevent the relapse? Or what could you have done\/do to get yourself back on track?\n\n_Reframing relapse_\n\nAs in our discussion of failure, a relapse can provide you with a wealth of information you can use to continue down your path to wellness. If you experience a relapse, use it as an opportunity to increase your self-knowledge. Make note of everything that led up to it: your life circumstances, the triggers you experienced, the self-deception that you now recognize. You should ask yourself how you can avoid or improve the circumstances leading to relapse, or whether you ignored feelings welling up in you that signaled where you were heading. Did your decision to indulge make you feel as if you were doing something good for yourself, like loosening a noose around your neck? What benefit, exactly, were you seeking? What in your life represents the noose? Are there parts of your life that you have been ignoring while seeking to improve other areas? If so, what changes can you make in your situation that will relieve some of the burden you feel?\n\nYou are now engaged in truth seeking about your addiction\u2014where, when, and why it arises. Do your best to discover the truth. This is actually step one of mindfulness practice, recognizing and responding to cravings and other urges to resort to addictive behavior. If you have not yet been able to incorporate your mindfulness practice into your daily schedule, now is the time to make it a priority. Turn back to Chapter 4 to review your meditation and other techniques. This is a skill that will serve you enormously in relapse prevention, because it allows you to recognize and to ride out\u2014or to recuperate from\u2014uncomfortable feelings, like cravings, with the knowledge that they will pass. The practice of mindfulness will also expand your horizons, allowing you to identify the range of your options. Where before you might not have realized you had any choices, you now know there are a host of responses to insert between your urges and your addiction. Finally, continuing to exercise mindfulness in relapse prevention develops your ability to turn your attention where you choose to, away from triggers.\n\nThe central concept to keep in mind where relapse is concerned is that it is not failure. This means that, if you relapse, you aren't \"starting over.\" In fact, \"starting over\" has no real meaning. Twelve-step programs make a virtue of \"time.\" Members count their days\u2014even hours and minutes\u2014of \"sobriety.\" They require people to start their count over if they have a relapse. So, if you have been \"sober\" for five years and then have a beer one day, you're back at day one. I would say this was silly if it weren't so destructive. Please recall my discussion of \"hitting bottom\" in Chapter 4. Go beyond this superstitious, irrational way of thinking, one that has created such ineffective approaches to recovery.\n\n_Getting back on track_\n\nBelieving that you have completely and irreparably botched recovery is an example of the all-or-nothing perfectionist thinking that underlies addiction. It is clearly lacking in self-compassion. You always, always have the option to gather yourself and continue on your path. This is as open to you as\u2014in fact, it is more common than\u2014the AA-endorsed view that you have to throw in the towel. Even considering the latter as a possibility is wrong. At this point, you have the understanding, skills, resources, and perspective to make a conscious decision to continue on your path with mindfulness and self-regard. Remember Renee from Chapter 3, who, after six years' abstinence from alcohol, went into a bar, drank, got intoxicated, drove drunk, and lost her license, her job, and her husband? All of that was unnecessary. Even so, she quickly righted herself and didn't return to a life of drinking. By that point, recovery remained for her\u2014despite her bad decisions and choices\u2014the most relevant, easily accessed option in life.\n\nExercise: Relapse Moments of Truth\n\nAt times, you may be tempted to return to your addiction, when you have cravings\u2014even compulsions\u2014to use, say, when you are in an environment where you previously used, when you are vulnerable emotionally, when life has thrown you a number of challenges and defeats, or even sometimes triumphs and successes! How you deal with these moments determines your ability to navigate your recovery. Answer these questions in your PERFECT Journal:\n\n1. Describe three situations in which you are most likely to use.\n\n2. Visualize each situation and describe your feelings in it.\n\n3. Describe a strategy for each that you can rely on instead of using.\n\n4. Who would you call if you were thinking about using but wanted to resist? Why?\n\n5. Who would you call if you had been using but wanted to avoid further damage? Why?\n\nShould you discuss these roles with those individuals right away?\n\nI have emphasized the idea that every moment is an opportunity to make a good decision. In other words, just because you have taken a single step in the direction of a steep cliff, it doesn't mean that you are now required to take a running leap off the edge. This image opposes the 12-step or hijacked-brain notion that your misstep has propelled you off the cliff and your relapse is, like gravity, an irresistible force of nature. Relapsing after using is not like gravity. Your mindfulness skills will help you identify your moments of grace and give you the presence of mind to act on them at any point after the moment you veer off course so as to realign yourself with your values.\n\n* * *\n\n**CASE:** Martha, who has been battling an addiction to prescription painkillers, has recently decided to go cold turkey. She's had some difficult moments, but has been able to stay on track by keeping her focus on creating order out of chaos. That has brought her a great sense of fulfillment and peace of mind. One day, as she was in the middle of cleaning a hallway closet that she had been using to stow all sorts of unusable junk, she was overcome by a seemingly random urge to stop what she was doing and visit a friend of hers who kept a well-stocked pharmacy in her pocketbook. Almost as soon as the thought crossed her mind, Martha jumped up and called her friend (\"I'm so sick of sorting all this junk! I've been good for a month already!\"), who was more than happy to accommodate her. Martha threw on a pair of jeans, drove to her friend's house, plunked herself down on the couch, and swallowed the pills offered to her with a freshly opened beer. (Remember that, besides this being a relapse, it is also always dangerous to combine painkillers with other drugs or alcohol.) The two of them spent the night watching reality shows and giggling senselessly, and everything seemed to fall back into place.\n\nThe next morning, Martha woke up feeling terrible\u2014and the self-recrimination was worse than the hangover.\n\n* * *\n\nWhat happened? At what point did Martha lose her perspective? It was as if a tornado picked her up out of the blue, right out of the messy closet, and plunked her down on her friend's couch with a couple of pills in one hand and a beer in the other. And what now? How does she handle the cravings and old habits?\n\nWhat happened? Martha's \"dominant hand\" simply asserted itself and began to function on auto-pilot, as it will do. Habits, well-established patterns of thought and behavior, can take over in moments of vulnerability\u2014this cannot be avoided all the time. Remember that as you progress, these moments will become fewer and farther between. But you may encounter them quite often at the outset. The key is not to pretend that you can\u2014or should\u2014evade them every time, but to recognize that you're off course and take steps to correct.\n\nConsider how many opportunities Martha has to avoid full-blown relapse and to realign her actions with her values. Perhaps, at this early stage in her journey, she wasn't able to correct course as soon as she would have liked to. Blindsided by an urge whose momentum she couldn't fight, she ended up on a trajectory that led her to a familiar, painful place. She may remember that this overwhelming urge hit her when she was sorting through some items that brought back painful memories or reminded her of a time when she was enjoying the situations that led to her addiction. Or, perhaps, she was overcome by the tedium of the task, or she was berating herself for letting things get so out of control. Or, perhaps, she was even thinking how great she was doing in her new life!\n\nFIGURE 8.1\n\nNavigating Relapse\n\nAt any time, before or after you veer off your course, you can tack back to your true path by using the skills, practices, knowledge, and exercises you have learned through The PERFECT Program.\n\nNo matter how far off you go, there is always a way back.\n\n_The PERFECT Program tacks back to your true course._\n\nAt the moment she wakes up, overcome with regret, she has a choice: to give up on herself or to forgive herself, take an honest look at what happened, and make some decisions. There is always a window of opportunity, allowing you to correct course, no matter how far down the wrong path you have gone, as Figure 8.1 shows.\n\nRemember these things about relapse:\n\n\u2022 Relapse is not failure; it's information.\n\n\u2022 Relapse does not mean starting over from scratch.\n\n\u2022 Relapse does not mean that you will never recover.\n\n\u2022 Relapse can be reversed at any stage\u2014you do not have to pursue it to \"rock bottom.\"\n\n_You have the skills to realign yourself and continue with your recovery._\n\n_Avoiding relapse for love, eating, and other non-abstinent addictions_\n\nSome activities that some people find addictive, as I discussed in Chapter 3, can never be completely avoided. How can addicts avoid relapse when, in a sense, they have never stopped doing the activity? Think of eating. You will continue to eat on a weight-loss program. You may carefully avoid some foods, maintain your weight, and support weight loss with exercise. But you will not always follow your diet perfectly; no one can, and to attempt perfection\u2014as always\u2014can cause problems, in this case the sister addictions of obesity (i.e., bulimia and anorexia).\n\nAnd, so, what happens when you as a dieter\u2014say, one who has lost a considerable amount of weight\u2014eats pasta or bread, or a cookie or some other sweet, that you have been rigorously avoiding? Indeed, _how_ you handle these events is a mark of the _success_ of your recovery. Say you have some pie or pasta. You will want to have a reasonable portion, which you can define differently according to the situation or where you feel you are in your recovery. Being able to eat these foods mindfully, both enjoyably and carefully, provides you with sufficient rewards that you no longer crave them as \"forbidden fruits.\"\n\nAt the same time, you\u2014while eating the food\u2014will be mindful that this is the kind of food that has hurt you in the past and that you cannot start indulging in the way you used to. You might surface an image of your former self eating this dish indiscriminately\u2014even imagining yourself at your former weight. And it is summoning such images, with the commitment not to return to the misery, unhealthiness, and fear they inspire, that is the best guarantee that you will limit potential eating binges. Of course, to regain all of a considerable amount of lost weight is the result of more than one\u2014more than several\u2014such episodes. To return to your former weight would require you to altogether abandon your new lifestyle and way of eating, and the rewards your fitness and appearance have given you, in favor of those fleeting rewards provided by sweets, carbohydrates, and other comfort foods and snacks. You just don't relapse in an instant; doing so means that you have reversed the entire recovery journey you have been on for months and years.\n\nBalance\n\nGetting started on your life's journey with a sense of perspective\u2014informed by mindfulness, self-awareness, and compassion; your values, mission, goals, and your skills and resources\u2014is a monumental step. Knowing who you are, where you want to go, what you want to accomplish, how you're going to accomplish it, and how you will stay focused on the path you have created for yourself, while skillfully navigating all the bumps in the road\u2014like failure and relapse\u2014is a lifelong process. It's essentially what life is all about. It's the very foundation of wisdom. To keep moving forward on your journey requires an ability to keep your attention constantly on your path. But it also requires your ability to _return_ your attention to your path when you have lost track. Your mindfulness practice will strengthen your ability to return your focus to where it belongs, and your self-acceptance will give you the perspective and balance that allow you to do so.\n\nMoving Forward\n\nLaunching your recovery and leaving addiction behind is not a bed of roses\u2014you will encounter troubling moments that expose your vulnerabilities. But the odds favor your moving forward, and this chapter has helped you find the frame of mind\u2014along with the techniques\u2014to make sure this will happen. Balance is key. But maintaining balance requires strength and movement. These will develop as you continue on your path, learning to keep your perspective when things go wrong. You are on your way! Fully experiencing the non-addictive rewards you are finding will make clear your preference for this new life. Your decision to embark on this path is something to acknowledge and focus on; it is sufficiently important that the next chapter is devoted to celebrating your accomplishments, as well as all of the rediscovered facets of your life that bring you satisfaction, meaning, and joy.\n\n*All analogies are inexact, and the \"handedness\" example is so because, unlike addiction, handedness, in most cases, is largely determined in the brain and is inborn. This example has the added disadvantage that there is a history of bias against left-handers that has sometimes taken the form of forcing them to use their right hand (I write with my left hand). The ball-catching example is the better example of learned handedness than writing, since most kids learn to catch best with the hand on which they wear their glove\u2014the opposite hand from the one with which they throw a ball, not because that hand is especially adept at catching.\n\nCHAPTER 9\n\n_Celebrate_\n\nJoy\u2014Honoring your accomplishments while living mindfully and meaningfully\n\n* * *\n\n**CHAPTER GOALS**\n\n\u2022 To learn to replace the superficial rewards of addiction with genuine fulfillment\n\n\u2022 To track your successes\n\n\u2022 To honor your accomplishments\n\n\u2022 To practice what you value\n\n\u2022 To create traditions and reasons to celebrate\n\n\u2022 To discover joy\n\n**Purpose:** If the consequences of addiction weren't so destructive, you wouldn't be on this journey to wellness; but before you ever experienced the consequences, you experienced the rewards of addiction. Yes, rewards. Imagine that every time you took a drink you skipped right over the part where you felt relief, relaxation, and inebriation and were, instead, socked with an instant hangover. You simply wouldn't do it. Through addiction, we learn to expect instant gratification in the form of oblivion and euphoria, among other benefits. These are powerful, but fleeting, experiences. When enmeshed in addiction, however, we don't recognize\u2014let alone experience and revel in\u2014the many rewards we are blessed with daily, just by living mindfully and meaningfully. This recognition is a crucial life skill to develop, because the reason you are making this journey is to move _from_ addiction and _into_ fulfillment. And reaping the rewards of your efforts is what it's all about! Learning to replace the superficial, indeed infantile, rewards of addiction with the deep and abiding joys of freedom is the linchpin of your recovery. Doing so will reinforce your sense of momentum and your faith in your abilities, allow you to see how far you have come, and connect you with the joy and satisfaction of living according to your values.\n\n* * *\n\nHow Far You Have Come\n\nMany of us gloss over our successes and milestones, perhaps believing that it would be unseemly to make a big deal about them or that it would be premature to go counting our chickens before they're hatched. We may feel we don't deserve to recognize achievements that should have been a matter of course all along (\"Why should I celebrate cleaning out the fridge\u2014normal people have clean refrigerators and don't throw a party over it\") and that we shouldn't start patting ourselves on the back until we can plant our personal flag on the moon. If this describes you (as it does, to some extent, all of us), perhaps it's time to balance your perspective. Making note of your achievements and milestones is not just a trivial self-indulgence. It is a process that, first, ensures that you maintain your non-addictive path forward. Second, knowing how to recognize and celebrate your often hard-won successes is the essence of a joyful life.\n\nIn terms of The PERFECT Program, you certainly have come a long way! Let's take a look back at where you have been on this journey and what you have accomplished so far, before you embark on your home stretch. You have, among other things:\n\n\u2022 Achieved a realistic understanding of the nature of addiction and recovery\n\n\u2022 Gained clarity on how addiction has manifested in your life\n\n\u2022 Developed basic mindfulness skills that will support your recovery\n\n\u2022 Learned to treat yourself\u2014and others\u2014with compassion\n\n\u2022 Rediscovered your priorities: what brings meaning, value, and purpose to your life\n\n\u2022 Implemented anti-addiction techniques in your daily life\n\n\u2022 Started honing the life skills you need to navigate effectively in the world\n\n\u2022 Created a vision for your future\n\n\u2022 Set achievable goals in many different areas of your life\n\n\u2022 Started taking action to achieve your goals\n\nIf you have not had the opportunity to absorb your accomplishments so far, please take a moment now to reflect on this list. And, if you feel you're not where you should be\u2014haven't touched every base\u2014I hope you will reassess your judgment with self-compassion. Remember that while the nature of a book requires that it progress in some logical order, your path out of addiction is uniquely your own. You may have to linger longer than you'd like in different phases of your recovery. It's not a race. And remember, as I mentioned in the last two chapters, you can't avoid obstacles and setbacks, but you can navigate them in a way that's true to yourself and your vision.\n\n**PERFECT JOURNAL:** Look back over your journey so far and make note of all the things you are proud of and all the steps you have taken, including meaningful shifts in perspective. Forget anything you think should mitigate or negate your sense of accomplishment (say you were abstinent for a month, but had a setback); just focus on every positive step.\n\nCelebrating your successes means taking every opportunity you can to absorb and reinforce the sense of fulfillment you are striving for. Just as there is no sense in waiting to make a positive decision, there's no reason to wait for some arbitrary milestone or ultimate fantasy to materialize before you can begin taking joy and satisfaction from your journey. That doesn't mean you have to take out an announcement in the local paper every time you complete a task. It simply means recognizing and enjoying what you have accomplished\u2014and of course, some accomplishments will warrant a much grander display. Making a habit of honoring yourself and your values\u2014like everything else you have been doing\u2014takes practice, since it may not be your natural impulse.\n\nTracking Your Progress\n\nOne of the most practical ways you can begin creating this new habit of joyous self-appreciation is by tracking your progress daily. I encouraged you to begin this practice in the last chapter because it is a powerful way of keeping yourself focused. At the same time, marking your progress also allows you to see, very concretely, how far you have come and provides the basis for experiencing a sense of pride in your advances. Tracking is an essential practice in that it offers a balanced and objective view of where you are. We often don't recognize how much we are changing; instead, we take our current assets and grace as simply givens, or else miss them entirely. When you look at your chart, you can't deny that you have actually done positive things\u2014it's right there in black and white!\n\nThere are many ways to track your progress. You might keep your goals chart next to your bed or on your desk, where you will see it every day. There are computer programs that allow you to do this; you can set such a program to open as soon as you turn on your computer. Many people find the very act of tracking enjoyable. You may get a lot of satisfaction from checking in on a daily basis and entering your facts and figures. Since we are all wired differently, the process might, on the other hand, seem painstaking to you. Don't worry. There are as many ways of tracking as there are people, and you can find the one that jibes best with your personality.\n\nYou want to make sure that whatever method you choose is one you will actually use. If you enjoy keeping lists and charts, you may find that a free website like sparkpeople.com is right up your alley. It offers incentives to log on every day and track your goals\u2014whether those are weight-, wellness-, or fitness-related\u2014using an array of online tracking tools, including your own personal blog. But if you would feel overwhelmed by such an energetic and relentless tracking system, you might consider using Jerry Seinfeld's famous \"Don't Break the Chain\"* approach, which simply requires you to put an _X_ on every day that you meet your daily goal, with the intention, eventually, of keeping the chain of _X_ s intact. You will be able to see in a quick glance just how many days you stayed on track and take satisfaction in seeing your chain lengthen.\n\nYou may also find that a dedicated notebook or calendar works well for you. For example, suppose you want to track your addiction, with the intention of achieving complete abstinence. You might create a simple chart for yourself that you can fill in daily, with headings that are relevant to your goals. For example, see Table 9.1.\n\nYou can create your own charts based on whatever addiction-specific goals you are aiming for. Even if you are not meeting your goals on the schedule you have set for yourself, remember to acknowledge your efforts\u2014which are valuable in themselves\u2014and to focus on your forward momentum. And, as with anything else I have discussed, take account of what works best for you. This isn't an abstract program invented who knows where by who knows whom\u2014it's your life.\n\nTABLE 9.1: **Addiction Use Goals**\n\nHonoring Your Successes\n\nHow, exactly, do you honor your successes? What does that mean and what do you do? Say you have made some progress. What do you do about that? I'm not going to present a self-congratulations chart. But what you do and think is measured against the criterion that it enriches your life\u2014including the idea of \"joy.\" Your journey is not about putting your head down and forging on like a martyr until you arrive at a certain destination, upon which you can finally put your feet up and relax. There is no such place. The sun always comes up; you always have challenges to meet, milestones to celebrate, and places to go. Fulfillment is not the end of the road. It is the road.\n\nSay, for instance, that one of your goals is to lose a significant amount of weight (something I have done). You embark on a plan that really works well for you: You cut out desserts and begin a walking or gym routine. You feel much more energetic and alert because of your lifestyle change. But, when you step on your scale after the first month, you find that you have lost only six pounds, when you were expecting to have lost ten or more. In that one instant, all the self-esteem, enthusiasm, renewed clarity of mind, and joy you experienced from your daily walks deflate. You are left disappointed, maybe even hopeless. Your feeling of success evaporates, as if none of the benefits you enjoyed meant anything compared to an arbitrary figure on the scale.\n\nThis scenario is an example of the baffling ability we have to know and not know something at the same time. Surely, we can all see plainly how irrational it is to disregard our tangible experience of well-being in the face of not measuring up to a meaningless number! It's possible that this experience is the result of conflicting values. You have tagged the number on the scale with some emotional meaning so that you feel that nothing matters until you reach your goal weight, when everything in your life will fall into place. _That's_ when you'll really be able to feel proud of yourself and to participate in the world like a \"normal person.\"\n\nWhat could inform a misguided belief like that? It may well be true that achieving a significant weight loss\u2014or meeting any particular goal\u2014will bring enormous benefits. However, it is important to delve into your belief that you don't deserve peace of mind until you achieve that goal. The practical, self-change reason for exploring this issue is that if your journey toward your goal is fraught with self-recrimination you are less likely to retain your focus and to make that journey (as I showed in Chapter 5). Put simply, people don't like bad thoughts, even when they are used to motivate good behaviors. The further, PERFECT Program reason for reassessing your disappointment and gloom is simply that life comes with setbacks and disillusionments. But you are alive here and now, and the moment is precious.\n\nWhat could be the underlying belief that causes you, or me, to tie our sense of accomplishment to an abstract number on the scale rather than to real, important benefits we have already experienced? It could be that\u2014as I discussed in connection with self-acceptance\u2014you feel you don't deserve to feel good about yourself unless you are a certain weight. The reason for your fixation with the scale number is that you aren't following your true values and priorities. There are two deductions from this example if it applies to you: first, to recognize that you are not measuring yourself by or following your own values and priorities; second, to explore whatever underlies your irrational perspective. This mindfulness exercise adds to the information you need to realign yourself with what's most important to you.\n\n**EXERCISE:** When you consider your efforts to meet a goal or make a significant lifestyle change, can you remember a time when you were stymied or derailed by a setback? Why was that event so catastrophic? What were the underlying feelings that caused your extreme reaction? Do they seem reasonable in the light of day? What more genuine values of yours do they contradict?\n\n_Perfectionism_\n\nPeople\u2014all of us\u2014create perfectionistic goals that prevent us from really being who we can be and succeeding as best we can. Maybe it has even kept you from love, when you rejected a \"non-perfect\" relationship that was nonetheless loving and ultimately could have been highly fulfilling. At the same time, please keep in mind, reacting to an event like a possible \"lost love\" as a tragedy of unbearable enormity is a perfectionist response to the sin of perfectionism! If you have overcome the emotional pain and withdrawal of losing a love, don't add this additional, perpetual longing and grief reaction. (These reactions are not uncommon, it seems. I once was stuck at a workshop where each person was obligated to go up to everyone in the group and whisper what they wished they had told someone, but didn't. Every single person whispered in my ear: \"I love you.\") Now that it's done, carry on with your choice\u2014there were, after all, reasons that caused you to choose as you did\u2014and look for the love still available to you.\n\n* * *\n\n**CASE:** Willow ran an important nonprofit, inner-city agency. It had worthwhile goals, incredible challenges, and was underfunded and understaffed. Willow had never trained for a management position\u2014she had started out as a volunteer. But soon her conscientiousness and commitment impressed everybody involved with the group\u2014and she ended up heading the agency.\n\nWillow was often depressed when she didn't accomplish all that she had hoped to. Nor were her tremendous efforts always appreciated in the welter of the city's and the agency's affairs. But everyone agreed that her impact was tremendously positive\u2014that the agency had never functioned as well and done so much.\n\nNonetheless, Willow was seriously considering leaving her job\u2014it was simply too draining. One day, as she left the public school where her office was housed, one of the kids who participated in Willow's program saw her leaving. He shyly came up to her, and said, \"Miss ____. I have never been this happy in my life.\"\n\n* * *\n\nWillow realized instantly why she put up with the trials and tribulations of her work\u2014that in many ways she was a rare and fortunate person.\n\n_Experiencing here-and-now rewards_\n\nAs you go through your day, pursuing your goals, make it your plan to stop and recognize where you are and what you're doing that is different from what you would be doing were you still immersed in your addiction. For example, suppose you were accustomed to waking up with a painful hangover, piecing together details of the night before, but are now waking up refreshed. Take a moment before you get up to revel in the cozy feeling of being well rested and clear-minded in your bed, with nothing to regret. You may have farther to go. This period of sobriety may not turn out to be permanent. But allow yourself to realize that this is, indeed, a big deal, and how fantastic it feels. Meanwhile, don't lose sight of the \"practical, self-change\" reason for practicing these techniques while celebrating your good feelings in the moment. As we saw in Chapter 5, such self-rewarding makes it _much more likely_ that you will progress, while self-criticism or lack of self-appreciation does the reverse.\n\nIf what you're doing during your day feels tedious\u2014say you are filling out paperwork\u2014acknowledge that you're doing something that is necessary, perhaps even important, in service of your larger goals. And when you're done, don't just move on to the next thing, as if nothing had happened. Reflect on this small triumph just to feel good about your day. If, beyond this, you meet a major milestone at work or in your personal life, celebrate fully. And especially do so when it comes to your addiction. Did you successfully navigate a trigger situation? Did you go a month without a drink? Did you finally do something that your addiction had always gotten in the way of?\n\nOf course, although there are occasions when it's just the ticket, if you go out and buy yourself a present or treat yourself to a hot fudge sundae or a drink every time you accomplish something, this itself can be part and parcel of an addiction. But do allow yourself to revel in the satisfaction you derive from a job well done. Don't waste any opportunity to experience a sense of satisfaction. If you get on the scale and you've lost six pounds, if you can now walk around the block five times where previously you could only do it twice, if you aren't out of breath every time you climb the stairs the way you used to be\u2014go with it! It's not everything you wanted\u2014the whole enchilada\u2014but it's a joy worth experiencing.\n\n**PERSONAL JOURNAL:** When you go to bed, take a moment to list the pleasures, successes, and progress in your day. List at least five. Let the negatives take care of themselves.\n\n**EXERCISE:** How many ways can you think of to acknowledge a success? For example, pausing to recognize it, calling a friend or supporter, or doing something special for yourself. Be as specific as possible, and try to practice these regularly. Make each a new habit, and even list these small celebrations on your tracking chart.\n\nHonoring What You Value\n\nCelebrating your successes is all about taking note of where you are at this moment and acknowledging how far you have come to get here. But there are valuable elements of your life that have remained constant, and recognizing those things on a daily basis (yes, you might call these \"affirmations\") is just as important. Giving yourself opportunities to remember who you truly are can help keep what's most important to you, and why you're doing what you're doing, in the forefront. This might include keeping photographs of people important to you where you can see them all the time\u2014on your computer desktop, in your wallet, on your refrigerator. You might dust off the artifacts of your life that remind you of what's meaningful to you and place them prominently in your home\u2014an instrument you used to (or still occasionally) love to play, a memento from a special trip or time in your life, a gift or card from someone you love.\n\n**ACTIVITY:** Clear a space somewhere in your home\u2014on a table or shelf or corner, perhaps close by your meditation spot. Gather some items that represent the best of who you are and what is most valuable to your heart. These could be childhood pictures of yourself or pictures of or items belonging to your children. You could include plants, candles, diplomas, creative works, products, religious symbols\u2014as long as each represents an aspect of you and your life that brings you pleasure and a sense of value. Arrange these items in the space you have cleared, handling and placing your items with the intention of holding what each one symbolizes in your heart. Use this little altar as a touchstone\u2014return to it whenever you can, to remember and meditate on what is truly meaningful to you.\n\n_But avoid fetishes_\n\nYour \"values altar\" is meant to be a guidepost for your life. As with the example of not making a fetish of the \"lost love\" that would have made your life okay, here, too, I should caution about the shrines some people keep with photos of dead parents, spouses, or children or long-lost lovers (sometimes under candlelight or small bulbs), or their school athletic trophies signifying things they can't do anymore and a kind of accomplishment and recognition they haven't since had. This kind of display can reinforce a negative focus on the past, against which the present and future look all the more bleak (\"my best is behind me\"). It is in the nature of balance that virtually every recommendation in _Recover!_ carries with it a need to see the dangers in taking it to an extreme\u2014in this case honoring things or people morbidly\u2014and to be clear about the difference.\n\n_Going forward in honor_\n\nWhat is most important is that you honor your values, commitments, and love going forward. If there are people whose company you have neglected\u2014perhaps feeling unworthy of their love\u2014reach out. Schedule time with your family into your calendar, or commit to a weekly activity with your children. Contact an old friend. Seeing pictures of people important to you is nice, but actually contacting them from time to time is even better. You may have burned bridges in the past, or the people you love may be wary of opening themselves up to you again. In those instances it's important to respect their boundaries. Sometimes honoring someone you care about means giving them their space, while living in a way that reflects your feelings for them. Suppose, for instance, you have taken advantage of a good friend or a family member, and he cut you out of his life to protect himself from further harm. He or she plainly doesn't trust you, and there's nothing you can do about that (recall Harry and his daughter Anne in Chapter 5). Your decision to clean up your act does not obligate him to allow you back into his life, or even to hear your apology. You can still honor this person by changing your life and treating people the way you wish you had treated him.\n\nRituals, Traditions, and Celebrations\n\nFrom the beginning of time, people have come together as families and communities to recognize and celebrate joyful or tragic events, rites of passage, milestones, harvests, the changing of seasons. Religious ceremonies, feasts, wakes, holidays, parties, rituals, and even more routine practices, like family meals, a kiss on the cheek before leaving the house, a weekly phone call, or a yearly block party are all part of the rhythm of life that makes us feel connected, part of something larger than ourselves. These events reinforce our human bonds, give structure to our lives, allow us to honor each other, our culture, and our humanity, and infuse our lives with meaning. This is yet another aspect of life that addicted people often neglect, opting out of gatherings where they won't have an opportunity to indulge or in order to isolate themselves, feeling ashamed to be around other people (remember Rose missing her daughter's party?), not feeling ties to their communities, or simply being unable to shift their focus away from the myopic and consuming involvement with addiction\u2014and the empty rituals they share with fellow addicts.\n\nRecognizing the profound importance of ritual can also be very personal and private, for instance, daily meditation or prayer or getting up early to watch the sun rise. Whereas previously your daily rhythm was driven by your addiction, you can now replace that frenetic, mindless activity with activities that draw you to life. Creating new personal rituals is a gentle place for you to start reconnecting. It allows you to enrich and fill your own life with a sense of reverence and respect for the world that surrounds you.\n\n**EXERCISE\u2014CREATING RITUALS:** Consider the ways you might begin introducing rituals into your personal or family life. Think about your daily schedule and what you can do to incorporate life-enhancing practices, like reading from an inspirational book or affirming your daily positives at bedtime; spending a few minutes mindfully exploring your values altar; or sharing an after-school snack with your child and talking about her day or reading to her in bed before she goes to sleep. Similarly, consider the more community-oriented rituals that you'd like to partake of, like joining a church or meditation group, attending community meetings, or walking with family or nearby friends after dinner. Begin making these occasions, these points of contact, a regular feature of your existence.\n\nTraditions are family treasures. They are one of the touchstones that give us a sense of belonging and comfort. But, say, you are separated from your family or haven't inherited or don't practice any family or religious traditions. Then you can always start some yourself. For instance, some people volunteer at a soup kitchen on Thanksgiving or Christmas. Some families pass down a special heirloom on a significant birthday. A tradition can be as simple as a monthly Sunday dinner or as elaborate as a family reunion. Make a list of traditions, family or cultural, that are important to you, or traditions you would like to start. Perhaps you have seen others practicing a tradition that you found meaningful. Go on\u2014steal it!\n\nCommemorating major events with a celebration or remembrance is how we honor and attach value to one another\u2014even when you throw a celebration for yourself. What better way to honor your friends and family than by asking them to share your significant life event? There are so many opportunities to celebrate: graduations, wedding or baby showers, birthdays, holidays, work promotions\u2014significant recovery anniversaries. (AA has something there, although from the perspective of this book, as time goes on, that should fade in importance as you come to have more substantial, positive accomplishments and milestones.) Don't gloss over these events; instead, acknowledge them, whether by going out for dinner with a few special people, having a small party, or throwing a bash.\n\n* * *\n\n**CASE:** Richard had an ugly divorce, and his college-age son and adult daughter preferred being with their mother, who, after all, had always been the primary caretaker in the family. So Richard fiddled and fumed while he waited for his children to arrange get-togethers.\n\nOnce, as his birthday approached, it suddenly occurred to Richard that he could host his own party. He cleaned up his apartment, ordered some pizza and salad, and invited a couple of friends\u2014along with his children and their dates. Although he was beset by anxiety about playing the unfamiliar role of host, the evening surprised Richard by being a resounding success.\n\nAs his son left, he told Richard, \"That was great, Dad\u2014let's do it again soon!\"\n\n* * *\n\nSimilarly, take the opportunity to grieve with others or share the sorrow of tragic events like deaths and illnesses. Sit Shiva or attend a wake; spend time with a friend with cancer. Being there for people is a major way of ensuring that you remain in the midst of humanity and acknowledge the humility of our existence in the universe. To put it in starker terms, we're all going to die. From The PERFECT Program perspective, appreciating the lives people have lived, their sheer presence on earth\u2014which is the essence of mindfulness\u2014gives your life a kind of immortality. In the words of John Donne: \"Therefore never send to know for whom the bell tolls; it tolls for thee.\"\n\nAnd while these ceremonies engage you with the people you cherish, they also impose on you accountability and responsibility to others, which is why it can be difficult for addicted people to participate in these activities. Anything that brings fulfillment to your life will push addiction away\u2014and the flipside is also true: Neglecting these things will permit both the time and the psychic emptiness that invite vapid and destructive behavior. Rituals, traditions, and celebrations are not frivolous pursuits. They are essential, non-addictive links to your world.\n\nDiscovering Joy\n\nHave you ever heard New Yorkers say they can always spot the tourists, because they walk around the city like rubes, with their mouths agape and their heads up, marveling at the sites and skyscrapers? For some reason, cynicism and world-weariness are considered admirable qualities in our culture, with \"whatever\" perhaps being the catchphrase of our era. Is reveling in a feeling of wonder a mark of lack of sophistication? I don't think so. (Although, as a New York resident, I _do_ think Madame Tussauds is a rip-off and going up to the observation deck of the Empire State Building a waste of time for adults. Sorry.)\n\nI'm going to speak now to your inner rube\u2014the aspect of you that has been waiting around for an opportunity to be completely blown away by double rainbows and tall buildings. The pleasures and rewards of addictive behavior will blind you to joys you might never have known existed\u2014or that couldn't hold your interest in the face of your addictive urges. How many opportunities to revel in something delightful have you missed? What beauty has escaped your notice? Now that you are headed down the path of your real life, you might feel as if you were blinking into the sun. Things you never noticed before might capture your attention and make you smile or marvel. I have written at length about linking yourself to the values that you know will bring joy and satisfaction to your life. Let's explore at the same time recognizing and discovering new joys. You cannot find too many ways of replacing the superficial rewards of addiction with the genuine rewards you gain from living a life of freedom.\n\n* * *\n\n**CASE:** When Thomas stopped smoking marijuana, he felt that he didn't know how to see and feel. After all, everything had been mediated by his being stoned\u2014sometimes involving just staring at the wall! He found that there were two sides to this phenomenon. On the one hand, he had to immerse himself in appreciating every single aspect of every single day\u2014including simply recognizing the passage of time, which being stoned hadn't permitted him to do. On the other hand, for the first time in a while he had the chance to indulge mindfully in the simple, pure joy of unadorned sensation and perception. In a way, \"getting high on the natch\" (natural) was the greatest trip of all.\n\n* * *\n\n_Mindfulness in the wake of an addiction_\n\nWe have discussed mindfulness as bringing unnoted reactions, emotions, and motivations to the surface of present consciousness. Thus, Thomas's story takes on a double meaning for mindfulness as a badge, a tool in recovery, particularly newly minted recovery.\n\n* * *\n\n**CASE:** At the time Liza quit drinking, after she had walked around in an alcohol haze for years, she really wondered what she was going to do with herself. Every single thing in her world had revolved around her drinking\u2014every activity accompanied or was a precursor to drinking. In many cases, she had to learn for the first time the most basic aspects of having fun and filling her time\u2014of living. After she had gotten beyond the miseries of quitting, she walked gingerly along the sidewalk, listening to the birds, watching the sun. It was a novel experience! She had to learn to be with people without alcohol, to go to the movies, to listen to music, and to do everything else stone cold sober. She began a list of things she could experience anew, some as simple as revisiting the supermarket. But there were also many new activities for Liza, like bike riding and cooking and sewing. She had plenty to choose from\u2014it was as though she were a newborn.\n\n* * *\n\nVenturing away from addiction takes effort and focus\u2014dealing with cravings, recovering after losing your footing, doing all these exercises, trying to be mindful. But even at the beginning of the journey, you may start noticing times when you're feeling pretty good or enjoying something you never bothered with before. For instance, on a walk, you might focus on the movement of your muscles working and enjoy the rhythm of your body, rather than thinking about the slog and how much longer it will take you to get home. (These are sensations encouraged by yoga and Feldenkrais, which I reviewed at the end of Chapter 4.) If you've stopped smoking, surely you'll appreciate the freshness of the air and your ease of breathing! Or, if you've given up drinking alcohol, you might notice how satisfying it is to down a cool glass of water. It could be that you never so much went to bed as passed out; now you are reminded of how good it felt to crawl under the covers as a child. There are an infinite number of ways to take pleasure in everyday life, and doing so is a choice and an exercise of mindfulness. In fact, if you pause right now, lift your head from your reading, you will surely be able to discover something that brings you some joy: perhaps you are feeling relaxed as you read or are sensing the sun on your skin, maybe there's a cat purring on your lap, or the tea you have next to you smells lovely. What do _you_ notice?\n\n_Mindfulness en route to joy_\n\nSimply noticing and appreciating pleasant sensations or beautiful surroundings is one way of discovering joy. Another way is to intentionally seek out such sensations and surroundings. Make the effort to venture out into the world to create experiences that will bring you joy: Go for a hike through the park for no other purpose than to look around; smile at the people you pass; sit under a tree. Visit an unfamiliar part of town or go to another town or city; linger at shop windows; read the paper at a cafe. Or, staying closer to home, simply go out onto your step or into your back yard on a nice day to breathe deeply and smell the air and enjoy the sunlight on the trees. Staying indoors, read a book (okay, an e-book), or put on some new music. One way or another, open your heart and mind and senses to the world around you and acknowledge those things that inspire a sense of wonder or contentment. And before you fall asleep at night, recall those new experiences in as much detail as possible\u2014especially the new joys they have brought you.\n\n***\n\nMuch of your progress through The PERFECT Program has been on learning to cope with difficult feelings by strengthening your core, or inner wisdom and free will, and by replacing what is superficial and mindless with purpose, value, meaning, and mindfulness. It's a colossal effort, and the work you have been doing may bring you a real sense of satisfaction. One reason it may seem so hard to experience joy is our tendency to believe that we learn solely through difficulty and continuing trial. This tendency is strongly reinforced by the recovery movement mantra embodied by the white-knuckle phrase, \"one day at a time.\" Just a reminder: Recovery\u2014living\u2014is more than not succumbing to addiction.\n\nI believe\u2014and I tell addicts\u2014that they have been improved by the suffering and hardship they have endured\u2014even if it was self-induced. There are things you may know about yourself and life that you wish you hadn't had to learn, but that make you a deeper, more complete person now that you have. The lessons we learn from hardship are abiding and true. But they are far from the only truths you are going to gain in life. Understanding that some of your wisdom is hard won shouldn't make it harder for you to accept the wisdom that is earned through experiences of peace, satisfaction, fulfillment, and wonder. Shifting your perspective on this\u2014toward valuing the insights you gain in joy as much as in hardship\u2014is another way of bringing balance into your life. In short, knowing what works is even more important than knowing that addiction doesn't.\n\nPutting It All Together\n\nI've cited cases of mindful recovery earlier in this book. I want to end this phase of The PERFECT Program (before turning to the aftercare element presented by Chapter 10) with a case where a woman stabilized her life around a serious addiction\u2014a set of addictions, really. This woman, Nona Jordan (whose program for women's financial self-management is a resource referenced in Chapter 10), describes how she took control of her life over the long run, instituting changes that brought her a permanent set of rewards that finally guaranteed that her addictions would never reappear. Nona narrates her experience in her own words. The title of her case is her own.\n\n* * *\n\n**CHANGE** Is for Everyone Who Wants It\n\nLots of people are content with their lives and have no desire to change a thing. I've never been one of those people. My very earliest memories are of wanting to be my very best, to express the most perfect version of myself during this lifetime no matter what I'm doing.\n\nIn my late twenties, I was working in corporate accounting. I was good at the job but didn't really like it. I worked long hours and was constantly anxious about my performance. My favorite way of reducing stress was getting drunk at the local bar and smoking cigarettes until my throat hurt. Alcohol abuse is putting it mildly. Coming from a long line of alcoholics, I knew better\u2014but it didn't stop me.\n\nMy relationships were disasters. The men I dated were poor choices and my friendships were all based on drinking. Despite my active social life, I felt isolated. I hid my drinking, which was getting harder to do. I was overweight from all the drinking. Drinking the way I was isn't cheap, either, and so I was in debt, even though I made a good living. I blamed others and my past for all of my problems.\n\nIt wasn't a pretty picture.\n\nAll this time, all through the drinking, I had continued to study and practice yoga and meditation. They seemed to be having very little benefit, but, little did I know, these practices were seeping into my life.\n\nMy moment of clarity arrived as the sun was setting one evening. I had finished a 6-pack already and was feeling ZERO effects from the beer. I was reading a book about Buddhism, which emphasized the idea of avoiding intoxication in order to clear away the cobwebs and experience life fully. As a way to really love yourself and grow from, and into, your life.\n\nI looked up and I looked inward\u2014I clearly saw the huge chasm.\n\nWay over to the left was my current life: drunk, lonely, bad relationships, overweight, in debt, dissatisfied at work, no prospects in sight. Way over to the right was the life I knew I was meant to live: clear and happy, connecting to wonderful people in good relationships, healthy, helping others, doing work I love, with endless possibility for growth and change.\n\nThat night, I knew I was ready. I wanted to bridge that gap.\n\nA few weeks later, I was sitting in the office of a Buddhist therapist that a girl at work had casually mentioned to me. It was my second day of not drinking and I felt horrible. But I knew if I was going to get the most out of therapy, I had to recognize my feelings. I was walking toward the version of me that I knew, deep down, I could be.\n\nThat was the beginning of the most life-altering, challenging, and\u2014ultimately\u2014profound period of my life. I broke up with my boyfriend. I stopped working so many hours (although, today, I work just as hard, only at gratifying things that I love). I started investigating yoga-teacher training programs. I started working out and honoring my body. I lost 30 pounds, almost effortlessly. I meditated; I got on my yoga mat and practiced for hours.\n\nAnd I sat with my feelings and cried a lot. I worked hard with my therapist to clear away the rotten thoughts and beliefs that were mucking up my mind and my heart. I volunteered; I sought out healthy friendships; I paid off my debt.\n\nI realized, in my heart\u2014no, in my bones\u2014that my life was my own. Happiness was in my hands, and my hands alone.\n\nThat was eleven years ago.\n\nAs of today, I am a married to a wonderful man and I have a beautiful daughter. I am a CPA, a yoga teacher, and a master coach. I work with women who want to create success on their terms. I have the pleasure of supporting them in finding the peace and ease that comes with creating a life and a financial legacy of their choosing.\n\nMy life is better than I would have ever imagined on that dark night so many years ago. There have been rough spots\u2014really rough spots. This journey has not been easy, effortless, or flawless. But every year, I can say without fail, I more deeply love the life I have created for myself.\n\nIt's easy to say our situation is too hard, that someone else is holding us back, or that we're too damaged, broken, weak, or poor. But it's simply not true.\n\nLife is what we make of it. Change is for anyone who wants it.\n\nAnd that is the best news I can possibly give you on this fine day.\n\n* * *\n\nMoving Forward\n\nYou have learned the practice of The PERFECT Program for addiction, how to remove addiction from your life and replace it with genuine joy and accomplishment by homing in on your true self. You have learned to recognize and honor your success, to institute practices that reinforce and cement your ties to the things that make your life meaningful\u2014your personal pleasures; your spiritual, familial, community, and cultural centers\u2014and to cultivate new experiences of joy and wonder. Arriving at a place where you see the genuine value in celebrating your life in a way that is not narrowly self-involved and does not feel like a frivolous pursuit is a key stage in your recovery. This is this spirit that informs The PERFECT Program.\n\nThe following chapter is titled \"Triage,\" which means dealing first with critical needs or circumstances, with emergencies. This is the chapter to turn to when you are feeling at a loss, or trying to remember your priorities in an overwhelming or difficult situation. It contains ideas and resources for dealing with cravings, relapse, life's curves, and other circumstances that require immediate guidance and perspective as you follow your new path.\n\n* At the beginning of each year, Jerry hangs up a \"year-at-a-glance\" calendar; each day he composes new material he marks with an _X_. This is one way for creative people to impose structure and enforce self-discipline in a lonely form of work.\n\nCHAPTER 10\n\n_Triage_\n\nRealignment\u2014Resources and actions for regaining lost footing\n\n* * *\n\n**CHAPTER GOALS**\n\n\u2022 To deal with mishaps, discouragement, and persistent problems\n\n\u2022 To plan for problem solving and realignment in the moment\n\n\u2022 To review and consolidate the key ideas in The PERFECT Program\n\n\u2022 To discover resources for support and exploration: helpful books, websites, meditations, and apps\n\n**Purpose:** For moments when you feel overwhelmed or out of options, this chapter recaps key ideas, activities, and exercises from various parts of The PERFECT Program. It is a resource to give you quick reference points for shifting your perspective, moving forward, or regaining your footing. I also list other resources that can help you\u2014some included in the previous chapters, some new\u2014including books, websites, and guided meditations. If you find yourself at a loss, flip to this chapter, review your options, and pick a place to start. This is your on-the-spot reference and guide.\n\n* * *\n\nAs you begin developing your skills and strengths, you may occasionally find yourself wondering how to get through the next moment without going off course. Perhaps you feel overwhelmed by urges, lost in the universe, unmotivated, depressed. This chapter is titled \"Triage,\" which means dealing with the important things first, as they arise. This is a chapter that you can turn to when\u2014whether having progressed this far in the program or not\u2014you are feeling at a loss, or trying to determine what your priorities are in an overwhelming or difficult situation. These are ideas and resources for dealing with cravings, relapse, curves and dips in the road, and other events that require immediate guidance and perspective as you navigate the life of freedom you have created for yourself.\n\nThese ideas and resources can help you refocus in the moment. Some may not be for you; others might be just the thing. I will cover, in order:\n\n\u2022 Difficulty with meditation\n\n\u2022 Addictive urges and compulsions\n\n\u2022 Relapse and harm reduction\n\n\u2022 Feelings of unworthiness\n\n\u2022 Lack of motivation\n\n\u2022 Loneliness\n\n\u2022 Feeling overwhelmed\n\n\u2022 Anxiety or depression\n\n\u2022 Abusive relationships\n\n\u2022 Finding a therapist\n\n\u2022 Education and career\n\n\u2022 Financial management\n\n\u2022 Other resources\n\nDifficulty with Meditation\n\n_Mindfulness refers to keeping one's consciousness alive to the present reality. It is the miracle by which we master and restore ourselves._\n\n\u2014Thich Nhat Hahn\n\nFirst, remember that meditation does not mean clearing your mind of all thoughts. Nor does it mean achieving total calm or enlightenment. Second, remember that the only right way to do it is to do it. Whatever _is_ happening while you're doing your meditation is exactly what _should_ be happening. If you are experiencing pain, strong emotions, fidgeting, obsessing\u2014meditation is not meant to alleviate those things. They are, in fact, your meditation companions\u2014your guides, so to speak. To paraphrase Rumi, graciously invite in whatever devils show up\u2014they all have something to teach you. So, before you begin, dispel any ideas you may have about what you should feel, how you should respond, what should happen. Whatever you feel, however you respond, and whatever happens is good.\n\nRather than teaching you to master your thoughts, feelings, or physical sensations, meditation is meant to help you master your ability to notice and accommodate them with compassion and a balanced perspective. Mindfulness is practice in paying attention to yourself, as well as in turning your attention where you will it. It is an exercise of your free will. It should be challenging, but when that challenge seems too much for you, here are some strategies you can implement. And, of course, I encourage you to search on your own for comparably valuable aids and resources.\n\n\u2022 If you are having a hard time focusing your attention on your breath because you can't stop shifting and feeling antsy, turn your attention to those feelings instead of your breath. With a spirit of curiosity, explore that fidgety feeling: Where in your body is it located? Can you describe the sensation to yourself? Keep bringing your focus back to those feelings and notice what they do: Do they mutate? Do they intensify?\n\n\u2022 Name what you're feeling, in your mind, as you experience it. Say to yourself, \"Restlessness,\" \"Thinking,\" \"Ruminating,\" or \"Listening to sirens outside.\" Once you have acknowledged what's happening, turn your attention back to your breath. Do this as many times as you need to. Your goal is not to prevent your mind from wandering. In fact, the heart of this practice is the intentional act of returning your attention to your breath as many times as required.\n\n\u2022 Maybe, rather than feeling agitated, you experience a torpor that may mimic a deep, profound state of meditation. This can feel like a sinking into the mind, a dreamy heaviness that may even put you right to sleep! If you are experiencing this torpor and are unable to keep your mind alert, you can meditate in an upright chair or do a walking meditation. You may also find it helpful to choose a basic guided mindfulness meditation CD or MP3.\n\n\u2022 After the discussion here, review the section on mindfulness meditation in Chapter 4 (\"Pause\"), and particularly the section \"User-Friendly Mindfulness Meditation\" (page 98).\n\n_Resources for mindfulness meditation_\n\nBOOKS\n\n_Insight Meditation: A Step-by-Step Course on How to Meditate_ , by Sharon Salzberg\n\n_Mindfulness for Beginners: Reclaiming the Present Moment\u2014And Your Life_ , by Jon Kabat-Zinn\n\n_The Miracle of Mindfulness: An Introduction to the Practice of Meditation_ , by Thich Nhat Hahn\n\nAUDIO\n\n_How to Meditate: A Practical Guide to Making Friends with Your Mind_ , by Pema Ch\u00f6dr\u00f6n\n\n_Mindful Movements_ , by Thich Nhat Hanh\n\n_Mindfulness for Beginners_ , by Jon Kabat-Zinn\n\nWEBSITES\n\nAudio Dharma: www.audiodharma.org (search for \"Introduction to Mindfulness Meditation,\" by Gil Fronsdal)\n\nU.C.L.A. Mindful Awareness Center: Free Guided Meditations \n\nUniversity of Massachusetts Medical School Center for Mindfulness: Mindfulness Stress Reduction Programs: \n\nAddictive Urges and Compulsions\n\n_If you do not change direction, you may end up where you are heading._\n\n\u2014Lao Tzu\n\nIf you are feeling overcome by strong addictive urges, you can shift your perspective in the moment by choosing one or a few of the following actions:\n\n\u2022 **Mindfulness Meditation** with a focus on \"Urge Surfing\" (see \"Guided Meditation,\" below).\n\n\u2022 **S.P.O.T. Exercise,** Chapter 4 (\"Pause,\" page 95).\n\n\u2022 **Distract** yourself with an activity from the list you created in Chapter 7 (\"Fortify,\" page 155).\n\n\u2022 **Take a nap.**\n\n\u2022 **Read an engrossing book.**\n\n\u2022 **Eat a healthful snack,** like a handful of nuts or a piece of cheese or fruit.\n\n\u2022 **Drink a full glass of water.**\n\n\u2022 **Call a supportive, trusted friend.**\n\n\u2022 **Walk.**\n\n\u2022 **Bathe** and put on fresh, clean clothes.\n\n\u2022 **Play some music** that is meaningful to you, either on a musical instrument or a recording.\n\n\u2022 **Change your environment:** Go to a cafe, a friend's house, to the beach or park.\n\n\u2022 **Start on a project,** something that has been waiting for your attention.\n\n\u2022 **Give yourself permission** to use later (Chapter 7, page 158).\n\n\u2022 **Remind yourself of your values:** Look at your photographs, explore your altar, pull out your lists of reasons to stay on track.\n\n\u2022 **Watch a movie** that will make you laugh, or feel inspired by ideas and possibilities.\n\n\u2022 **Consider the consequences:** Compose a story about what will happen if you indulge your addiction\u2014from how it will make you feel in the moment all the way to the nearly inevitable consequences (depression, hangover, shame, etc.).\n\n_Resources for dealing with addictive urges and compulsions_\n\nBOOKS\n\n_Her Best-Kept Secret: Why Women Drink\u2014And How They Can Regain Control_ , by Gabrielle Glaser\n\n_How to Change Your Drinking: A Harm Reduction Guide to Alcohol,_ 2nd ed., by Kenneth Anderson\n\n_The Mindfulness Workbook for Addiction: A Guide to Coping with Grief, Stress, and Anger that Triggers Addictive Behaviors,_ by Rebecca E. Williams and Julie S. Kraft\n\n_7 Tools to Beat Addiction_ , by Stanton Peele\n\n_Sex, Drugs, Gambling & Chocolate: A Workbook for Overcoming Addictions_, by A. Thomas Horvath\n\n_The Tao of Sobriety: Helping You to Recover from Alcohol and Drug Addiction_ , by David Gregson and Jay S. Efran\n\n_The Truth About Addiction and Recovery_ , by Stanton Peele and Archie Brodsky\n\n_You Are Not Your Brain_ , by Jeffrey Schwartz\n\nGUIDED MEDITATION\n\n\"Urge Surfing,\" by Sarah Bowen: \n\nCOMMUNITY SUPPORT\n\nHAMS, Harm Reduction for Alcohol: \n\nModeration Management: \n\nSMART Recovery\u00ae: www.smartrecovery.org\n\nQuit Smoking Support: \n\nWe Quit Drinking: wqd.netwarriors.org\n\nRelapse and Harm Reduction\n\n_When flowing water . . . meets with obstacles on its path, a blockage in its journey, it pauses. It increases in volume and strength, filling up in front of the obstacle and eventually spilling past it . . . . Do not turn and run, for there is nowhere worthwhile for you to go. Do not attempt to push ahead into the danger. . . (rather) emulate the example of the water: Pause and build up your strength until the obstacle no longer represents a blockage_.\n\n\u2014Thomas Cleary, _I Ching_\n\nYou can be especially disheartened when you are in the thick of relapse, as the resolve you remember feeling seems so, so foreign and distant. But it is _always_ within your power to regain your footing and focus. If you have relapsed, remember that there is no such thing as a \"point of no return.\" Relapse is not evidence of failure or hopelessness. Your North Star is always in sight.\n\n\u2022 Practice self-acceptance and compassion (see the following section on \"Feelings of Unworthiness\").\n\n\u2022 Immediately begin employing harm-reduction techniques. Review in Chapter 3, pages 69\u201372.\n\n\u2022 Review the section on relapse in Chapter 8, page 206.\n\n\u2022 Remember that there is no such thing as starting over. If you have relapsed, broaden your perspective to see it as just a part of your whole journey to wellness.\n\n\u2022 Remember that you can realign with your vision for yourself from any point, no matter how far off course you have traveled. Review the \"Navigating Relapse\" chart on pages 212\u2013213.\n\n\u2022 Take time to explore the circumstances or life events that may have triggered your relapse. Sometimes it's not clear, but more often you will be able to see exactly what triggered you to veer off course and why you were unable to steer through these circumstances. Consider what you could have done differently and establish future coping strategies, in the highly likely event you encounter the same triggers again.\n\n\u2022 Reintroduce The PERFECT Program into your daily life:\n\n\u2022 Begin practicing your mindfulness and loving kindness meditations, with an emphasis on riding out cravings and discomfort, in \"Anti-Addiction Skills\" section of Chapter 7, page 154.\n\n\u2022 Pay attention to your moments of grace and turn your attention to the messages you receive from your wise inner self.\n\n\u2022 Reconnect with your values and sense of life purpose and meaning in Chapter 6 (\"Rediscover\").\n\n\u2022 Set some immediate goals.\n\n\u2022 Engage in the life-affirming activities you have created for yourself.\n\n\u2022 Consult \"Reframing Failure,\" Chapter 8 (\"Embark,\" page 204).\n\n\u2022 Quick reference: Alan Marlatt's mindfulness-based relapse prevention S.O.B.E.R. exercise\n\n**S** \u2014 **_Stop:_ pause wherever you are.**\n\n**O** \u2014 **_Observe:_ what is happening in your body and mind.**\n\n**B** \u2014 **_Breathe:_ bring focus to the breath as an \"anchor\" to help focus and stay present.**\n\n**E** \u2014 **_Expand_ awareness to your whole body and surroundings.**\n\n**R** \u2014 **_Respond_ mindfully versus automatically.**\n\nDr. Marlatt explains:\n\n**S.O.B.E.R.** is one of the meditation breathing spaces we've developed. You can use it when you're right on the verge of taking a drink. It enhances meta-cognition, giving you a chance to stand back and look at what's going on. Say you're walking by a bar you used to visit and the thought arises: \"Maybe I'll just pop in and see if anybody I know is inside:\" S is for \"stop\" where you are. Stop walking. Then O, \"observe\" how you're feeling\u2014what are the physical sensations and cravings? B, focus on your \"breath.\" Take a deep breath, then another breath, and center your attention there. And E \"expand\" your awareness so that you'll have a larger sense of what would happen if you did go in the bar. How would you feel? . . . ] Finally, R, \"respond\" mindfully.\u2014Alan Marlatt, Interview, _Inquiring Mind_ , 2010, [www.inquiringmind.com\/Articles\/SurfingTheUrge.html **.**\n\n_Resources for understanding and dealing with relapse and harm reduction_\n\nBOOKS AND PAPERS\n\n_Addiction: A Disorder of Choice_ , by Gene Hayman\n\n_Enough! A Buddhist Approach to Finding Release from Addictive Patterns_ , by Ch\u00f6nyi Taylor\n\n_Harm Reduction Psychotherapy: A New Treatment for Drug and Alcohol Problems_ , by Andrew Tatarsky\n\n_How to Change Your Drinking: A Harm Reduction Guide to Alcohol_ , by Kenneth Anderson\n\n_Overcoming Your Alcohol or Drug Problem: Effective Recovery Strategies Workbook (Treatments That Work),_ by Dennis C. Daley and G. Alan Marlatt\n\n_Over the Influence: The Harm Reduction Guide for Managing Drugs and Alcohol_ , by Patt Denning, Jeannie Little, and Adina Glickman\n\n_Relapse Prevention: Maintenance Strategies in the Treatment of Addictive Disorders_ , by G. Alan Marlatt and Dennis Donovan\n\n\"Alcohol Harm Reduction Compared to Harm Reduction for Other Drugs,\" by Kenneth Anderson, \n\nGUIDED MEDITATION\n\n\"Urge Surfing,\" by Sarah Bowen: \n\nWEBSITES\n\n\"The Clean Slate Addiction Site,\" by Steven Slate: www.thecleanslate.org\n\n\"HAMS: Harm Reduction for Alcohol\": \n\n\"Harm Reduction Network,\" by Kenneth Anderson: www.hamsnetwork.org\n\n\"How to Taper off Alcohol,\" HAMS Website: \n\n\"The Life Process Program,\" by Stanton Peele: peele.net\n\nModeration Management: \n\nQuit Smoking Support: \n\nSMART Recovery\u00ae: www.smartrecovery.org\n\nWe Quit Drinking: wqd.netwarriors.org\n\nFeelings of Unworthiness\n\n_You yourself, as much as anybody in the entire universe, deserve your love and affection._\n\n\u2014Buddha\n\nI discussed at length in Chapter 5, on self-acceptance, knowing and believing that you are worthy of being in the world and of the things you value most, and that you have just as much right to create and participate in your own full life. Even the most seemingly well-adjusted people can feel unworthy to have these essential feelings. If you have trouble overcoming self-debasing thoughts or self-talk, or feel that you don't deserve love or success, please pursue some or all of the following suggestions:\n\n\u2022 Reread the Chapter 5 section on self-acceptance (pages 116\u2013120) and work through the exercises.\n\n\u2022 Complete the self-compassion exercise, Chapter 5, page 118.\n\n\u2022 Complete the self-forgiveness reflection, Chapter 5, page 122.\n\n\u2022 Visit your altar or create one, Chapter 9 (\"Celebrate,\" page 226).\n\n\u2022 Reach out to someone who loves you.\n\n\u2022 Practice your loving kindness meditation with dedication, Chapter 5, page 129, focusing specifically on self-compassion.\n\n\u2022 Remember to write down five things you are grateful for, every morning or night.\n\n\u2022 **Exercise:** In your Personal Journal, list the negative or harsh thoughts you are having about yourself or describe your negative feelings about yourself. Then review what you have written: Do you feel that you are fundamentally broken and irredeemable?\n\nThat you're a bad person? That you're not meeting expectations or goals? That you're less than everyone else? Now, explore your findings from a different perspective. Imagine that you are reading the words of someone you love\u2014a child or close friend\u2014or even a stranger. Does your self-assessment seem reasonable or realistic when you imagine directing these words at someone else? Rewrite your entry from this more compassionate perspective.\n\n_Resources for supporting feelings of self-worth_\n\nBOOKS\n\n_The Gifts of Imperfection_ , by Bren\u00e9 Brown\n\n_The Mindful Path to Self Compassion_ , by Christopher K. Germer\n\n_Radical Acceptance_ , by Tara Brach\n\nGUIDED MEDITATIONS\n\n\"Lovingkindness Meditation,\" by Sharon Salzberg: www.soundstrue.com, www.sharonsalzberg.com\n\n\"Men, Women, and Worthiness,\" by Bren\u00e9 Brown: www.soundstrue.com, www.brenebrown.com\n\n\"Radical Acceptance Guided Meditations,\" by Tara Brach: www.tarabrach.com\n\nAll of the above meditations are also available from www.amazon.com.\n\nWEBSITES\n\nBefriending Ourselves, by Ali Miller: www.befriendingourselves.com\n\nSelf-Compassion, by Kristin Neff: www.self-compassion.org\n\nLack of Motivation\n\n_Nothing is a waste of time if you use the experience wisely._\n\n\u2014Auguste Rodin\n\nA lack of motivation to act can seem like plain old laziness. But this paralyzing torpor is more likely generated by your fear, self-doubt, or irrational imagination. You may not know where to start, may be afraid of what you will discover if you start going through that pile of mail on your desk\u2014or those feelings that await you just below the conscious level. Perhaps you can't bring yourself to start exercising, believing you'll just let yourself down in a couple of days anyway. You could be avoiding a phone call or work assignment, afraid of being judged or confronted in some way. Or you might just be exaggerating the potential tedium of whatever it is that you're avoiding. Granted, you may be right about all of it: Maybe there is a serious credit issue hiding in the pile on your desk; and maybe you do have an excruciatingly tedious task to face or an enormous project to tackle. Perhaps you're telling yourself that you're just waiting for the right moment or the right inspiration. Forget it. As Picasso said, \"Inspiration exists, but it has to find you working.\" Let's get you moving:\n\n\u2022 **Start small.** Give yourself only one task to accomplish for the day and commit to that single thing.\n\n\u2022 **Give yourself a time limit** \u2014say an hour or two\u2014to work on a task. Buy and use a timer.\n\n\u2022 **Use your tracking chart in your PERFECT Journal** to make note of everything you accomplished. Don't let this slide.\n\n\u2022 **Choose an activity or event to attend** and put it on your schedule, even if it is for the following week. Make a coffee or walking date with a friend, find a volunteer opportunity, and so on.\n\n\u2022 **Set a goal** and decide what steps you need to take to accomplish it. Break it down into mini-goals, then make a to-do list out of your mini-goals.\n\n\u2022 **Write down the rewards** you will experience if you complete a task or project. For instance, how will you feel after making a dreaded phone call or cleaning your kitchen?\n\n\u2022 **Find accountability in community.** Join a co-op or a book group; find an exercise partner or commit to helping someone.\n\n\u2022 **Get showered and dressed for the day,** every day, even if you're not going somewhere.\n\n\u2022 **Moments of grace.** Be mindful of and take advantage of your windows of opportunity to act. If you are surfing the Internet and feel the sudden urge to shut it off and get up, do it. Don't wait for the feeling to pass.\n\n\u2022 **Put on some motivating music or listen to a podcast or an audio book** when you're working on a boring chore that doesn't require your full attention.\n\n_Resources to help spark your motivation_\n\nBOOKS\n\n_Drive_ , by Daniel Pink\n\n_Getting Things Done_ , by David Allen\n\n_Making Habits, Breaking Habits_ , by Jeremy Dean\n\n_Willpower_ , by Roy F. Baumeister and John Tierney\n\nAUDIO BOOKS\/CDS\n\n_Getting Unstuck: Breaking Your Habitual Patterns and Encountering Naked Reality_ , by Pema Ch\u00f6dr\u00f6n\n\n_The Willpower Instinct: How Self-Control Works, Why It Matters, and What You Can Do to Get More of It_ , by Kelly McGonigal: .\n\nWEBSITES\n\n\"Flylady,\" www.flylady.net\n\n\"43 Folders,\" by Merlin Mann: www.43folders.com\n\n\"The Happiness Project,\" by Gretchen Rubin: www.happiness-project.com\n\n\"Procrastination,\" _Psychology Today_ : \n\n\"Spark People,\" www.sparkpeople.com\n\nOTHER\n\niTunes: Whether you have an Apple device or not, you can download iTunes, where you will find free music channels _and_ podcasts on the subject of productivity. www.itunes.com\n\nLoneliness\n\n_Be thine own palace, or the world's thy jail._\n\n_\u2014_ John Donne\n\n_I've been lonely too long, I've been lonely too long \/ In the past it's come and gone. I feel like I can't go on without love._\n\n\u2014Eddie Brigati and Felix Cavaliere (The Rascals)\n\nLoneliness is the devastating and painful emotional state of feeling alienated and isolated, which can be a powerful addiction trigger. You can experience loneliness whether you are physically alone or surrounded by friends, family, or community. After all, even connected people are often alone, or at least not immediately engaged with others (like working in an office cubicle). At the same time, you may not be in a committed relationship or part of any kind of larger community\u2014at least in any immediate sense. Since our society is organized around couples and families, this kind of loneliness can make you feel as though you are especially deprived.\n\nSo, loneliness is a complex condition, with no single trigger\u2014or even any trigger at all. People living with loneliness don't like to reveal it, because saying \"I am lonely\" is excruciatingly exposing and at the same time is easily dismissed as whining. But it's real, and it can be crippling.\n\nBecause loneliness is such a complex and persistent condition, patronizing instructions to get out and meet people don't help, especially because they don't take into account that many people who are plugged into communities can feel lonely. And, sometimes, forcing yourself into social situations can worsen feelings of isolation.\n\nMost important to remember is that loneliness is not about other people; it's about your own sense of authenticity, your place and belonging in the universe. With that in mind, I offer these suggestions to help you restore or recognize your value and the vital nature of your existence.\n\n\u2022 **Therapy:** Loneliness can lead to depression, addiction, even self-harm. If your loneliness is severe enough that you feel paralyzed or tempted to hurt yourself, please seek out effective treatment from a qualified therapist. See Chapter 7, page 163, Chapter 8, page 204, and \"Finding a Therapist\" later in this chapter for guidance in choosing a therapist.\n\n\u2022 **Unplug:** Online networking has become a necessary part of daily life. We join online communities\u2014like Facebook\u2014or participate on message boards, where we communicate with people all day long. We text and instant message, e-mail, and remain accessible to everyone at all hours, and still the epidemic of loneliness grows. Remember that your body is more than just a vehicle to carry your brain around. Although sitting in front of your electronics all day can give you the illusion of connectedness or activity, you may be neglecting the plain fact that your body exists in this world, too. Connecting your body to the air, the ground, the weather, the food you eat\u2014using all your senses every day\u2014is essential to your feeling of belonging to this world. Consider scheduling time for your online social activities and making yourself less accessible. For instance, answer e-mail or text messages once or twice a day; turn on your instant messenger only for a limited amount of time; put your phone away when you are visiting with other people.\n\n\u2022 **Volunteer:** Choose a cause that you believe in and offer your time and skills toward supporting it. Do so with the intention of engaging and furthering something meaningful to you. You might even find ways of spending time with other people who are lonely, like elderly neighbors or people who are housebound.\n\n\u2022 **Reinforce your place in the universe:** Whether you are spiritually minded, agnostic, or atheist, you can find fulfillment in the rituals, practices, and philosophies that bring you a sense of your own meaning in the grand scheme. Find some meeting place for people with a spirit similar to yours\u2014for meditation, yoga, hiking, church, or philosophical discussions.\n\n\u2022 **Find a regular place for yourself:** Go somewhere regularly, to work or to socialize or to sit and think. This can be a park, or a coffee house, or\u2014yes\u2014even a nice bar. Although this contradicts the idea of feeling lonely by being alone in a crowd, there is a point to \"having a place.\"\n\n\u2022 **Share your knowledge:** What skills do you have that you can share with others? Can you teach someone to sew? Garden? Do algebra? Fish? Offer to teach someone how to do something that you are good at, even if you are not an expert!\n\n\u2022 **Practice your loving kindness and compassion meditations and skills** from Chapter 5, with the intention of extending these feelings outward, to your friends, family, community, and further toward acquaintances, people you see daily, and even people you don't like.\n\n_Resources to help you cope with loneliness_\n\nReview the resources for \"Feelings of Unworthiness,\" page 247.\n\nBOOKS\n\n_Living Single_ , blogs and books by Bella DePaulo: \n\n_Lonely: Learning to Live with Solitude,_ by Emily White\n\n_True Belonging: Mindful Practices to Help You Overcome Loneliness, Connect with Others, and Cultivate Happiness_ , by Jeffery Brantley and Wendy Millstine\n\nFeeling Overwhelmed\n\n_You are the sky. Everything else\u2014it's just the weather._\n\n\u2014Pema Ch\u00f6dr\u00f6n\n\nFeeling overwhelmed is the sense that you are out of control, either of a situation or of your emotional response to it. It's the feeling that you are in way over your head, or that you cannot think rationally or act effectively. Perhaps you don't know where to begin tackling a big problem and have been allowing it to spiral into chaos. Or, perhaps you have too much on your plate. It could also be that you are so overcome by emotions that at this moment you cannot act effectively or think rationally. Anger, fear, stress, grief, exhaustion, and trauma can all contribute to the belief that you have no options. Here are some places to start:\n\n\u2022 **Mindfulness meditation:** This is essential for gaining and maintaining rational perspective, for centering yourself and finding repose.\n\n\u2022 **Delegate:** Ask for help.\n\n\u2022 **Break it down:** Dismantle any huge tasks into more manageable mini-tasks, and pick a place to start.\n\n\u2022 **Take a break:** Remove yourself from any volatile or emotionally fraught situation until you regain some control or perspective.\n\n\u2022 **Listen:** Talk through the situation with a friend or therapist. Remember to really listen to feedback and keep your mind open to possibilities. Resist the urge to say \"Yeah, but . . .\" and to dismiss options that have been presented to you. You don't have to follow through on everything you hear, but keep an open mind and make sure you are listening.\n\n\u2022 **Create opportunities:** Make a list of potential options and decisions you can make about your situation, especially if you're feeling stuck. Do this with a friend or helper, if possible.\n\n\u2022 **Review problem-solving skill:** Chapter 7 (\"Fortify,\" page 166).\n\n_Resources for helping you regain control when you're feeling overwhelmed_\n\nBOOKS\n\n_Calming the Emotional Storm,_ by Sheri Van Dijk\n\n_Emotional Intelligence 2.0_ , by Travis Bradberry and Jean Greaves\n\n_True Refuge_ , by Tara Brach\n\n_When Things Fall Apart_ , by Pema Ch\u00f6dr\u00f6n\n\nAUDIO\n\n_Don't Bite the Hook: Finding Freedom from Anger, Resentment, and Other Destructive Emotions_ , by Pema Ch\u00f6dr\u00f6n\n\n_Living Without Stress or Fear_ , by Thich Nhat Hahn\n\n_Stress-Proof Your Brain_ , by Rick Hanson\n\nWEBSITES\n\n\"Wisdom through Mindfulness\": wisdomthroughmindfulness.blogspot.com\n\nAnxiety or Depression\n\n_This being human is a guest house. Every morning is a new arrival. A joy, a depression, a meanness, some momentary awareness comes as an unexpected visitor . . . . Welcome and entertain them all. Treat each guest honorably. The dark thought, the shame, the malice, meet them at the door laughing, and invite them in. Be grateful for whoever comes, because each has been sent as a guide from beyond._\n\n\u2014Rumi\n\nAnxiety and depression are common mental health issues; they can cast a shadow over your life and make it difficult to maintain perspective or focus on your daily activities. As your mind and body adjust to your non-addicted way of life, you may experience periods of depression or anxiety. Avoiding these feelings can make reverting to addiction seem like the lesser of two evils. Remember that these feelings will likely pass\u2014or come and go\u2014but to make life bearable while you are in the thick of it, you can take steps to see you through them.\n\n\u2022 **Therapy:** If your anxiety or depression is chronic and severe enough to be debilitating, please visit a therapist who specializes in depression and anxiety. See \"Finding a Therapist\" later in this chapter for guidance on choosing a therapist.\n\n\u2022 **Go outside:** Expose yourself to the elements for at least fifteen minutes a day.\n\n\u2022 **Clean and declutter** your immediate environment.\n\n\u2022 **Stay on your schedule.**\n\n\u2022 **Reframe:** In your journal, write down the thoughts you are having about yourself or your situation and ask yourself how realistic or accurate those thoughts are. Have a friend help you, if possible.\n\n\u2022 **Eat healthfully:** Get rid of the junk food and sugar. If you're anxious, cut out caffeine.\n\n\u2022 **Change your environment:** Go somewhere open and peaceful, if that is a possibility for you. Head to a park or to a lake or ocean beach and absorb the new scenery. Or go downtown and people watch or window shop.\n\n\u2022 **Move:** Dance, exercise, walk the dog, ride your bike, swim, stretch. It doesn't matter what you do, but do something with your body.\n\n\u2022 **Consume information wisely:** Choose the media you consume with intention. Turn off the violence, the exploitative reality TV shows, and gossip. Avoid vitriolic Internet comments sections and mindless, time-sucking websites. Limit your media exposure, focusing your attention on what is informative, uplifting, inspirational, thought-provoking, and creative. Get your current events news from reliable sources such as a daily newspaper and\/or public radio.\n\n_Resources for managing depression and anxiety_\n\nTHERAPY\n\nReview \"Find Professional Help\": Chapter 7, page 163\n\nReview \"Mental Health\" (including types of therapy): Chapter 8, page 204\n\nSee \"Finding a Therapist\" later in this chapter.\n\nHakomi (meditation-based) Psychotherapy: \n\nBOOKS\n\n_Feeling Good_ , by David D. Burns\n\n_The Mindful Way Through Depression_ , by Mark Williams and John Teasdale\n\n_The Mindfulness Solution: Everyday Solutions for Everyday Problems_ , by Ronald Siegel\n\n_Psychotherapy Without the Self: A Buddhist Perspective_ , by Mark Esptein\n\n_When Panic Attacks_ , by David D. Burns\n\nGUIDED MEDITATIONS\n\n_Free Yourself from Anxiety_ , by Erin Olivo: soundstrue.com\n\n\"Guided Forgiveness Meditation for Depression,\" by Ronna Kabatznick, free from Audio Dharma: www.audiodharma.org\n\n\"Relieve Depression,\" by Belleruth Naparstek: healthjourneys.com\n\nAUDIO\n\n_The Fearless Heart: The Practice of Living with Courage and Compassion_ , by Pema Ch\u00f6dr\u00f6n\n\n_Living Without Stress or Fear_ , by Thich Nhat Hahn\n\nMIND-BODY ACTIVITY WEBSITES\n\nGaiam: www.gaiam.com\n\nFeldenkrais Method: www.feldenkrais.com\n\nMINDFULNESS PSYCHOTHERAPY WEBSITES\n\nThe Institute for Mindfulness and Psychotherapy: \n\nThe Mindfulness Solution:\n\n\n\nMark Epstein on Mindfulness and Psychotherapy\n\n\n\nAbusive Relationships\n\n_Never allow someone to be your priority while allowing yourself to be their option._\n\n\u2014Mark Twain\n\nLiving with abuse, mental or physical, including infidelity, is traumatizing and crazy-making. If you are being manipulated, bullied, lied to, intimidated, emotionally or physically abused, you can lose your faith in yourself, your sense of self-worth, and your ability to recognize and act on the real options you have\u2014all of which can reduce your ability to cope with addiction. If you are suffering with abuse, in any form, _it is vital_ that you remove yourself from the harmful, traumatizing domestic or social situation.\n\nEscaping abuse is much easier said than done when your finances or livelihood or sense of self-worth are dependent on your abuser, or when you have been so devastated that you don't trust yourself to make the proper choices. It may seem a paradox to say that your sense of self-worth is (or feels as though it is) dependent on the abuser. Yet, this is the basic dynamic in an addictive, abusive relationship\u2014abuse and dependence feed on one another. Clearly, the subjects of addictive and abusive relationships can be the basis for an entire book (like _Love and Addiction_ ). For the present purpose of avoiding falling back into an addiction, let me offer here some guidance and resources that can help you find support and sanctuary.\n\n\u2022 **Reach out to family and friends:** Often, people who are being abused are ashamed to admit it to the people closest to them, for a variety of reasons. Abusers also will take measures to isolate their victims from family and friends. It is important that you let your loved ones know what is happening to you. Not only will this allow people to help you, it will also bring you a sense of accountability to people outside of your abusive circumstances.\n\n\u2022 **Contact domestic abuse support:** Local shelters, abuse hotlines, police, and courts can advise you and provide you with a supportive network.\n\n\u2022 **Remember who you are:** People who are being abused often lose their sense of self, forgetting what inspires them and brings their life meaning. Removing yourself from an abusive environment, changing your physical perspective, even for a short time, can help ground you and remind you that the world is bigger than your immediate situation.\n\n\u2022 **Value, purpose, and meaning:** Review Chapter 6 (\"Rediscover\") to reestablish your priorities.\n\n\u2022 **Counseling:** Find a counselor or therapist who specializes in abuse. Be alert for and wary of people who use buzzwords and phrases like \"codependency\" and \"look at your part.\" For sure, you want to explore the reasons why you might find yourself accommodating an unacceptable situation, but do so with someone who is not locked into a 12-step philosophy. (See the next section of this chapter, \"Finding a Therapist.\")\n\n\u2022 **Review my discussion of permission in \"Self-Knowledge and Personal Choice\" (Chapter 8, page 188):** Remember that abusers (like addicts) don't abuse (or make poor choices) because they're \"passionate\" or \"out of control.\" We all go only as far as we have given ourselves permission to go.\n\n\u2022 **Review \"Boundary Setting\" (Chapter 7, page 176):** In essence, abuse is the failure to observe boundaries. Your boundaries\u2014or where you end and others begin, what you will or will not permit others to do to you (or what you will do to them)\u2014are critical in abuse.\n\n_Resources for dealing with abusive situations_\n\nBOOKS\n\nAlthough many books on abuse speak directly to women\u2014since 85 percent of abuse victims are women\u2014these should not be dismissed by men who are living with abuse:\n\n_Love and Addiction_ , by Stanton Peele with Archie Brodsky\n\n_The Verbally Abusive Relationship: How to Recover_ , by Patricia Evans\n\n_Why Does He Do That? Inside the Mind of Angry and Controlling Men_ , by Lundy Bancroft\n\nGUIDED MEDITATIONS\n\n\"Guided Meditations for Self Healing,\" by Jack Kornfield: www.jackkornfield.com, www.soundstrue.com\n\n\"Heartbreak, Abandonment, and Betrayal,\" by Belleruth Naparstek: www.lifejourneys.com\n\n\"Meditations for Emotional Healing,\" by Tara Brach: www.soundstrue.com, www.tarabrach.com\n\nThe meditations above are also available at www.amazon.com and itunes.\n\nWEBSITES\n\nNational Domestic Abuse Hotline: www.thehotline.org. This website contains a wealth of information, resources, links, support, and guidance.\n\nFinding a Therapist\n\nIf you believe it would be helpful to seek therapy for support in overcoming addiction or other mental health or emotional issues, here are some tips on finding someone who suits you. You are seeking someone who is qualified to address your particular problem areas, who is not locked into an agenda at odds with your own, whose point of view is simpatico with your values, and whose opinion you respect.\n\n\u2022 **Get referrals:** Ask trusted friends who share your sensibilities and worldview for recommendations.\n\n\u2022 **Research:** Go online and read client reviews or visit therapists' websites and read their philosophies and writing.\n\n\u2022 **Interview:** Your relationship with your therapist is an important one. Remember that you are seeking to hire someone for a service, and not everyone will possess the specific skills or perspective you are looking for. Inquire whether they offer free initial consultations, or at least speak with them by phone. Before you go in or speak with the person, make note of what qualities are important to you in a therapist. Ask questions about his or her approach and philosophy. Keep interviewing until you find someone who is a good fit for you.\n\n\u2022 **Ask about payment:** Some therapists will take insurance, others will offer a sliding scale to low-income clients. Ask about your options.\n\n\u2022 **Trust your gut:** Therapists will often encourage their clients to venture out of their comfort zone, which is appropriate. However, it's important for you to distinguish between challenging yourself and violating your values. It is a red flag if a therapist instructs you to do something that offends or compromises your values. Immediately express your reservations. Don't be pressured into doing anything you don't believe is right. If you are feeling bullied or manipulated, the odds are that your feelings are correct. Trust yourself and move on.\n\n\u2022 Review \"Boundaries and Addiction Treatment\" in Chapter 7 (page 180), \"Find Professional Help\" in Chapter 7 (page 163), and \"Mental Health,\" including types of therapy, in Chapter 8 (page 203).\n\n_Resources to help you find a therapist_\n\nHakomi (meditation-based) Psychotherapy: \n\n_Inside Rehab: The Surprising Truth About Addiction Treatment?_ and _How to Get Help That Works,_ by Anne M. Fletcher Psych Central, Therapist Directory: http:\/\/psychcentral.com\/find-help]\n\nPsychology Today, Therapy Directory: therapists.psychologytoday.com\n\nPsychology Today, Therapy Directory: therapists.psychologytoday.com\n\nEducation and Career\n\nThe PERFECT Program is based on the belief that you will overcome addiction when you connect with your true self instead of an addiction, follow your values and the purposes these lead to, and pursue the resulting goals you select. Any other form of addiction therapy or resolution is stopgap, and cannot have the fundamental link to your heart and mind that true recovery requires. Following are resources for pursuing your education and desired job or career.\n\nIf you are considering going back to school, but don't know where to start, let me offer you some practical help:\n\n\u2022 If you need to earn your GED (General Education Diploma), visit the GED Testing Service website (www.gedtestingservice.com) to find resources and information. You may even contact them by phone or e-mail to get help.\n\n\u2022 Stay away from the for-profit colleges you see advertised on TV. They're extremely expensive, their standards are low, and they are not as successful at finding placement for their graduates as established educational institutions.\n\n\u2022 Ask yourself if you want to pursue a degree or a trade.\n\n\u2022 Choose a few areas that interest you and that you believe you have an affinity for, and that might be a practical choice for your future. For instance, you might love philosophy, but consider what positions that field of study will qualify you to hold once you have earned your degree.\n\n\u2022 Get online and see if there are any local schools that offer what you are looking for.\n\n\u2022 Contact the schools and make an appointment with their admissions adviser or the adviser for the particular program or degree you are interested in.\n\n\u2022 Before your meeting, make sure you have a list of questions and goals, so that they can guide you effectively toward meeting or reassessing your goals.\n\n\u2022 There are many options for funding. Make an appointment with the Financial Aid office. You might find that you qualify for a loan, scholarship, or grant.\n\n\u2022 If you are short on time, check to see if your school offers online courses or night courses, as well as child care.\n\nIf your goals are occupation-oriented\u2014say you would like to work in a particular field, seek promotion in your current job, or even start your own business\u2014there is guidance and resources for you, too.\n\n\u2022 Many community colleges offer career-counseling services for students.\n\n\u2022 Visit your state's government page (which will normally be www.[fillinyourstate].gov and seek out their Employment Services under their Human Services Department. You might discover that your state has what's called \"Vocational Rehabilitation,\" which provides counseling in all aspects of finding employment.\n\n\u2022 A well-composed resume is required. Find a professional resume-writing service that can provide you with a neat, thorough resume. It is worth the money.\n\nIf you are seeking to advance in your current employment, there are several approaches you can take:\n\n\u2022 Complete your Goals Worksheet, but include some time-specific goals: for instance, where would you like to be in a year's time, five years' time? What will you have to do to meet these goals (e.g., more education or training)? Find out if your company will cover all or some of the costs of your further education.\n\n\u2022 Make contact with others at your employment who have already met the goals that you have set for yourself, and ask them for guidance.\n\n\u2022 Do the best job you can do in your current position.\n\n\u2022 Keep your ear to the ground and ask around, at work and on the outside! You might find that another business can offer you more opportunities for advancement.\n\nPerhaps you are interested in starting your own business. How do you go about that?\n\n\u2022 The first thing to do is to contact your local Small Business Association. They offer free business counseling, no matter what stage you are in\u2014even if you are just contemplating the idea. They also offer classes in several areas, from bookkeeping to preparing an effective business plan.\n\n\u2022 Speaking of business plans: This is a crucial step, even if you have no intention of presenting it to a bank for a loan. Doing so will help you clarify your goals and recognize whether or not you are being realistic.\n\n\u2022 Start small and let your business grow organically. There is always the temptation to throw all your time and money into a new business, because it's so exciting. However, there is a lot to learn along the way, and you don't want to miss those lessons\u2014or find yourself in too far over your head and in debt before you have an opportunity to make effective adjustments.\n\n\u2022 Do your research. This does not mean simply buying a book. Talk to others who are running businesses like the one you want to create. (You know the definition of an expert? Someone who has already done what you want to do.) If you have the opportunity, work for one of these businesses, so you can experience their reality.\n\n\u2022 Based on your goals, values, and journal exercises, examine whether it is realistic for you to devote yourself to the type of business you have in mind.\n\nFinancial Management\n\nFinally, no other strictly practical matter will sidetrack you from achieving recovery the way financial distress can do. Likewise, financial distractions will undermine your life goals almost as much as will legal, health, family, and emotional problems. Yet\u2014of these things\u2014finances are the easiest to control through limited, but concentrated, effort. So let's tackle finances and restore your peace of mind. No matter how much of a mess you have on your hands, you can pull yourself out of it and keep yourself out. Schedule time on your calendar to devote to this. When that time comes, shut off your phone, iPad, and so on, and then break this task down into a series of manageable mini-goals.\n\n\u2022 Organize all your bills. This process of organization should help you gain some clarity and sense of control over your situation. Even if you find that you are more in debt than you expected, or are overwhelmed by what you must face up to, you have taken an enormous step forward, and there is support available to help you prioritize and tackle your financial issues.\n\n\u2022 If you have unopened mail and bills accumulating around your house or on your desk, put them all in one place. Find a container\u2014perhaps a paper bag or a box\u2014to put everything in.\n\n\u2022 Once you have everything in one place, you're going to sort through it. Clear a workspace for yourself, perhaps a kitchen table or even the floor, and create two categories: Save and Discard. In your Save pile, put all the bills or paperwork that you will need to deal with either right away or at some point in the future, and then items you should file away. In the Discard pile, include everything that is redundant (save only the most recent of each type of bill). Be careful about how you dispose of the material in your Discard pile, because it may contain sensitive information. If you have access to a shredder, use it. Remove the Discard pile from your workspace as quickly as possible, to get it off your mind.\n\n\u2022 Now, you will want to break down your Save pile into a few more categories. Again, clear your workspace of clutter, especially your Discard pile. Your categories here will include items you can deal with immediately\u2014for instance, bills you can afford to pay on the spot; items you must take further action on or get more information about before they can be dealt with\u2014for instance, you may have to make a phone call about payment arrangements; and items that must be filed. So: Now; Later; and File.\n\n\u2022 In a notebook, create a checklist that corresponds to each pile. For the Now pile, simply create an entry for each item. For the Later pile, create an entry for each item, and underneath it write down the steps you need to take. If you have phone calls to make, copy down the contact information, your account number, how and when you will contact the debt-holder or other party, how much you owe, or any relevant information you'll need to take those further steps. You may be aware of financial obligations for which you have no paperwork on hand. Add these to your list, along with the steps you need to take to find out exactly what to do. For your File pile, examine your items one by one and determine what categories they belong in: financial statements, receipts, credit card statements, mortgage statements.\n\n\u2022 If there is anything you can handle right now, do it, and check it off your list.\n\n\u2022 Speak to a debt counselor. Now that you have a better handle on your situation and understand what needs to be addressed, you will have the information you need to present to a counselor who can help you. Be wary of the \"debt consolidation\" services you hear advertised on TV or radio. Instead, seek out an accredited, nonprofit organization whose counselors can mentor you in budgeting without ulterior motives. Check out the National Foundation for Credit Counseling (www.nfcc.org) to find counseling in your area. They offer a wealth of information and guidance in several areas of financial concern.\n\n\u2022 If you would like to know what your credit score is, be similarly wary of the businesses you see advertised. They may say they offer free information, but you often can find yourself paying for unnecessary information or services. All three credit-reporting agencies are required, by law, to provide you with a free copy of your credit report and score once a year, and they have set up a website where you can request your reports\u2014www.annualcreditreport.com. The best place for you to start is at the Federal Trade Commission website\u2014www.ftc.gov\u2014where you will find the clearest instructions.\n\n\u2022 Avoid predatory lenders! That includes car title loan businesses, check-cashing services, and car dealers or other businesses that promise to finance anyone, \"Bad Debt OK!\" These businesses exist solely for the purpose of putting you further into debt and ruining your credit. That, in fact, is their business plan. They exist to prey on desperation. There are always other options, including the following.\n\n\u2022 Contact your creditors for a payment arrangement. Utility companies, for example, normally will do everything they can to prevent cutting you off, if you are simply willing to make the phone call. Credit card companies likewise are motivated to arrange a \"workout.\" Don't ask how I know such things, which are explained at .\n\n\u2022 Contact your local social services organization. It's possible they can provide you with emergency help.\n\n\u2022 Make an appointment with the Credit Counseling Service, who may be able to direct you to other resources.\n\n\u2022 Seek the services of a reputable financial adviser or a group that works with people like you, and that is not oriented primarily towards hijacking additional fees from you. Such resources exist, as represented by Nona Jordan in the previous chapter: nonajordan.com.\n\n\u2022 Do not be afraid or ashamed to ask for help from friends or family or your church, if this is an option for you. They may be glad to help you in the service of your larger goals.\n\n\u2022 Implement a system: Create an inbox dedicated only to your bills, and carve out a time every month for taking action on each item. Have envelopes, stamps, pens, a calculator, and whatever other items you may need to facilitate the task. You can set up automatic bill-paying through your bank for almost any service you pay for, from your utilities to your credit card bills.\n\n\u2022 Review your bank statement regularly to determine whether there are any recurring expenses that you can't afford. For instance, perhaps in a state of inebriation you signed up for an online service and then promptly forgot about it! Are you being charged monthly for anything you're not using? (Again, something we all might know about.) Perhaps your bank is debiting a monthly service charge from your account that you were unaware of.\n\n\u2022 If you are technically adept, you can consider exploring a free money-management system, like mint.com, which allows you to set spending limits, make up a household budget, send yourself alerts when bills are coming due, and receive notifications when your balance is getting low or when you have been charged a service fee.\n\n\u2022 Explore free classes in money management.\n\n\u2022 Find books online, at the library, or at your local bookstore about basic financial management.\n\n\u2022 Really, it will all work out\u2014they no longer have debtors' prisons. Note: For relief take Dickens's _Little Dorrit_ \u2014DVD or book\u2014out from your local library, or read online (). Don't buy a copy of this or any other book or DVD (except for _Recover!_ ) and any other practical guides or make any other nonessential purchases.\n\nBeyond This Chapter\u2014And the Book\n\nThis chapter gives you a quick, comprehensive overview and ideas for managing various life circumstances that you may have difficulty coping with during your recovery. It is also worthwhile to create your own personal \"Triage\" list, based on your experience, focusing on areas you expect you will have trouble with and solutions you believe will work best for you. If you find that a challenge you anticipate was not covered in this chapter, you might still peruse the lists and resources I have provided. But if you cannot find what you're looking for, I encourage you to explore on your own. Get online. Local and state government agencies offer you public resources. Don't be afraid to make phone calls and ask questions, request direction, or ask for referrals. Pursuing resources on your own is an empowering exercise of the life skills\u2014of the life outlook\u2014that The PERFECT Program is about.\n\n_Afterword_\n\nWrite Your Own Conclusion\n\n_Recover!_ is a title in the form of an imperative\u2014something that you _should_ do. But this book tells you not to follow other people's scripts or philosophies other than those you develop for yourself from your own experience. You can abstain or moderate or curtail harms; you can join groups\u2014religious, AA, or otherwise\u2014or go it on your own. You can meditate while sitting upright, standing, walking, or\u2014from a yoga position\u2014standing on your head.\n\nIn telling you that how you proceed from here is up to you, I am simply stating the obvious. Still, I want you to get better\u2014to improve your state of mind, your life, your relationship to the people and the world around you, and to cease your addiction(s). But I want to send you off with more than good wishes. I want to remind you of all that you have accomplished by thinking about addiction and learning and practicing The PERFECT Program.\n\nYou began with deep concerns about yourself and your life. And you have embarked on a journey to recover your real self, the person you are capable of being, based on your values and purpose. This is the meaning of your existence\u2014much of which is already in place, perhaps for you to be reminded of, some of which it is yet for you to discover. As well as rediscovering who you are, you have developed the tools and skills to lead a positive, non-addicted lifestyle. You have worked on focusing your mind in new ways while accepting your true self as part of your permanent, true recovery; you have practiced communication, listening, and problem-solving skills, including how to quit your addiction and maintain your freedom; you have developed plans both for daily living and for your future\u2014including how you deal with work, finances, intimacy, your family; how you will spend your \"free\" time and with whom; and what your life goals are and will be. That's effort well spent.\n\nYou have learned through The PERFECT Program to be mindful of yourself and your world, to embrace your inner being and real self, to breathe easily, not to panic, to keep your goals and techniques in mind, and to move carefully but resolutely ahead. You have also learned two essential things. The first is to celebrate your existence on earth, to take full advantage of and appreciate this world and all that it contains\u2014people, nature, opportunities, pleasure, yourself.\n\nWhich leads to the second key thing that you have learned. You can\u2014you must\u2014count on yourself\u2014look to yourself as your own best advocate, supporter, and friend. You have been engaged in imagining and planning your life after reading this book. Now you must navigate that life. This isn't a command I'm giving you\u2014it's a statement of an inevitable reality. No one else can pilot your life for you\u2014at least if you are following The PERFECT Program.\n\nThere are many other people in your life who are wishing you well besides me and Ilse Thompson. For one thing, you can seek support and have contact with fellow travelers on this voyage\u2014and this does _not_ mean simply those who have suffered addictions identical to your own. There are _many_ people for whom you are becoming a new, non-addicted person\u2014children, spouses, partners, parents, teachers, faith leaders, friends, extended family, members of communities you choose to become part of\u2014all of whom will benefit from, and deeply appreciate, who you are becoming.\n\nI wish you a good journey as you go forth to realize your potential. This is not always a safe and sure journey\u2014there are rocks and turns on every path. But it is a journey that you are capable of making and that you will make\u2014sooner or later. The PERFECT Program is just a road map to make that passage a little quicker and easier.\n\nNow carry on with my and Ilse's best wishes,\n\n_Stanton Peele and Ilse Thompson_\n\n_Co-Founders, The PERFECT Program_\nNotes\n\nIntroduction\n\n. Centers for Disease Control and Prevention, _Smoking Cessation_. National Center for Chronic Disease Prevention and Health Promotion: Office on Smoking and Health, 2012, .\n\nChapter 1\n\n. Carl Hart's book, _High Price: A Neuroscientist's Journey of Self-Discovery That Challenges Everything You Know About Drugs and Society_ (HarperCollins, 2013), details the myths surrounding drugs, and particularly meth, whose uncontrollable, brain-destroying effects Hart's research contests. Hart \"even takes on 'meth mouth,' noting that the dry mouth symptoms that have been blamed for the terrible dental problems seen in some methamphetamine users also accompany the use of legal amphetamines and some antidepressant medications.\" Maia Szalavitz, \"Why the Myth of the Meth-Damaged Brain May Hinder Recovery,\" _Time Healthland_ , November 21, 2011, .\n\nChapter 2\n\n. Hillel R. Alpert, Gregory N. Connolly, and Lois Biener, \"A Prospective Cohort Study Challenging the Effectiveness of Population-Based Medical Intervention for Smoking Cessation,\" _Tobacco Control_ , January 10, 2012, .\n\n. Jacqueline Detwiler, \"The Ten Hardest Drugs to Quit,\" _The Fix,_ December 20, 2011, .\n\n. Stanton Peele, \"Proof That Treating Addiction with Drugs Doesn't Work,\" _Huffington Post,_ January 11, 2012, .\n\n. Benedict Carey, \"Nicotine Gum and Skin Patch Face New Doubt,\" _New York Times_ , January 9, 2012, .\n\n. Lindsey F. Stead, Rafael Perera, Chris Bullen et al. \"Nicotine Replacement Therapy for Smoking Cessation,\" _The Cochrane Library,_ November 14, 2012, .\n\n. Brad W. Lundahl, Chelsea Kunz, Cynthia Brownell et al., \"A Meta-Analysis of Motivational Interviewing: Twenty-Five Years of Empirical Studies,\" _Research on Social Work Practice_ 20(2):137\u2013160, 2010.\n\n. Stanton Peele, _The Meaning of Addiction_ , 2nd ed. (San Francisco: Jossey-Bass, 1998); .\n\n. American Psychiatric Association, _APA Corrects New York Times Article on Changes to DSM-5's Substance Use Disorders_ (Arlington, VA: American Psychiatric Association, 2012).\n\n. Stanton Peele, \"Addiction in Society: Blinded by Biochemistry,\" _Psychology Today_ , September 1, 2010, .\n\n. See \"The Amen Solution,\" http:\/\/www.amenclinicscom\/?p=5158&option=com_wordpress&Itemid=204.\n\n. Mika Brzezinski, _Obsessed: America's Food Addiction\u2014And My Own_ (Philadelphia: Weinstein\/Perseus, 2013).\n\n. Michael Moss, _Salt Sugar Fat: How the Food Giants Hooked Us_ (New York: Random House, 2013).\n\n. Stanton Peele with Archie Brodsky, _Love and Addiction_ (New York: NAL\/Signet, 1975).\n\n. James Burkett and Larry Young, \"The Behavioral, Anatomical and Pharmacological Parallels Between Social Attachment, Love and Addiction,\" _Psychopharmacology_ 224(1):1\u201326, 2012, .\n\n. Lindsay Abrams, \"'Sex Addiction' Redefined,\" _The Atlantic_ , October 19, 2012, .\n\n. Pernille Gronkjaer (director), \"'Love Addict' Movie Explores Love Addiction, 'Fantasy Universe,'\" _Huffington Post,_ October 22, 2012, .\n\n. National Institute on Alcohol Abuse and Alcoholism, \"Alcoholism Isn't What It Used to Be,\" _NIAAA Spectrum_ , September 2009, .\n\n. Shari Roan, \"You Can Cut Back,\" _Los Angeles Times_ , November 13, 2009, .\n\n. Centers for Disease Control and Prevention, \"Smoking Cessation: Nicotine Dependence,\" in _Smoking & Tobacco Use_, .\n\n. Stanton Peele, \"This Is How People Quit Addictions,\" _Huffington Post,_ September 13, 2011, .\n\n. I could fill this book, as I did my _Addiction-Proof Your Child_ (Random House\/Three Rivers Press, 2007), with examples and data demonstrating parental remission for alcoholics and drug addicts, like the woman who felt her baby kicking, put down her drink, and said, \"I'll never touch another drop,\" and didn't. Here are two more cases: While discussing Mika Brzezinski's best-selling book on her eating disorder, _Obsessed_ , fellow MSNBC host Al Sharpton described how he lost over one hundred pounds (and you think you have a tough addiction to quit?): \"My youngest daughter said to me, 'Daddy, why are you so fat?'\" Meanwhile, I was at a dinner party with parents of young children. I asked the six parents present if any had smoked\u2014all had. All had quit. I looked at one particularly attentive father of two young children, and said, \"I bet you and your wife knew you would sooner kill yourself than not quit\"\u2014his wife nodded vigorously.\n\n. Stanton Peele, \"The 7 Hardest Addictions to Quit\u2014Love Is the Worst,\" _Psychology Today Blogs_ , December 15, 2008, .\n\n. Lizzie Crocker, \"Mika Brzezinski on 'Obsession,' Her New Book About Food Addiction,\" _Women in the World_ , May 9, 2013, .\n\n. Keith S. Ditman, George G. Crawford, Edward W. Forby et al., \"A Controlled Experiment on the Use of Court Probation for Drunk Arrests,\" _American Journal of Psychiatry_ 124:160\u2013163, 1967.\n\n. Jeffrey Brandsma, Maxie Maultsby, and Richard J. Walsh, _Outpatient Treatment of Alcoholism_ (Baltimore: University Park Press, 1980).\n\n. William R. Miller, Verner S. Westerberg, Richard J. Harris, and J. Scott Tonigan, \"What Predicts Relapse? Prospective Testing of Antecedent Models,\" _Addiction_ 91(Supplement):155\u2013171, 1996, .\n\n. Think New York City\u2014and its population of immigrants\u2014where Prohibition was largely ignored. Mark Lerner, _Dry Manhattan: Prohibition in New York City_ (Cambridge, MA: Harvard University Press, 2008).\n\n. John Kobler, _Ardent Spirits: The Rise and Fall of Prohibition_ (New York: Putnam, 1973).\n\n. Stanton Peele, \"Why Medicine for Addiction Will Make Our Problems Worse,\" _Huffington Post,_ July 20, 2011, .\n\n. These points were made in the exhibit \"American Spirits: The Rise and Fall of Prohibition,\" at the National Constitution Center in Philadelphia, based on Daniel Okrent's _Last Call_ , which also inspired Ken Burns and Lynn Novick's 2011 PBS documentary, _Prohibition_. The exhibit examines \"the patchwork of strange liquor laws that began after the repeal of Prohibition and persist to this day. In Oklahoma, no one under 21, not even a baby in its mother's arms, can be in a liquor store; in Indiana, convenience stores can sell beer only at room temperature.\" Edward Rothstein, \"A Look at Prohibition, Hardly Dry,\" _New York Times_ , October 18, 2012, .\n\n. Stanton Peele, \"Alcohol: The Good Side,\" _Los Angeles Times_ , July 21, 2010, .\n\n. Carl Hart, _High Price: A Neuroscientist's Journey of Self-Discovery That Challenges Everything You Know About Drugs and Society_ (New York: HarperCollins, 2013).\n\n. Douglas Quenqua, \"Rethinking Addiction's Roots, and Its Treatment,\" _New York Times_ , July 10, 2011, .\n\n. Stanton Peele, \"Addiction in Society: Blinded by Biochemistry,\" _Psychology Today_ , September 1, 2010 .\n\n. Stanton Peele, \"Reductionism in the Psychology of the Eighties: Can Biochemistry Eliminate Addiction, Mental Illness, and Pain?\" _American Psychologist_ 36:807\u2013818, 1981, .\n\n. Stanton Peele, \"You've Got Your Nerves in My Depression,\" Reason.com, April 30, 2013. Review of Edward Shorter, _How Everyone Became Depressed_ (New York: Oxford, 2013), .\n\n. Stanton Peele, \"The Search for Mental Illness in the Brain, Part I: The Disappointment of the Human Genome Project,\" _Huffington Post,_ May 17, 2013, .\n\n. Abigail Zuger, \"A General in the Drug War,\" _New York Times_ , June 13, 2011, .\n\n. Howard Markel, \"The D.S.M. Gets Addiction Right,\" _New York Times_ , June 5, 2012, .\n\n. Ian Urbina, \"Addiction Diagnoses May Rise Under Guideline Changes,\" _New York Times_ , May 11, 2012, .\n\n. Maia Szalavitz, \"Naomi Wolf's _Vagina_ Aside, What Neuroscience Really Says About Female Desire,\" _Time_ , September 18, 2012, .\n\n. Sam Anderson, \"Angry Birds, Farmville and Other Hyperaddictive 'Stupid Games,'\" _New York Times Magazine_ , April 4, 2012, www.nytimes.com\/2012\/04\/08\/magazine\/angry-birds-farmville-and-other-hyperaddictive-stupid-games.html.\n\n. Claire Bates, \"Why Only Some People Become Addicted to Drugs: Scans of Cocaine Users Reveal Brain Shape Could Be to Blame,\" _Mail Online,_ January 18, 2013, .\n\n. Fulton Timm Crews and Charlotte Ann Boettiger, \"Impulsivity, Frontal Lobes and Risk for Addiction,\" _Pharmacology, Biochemistry, and Behavior_ 93(3): 237\u2013247, 2009.\n\n. Joseph LeDoux, _Synaptic Self: How Our Brains Become Who We Are_ (New York: Penguin, 2003).\n\n. Maia Szalavitz, \"Siblings Brain Study Sheds Light on Roots of Addiction,\" _Time_ , February 3, 2012, .\n\n. Marnia Robinson and Gary Wilson, \"Guys Who Gave Up Porn: On Sex and Romance,\" _Psychology Today Blogs_ , February 1, 2012, .\n\n. Rachael Rettner, \"'Sex Addiction' Still Not an Official Disorder,\" _Livescience_ , December 6, 2012, .\n\n. Maia Szalavitz, \"My Name Is John and I Am a Sex Addict (Or Maybe Not),\" _Time,_ July 23, 2013, .\n\n. Marnia Robinson and Gary Wilson, \"Was the Cowardly Lion Just Masturbating Too Much?\" _Psychology Today Blogs_ , January. 11, 2010, .\n\n. Robinson and Wilson, \"Guys Who Gave Up Porn: On Sex and Romance.\"\n\n. Alan Leshner, \"Addiction Is a Brain Disease, and It Matters,\" _Science_ , October 3, 278(5335):45\u201347, 1997.\n\n. \n\n. Marc Lewis, \"How I Quit. . . . At Least, How I Think I Quit,\" .\n\n. Maia Szalavitz, \"Why the Myth of the Meth-Damaged Brain May Hinder Recovery,\" _Time_ , November 21, 2011, .\n\n. Vincent J. Felitti, \"The Origins of Addiction: Evidence from the Adverse Childhood Experiences Study.\" English version of the article published in Germany as \"Urspr\u00fcnge des Suchtverhaltens\u2014Evidenzen aus einer Studie zu belastenden Kindheitserfahrungen,\" _Praxis der Kinderpsychologie und Kinderpsychiatrie_ 52:547\u2013559, 2003, .\n\n. Norman Doidge, _The Brain That Changes Itself: Stories of Personal Triumph from the Frontiers of Brain Science_ (New York: Viking Books, 2007).\n\n. Stanton Peele, \"Dr. Drew, Mindy McCready, and Me,\" _Psychology Today Blogs_ , March 15, 2013, .\n\n. This might be called \"free will.\" But, of course, today the idea that you direct your behavior and control yourself requires a neurological explanation. This has been provided by the iconoclastic but unimpeachable neurological psychologist, Elkhonon Goldberg, who proposes the brain's frontal lobes as the executor of your free will. But _Recover!_ is _not_ a treatise in philosophy and neuroscience.\n\n. Andrew Newburg and Mark Robert Waldman, _How God Changes Your Brain: Breakthrough Findings from a Leading Neuroscientist_ (New York: Random House, Ballantine, 2010).\n\n. Kelly McGonigal, _Maximum Willpower: How to Master the New Science of Self-Control_ (New York: Macmillan, 2012).\n\n. Health-care reform\u2014which is absolutely necessary\u2014coupled with parity legislation dictating that mental and addictive problems receive the same coverage as traditional illnesses will inevitably expand the rehab business. And, in the interests of disclosure, as the developer of a treatment program, I have received insurance payments and may well benefit from these further developments.\n\n. Thomas Rodgers, \"Why Do College Students Love Getting Wasted?\" _Salon.com_ , August 28, 2011, .\n\n. \n\n. \"Angelina Jolie: Humanitarian,\" _Time_ , May 14, 2013, .\n\n. \"Angelina Jolie Biography,\" _Scribe Town_ , December 30, 2011, .\n\n. Chris Laxamana, \"#050: Dr. Adi Jaffe and Dr. Marc Kern,\" _DrDrew_ , May 17, 2013. In this remarkable podcast, Dr. Drew interviews two leading practitioners of harm reduction, including the idea that many former addicts can use substances safely again. Dr. Drew repeatedly asserts that he is \"a scientist,\" while trying to explain away the reality of the information provided by Drs. Jaffe and Kern, including their own life experiences. .\n\n. NIAAA, \"Alcoholism Isn't What It Used to Be.\"\n\n. Deborah A. Dawson, Bridget F. Grant, Frederick S. Stinson, et al., \"Recovery from DSM-IV Alcohol Dependence, United States, 2001\u20132002,\" _Addiction_ 100:281\u2013292, 2005.\n\n. Bridget F. Grant and Deborah A. Dawson, \"Introduction to the National Epidemiologic Survey on Alcohol and Related Conditions,\" _National Institute of Alcohol Abuse and Alcoholism Publications_ , .\n\n. Effectiveness Bank Bulletin, \"Findings,\" October 30, 2013, . This bulletin incorporated the following three studies: Catalina Lopez-Quintero, Deborah S. Hasin, Jos\u00e9 P\u00e9rez de los Cobos, et al. \"Probability and Predictors of Remission from Life-Time Nicotine, Alcohol, Cannabis or Cocaine Dependence: Results from the National Epidemiologic Survey on Alcohol and Related Conditions,\" _Addiction_ 106(3):657\u2013669; Gene Heyman, \"Quitting Drugs: Quantitative and Qualitative Features,\" _Annual Review of Clinical Psychology_ 9:29\u201359, 2013; William L. White, _Recovery\/Remission from Substance Use Disorders: An Analysis of Reported Outcomes in 415 Scientific Reports, 1868\u20132011_ (Great Lakes Addiction Technology Transfer Center, Philadelphia Department of Behavioral Health and Intellectual Disability Services, and Northeast Addiction Technology Transfer Center, 2012).\n\n. Substance Abuse and Mental Health Services Administration, \"Substance Dependence or Abuse in the Past Year, by Detailed Age Category: Percentages, 2011,\" _National Survey on Drug Use and Health_ , Table 5.3B, .\n\n. Stanton Peele, \"Addiction: The Analgesic Experience,\" _Human Nature_ , September, 1978, .\n\n. Lee M. Robins et al., \"Drug Use by U.S. Army Enlisted Men in Vietnam: A Follow-Up on Their Return Home,\" _American Journal of Epidemiology_ 99:235\u2013249, 1974.\n\n. Harold Mulford, one of the great researchers and thinkers in the alcoholism\/addiction field, said it first: \"Contrary to the traditional clinical view of the alcoholism disease process, progress in the alcoholic process is neither inevitable nor irreversible. Eventually, the balance of natural forces shifts to decelerate progress in the alcoholic process and to accelerate the rehabilitation process.\" \"Rethinking the Alcohol Problem: A Natural Processes Model,\" _Journal of Drug Issues_ 14:38, 1984.\n\n. William R. Miller, Paula L. Wilbourne, and Jennifer E. Hettema, \"What Works? A Summary of Alcohol Treatment Outcome Research,\" in Reid K. Hester and William R. Miller, eds., _Handbook of Alcoholism Treatment Approaches: Effective Alternatives_ , 3rd ed. (Boston: Allyn & Bacon, 2003), pp. 13\u201363.\n\n. William R. Miller, Allen Zweben, and Bruce Johnson, \"Evidence-Based Treatment,\" _Journal of Substance Abuse Treatment_ 29:267\u2013276, 2005, .\n\n. Linda Brown et al., \"Participant Perspectives on Mindfulness Meditation Training for Anxiety in Schizophrenia,\" _American Journal of Psychiatric Rehabilitation_ 13(3):224\u2013242, 2010, .\n\n. Paula DeSanto, _Effective Addiction Treatment: The Minnesota Alternative_ (Minnesota: Minnesota Alternatives, 2012), .\n\n. Sarah Bowen et al., \"Mindfulness-Based Relapse Prevention for Substance Use Disorders: A Pilot Efficacy Trial,\" _Substance Abuse_ 30(4):295\u2013305, 2009. This work is from Alan Marlatt's group at the University of Washington. This book is dedicated to Alan's memory.\n\nChapter 3\n\n. The HAMS (Harm Reduction for Alcohol) Network, under Kenneth Anderson, has developed valuable materials for assessing and going through withdrawal. HAMS regards the most medically risky withdrawal as occurring with alcohol and benzodiazapines (tranquilizers). \"What Is Alcohol Withdrawal?\" . In the case of alcohol, major withdrawal (delirium tremens, which is marked by hallucinations) is most clearly life threatening, although the mid-level withdrawal Alex underwent is likewise medically challenging. \"Less than 50% of alcohol-dependent persons develop any significant withdrawal symptoms that require pharmacologic treatment upon cessation of alcohol intake. The lifetime risk for developing delirium tremens (DTs) among chronic alcoholics is estimated at 5\u201310%. Only 5% of patients with ethanol withdrawal progress to delirium tremens.\" \"Delirium Tremens,\" Medscape, . HAMS provides guidance on your likelihood of undergoing withdrawal. \"The Odds of Going Through Alcohol Withdrawal,\" . Whatever these risks, people undergo medically unsupervised alcohol withdrawal all the time. For people doing so, HAMS recommends tapering (drinking lesser amounts to suppress withdrawal\u2014in medical settings, doctors nearly always administer benzodiazapines to accomplish the same purpose). \"How To Taper Off Alcohol,\" . And, of course, people need a backup plan should they begin to show serious withdrawal symptoms.\n\n. Jane Gross, \"Plan to Become an Ex-Smoker for Good,\" _New York Times_ , November 12, 2012, .\n\n. Alan Marlatt and his colleagues have amply demonstrated this. See Mary E. Larimer, Rebekka S. Palmer, and G. Alan Marlatt, \"Relapse Prevention: An Overview of Marlatt's Cognitive-Behavioral Model,\" _Alcohol Research and Health_ 23(2):151\u201360, 1999, .\n\n. Substance Abuse and Mental Health Services Administration, \"News Release: A Working Definition of 'Recovery' from Mental Disorders and Substance Use Disorders,\" December 22, 2011, .\n\n. Substance Abuse and Mental Health Services Administration, \"Recovery Defined\u2014A Unified Working Definition and Set of Principles,\" May 20, 2011, .\n\n. Alex Copello, Jim Orford, Ray Hodgson, and Gillian Tober, _Social Behaviour and Network Therapy for Alcohol Problems_ (London: Routledge, 2009). In a trial, SBNT and motivational enhancement therapy were compared\u2014the treatments had equal efficacy as measured by improved mental health and quality of life, decreased alcohol use and dependence, and fewer secondary problems. .\n\n. Stanton Peele, \"The 7 Hardest Addictions to Quit: Love Is the Worst!,\" _Psychology Today Blogs_ , December 15, 2008. .\n\n. Rachel Yoder, \"Strung Out on Love and Checked In for Treatment,\" _New York Times_ , June 11, 2006, www.nytimes.com\/2006\/06\/11\/fashion\/sundaystyles\/11love.html.\n\n. Stanton Peele, _The Meaning of Addiction_ (Lexington, MA: Lexington Books, 1985; San Francisco: Jossey-Bass, 1998), .\n\n. Pamela Druckerman, _Bringing Up B\u00e9b\u00e9_ (New York, Penguin, 2012). See review by Susannah Meadows, \"Raising the Perfect Child, with Time for Smoke Breaks,\" _New York Times_ , February 7, 2012, .\n\n. Roy F. Baumeister and John Tierney, _Willpower: Rediscovering the Greatest Human Strength_ (New York: Penguin Books, 2012).\n\n. Sandra Aamodt and Sam Wang, \"Building Self-Control, the American Way,\" _New York Times_ , February 17, 2012, www.nytimes.com\/2012\/02\/19\/opinion\/sunday\/building-self-control-the-american-way.html.\n\n. Kate Taylor, \"Council Speaker Recounts Her Struggles with Bulimia and Alcoholism,\" _New York Times_ , May 14, 2013, .\n\n. Andrew Goldman, \"Billy Joel on Not Working and Not Giving Up Drinking,\" _New York Times Magazine_ , May 26, 2013, www.nytimes.com\/2013\/05\/26\/magazine\/billy-joel-on-not-working-and-not-giving-up-drinking.html.\n\n. Chris Laxamana, \"#050: Dr. Adi Jaffe and Dr. Marc Kern,\" _DrDrew_ , May 17, 2013. In this remarkable podcast, Dr. Drew interviews two leading practitioners of harm reduction, including the idea that many former addicts can use substances safely again. Dr. Drew repeatedly asserts that he is \"a scientist,\" while trying to explain away the reality of the information provided by Drs. Jaffe and Kern, including their own life experiences. .\n\n. Kenneth Anderson, \"First Do No Harm,\" _The Fix_ , March 27, 2013, .\n\n. Kenneth Anderson, \"Alcohol Harm Reduction Compared to Harm Reduction for Other Drugs,\" Presented at the Ninth National Harm Reduction Conference, Portland, OR, November 16, 2012, .\n\n. Megan McLemore, \"A Step Backward for AIDS Prevention,\" _Huffington Post_ , August 28, 2012, .\n\n. Harm reduction therapy for even intense drug users has been spearheaded by Patt Denning, Jeannie Little, and Adina Glickman, _Over the Influence: The Harm Reduction Guide for Managing Drugs and Alcohol_ (New York: Guilford, 2004).\n\n. Nick Heather and Ian Robertson, _Controlled Drinking_ (New York: Routledge, 1984).\n\nChapter 4\n\n. Ellen J. Langer, _Mindfulness_ (Cambridge, MA: Perseus, 1989).\n\n. U.C.L.A. Mindful Awareness Center, University of Massachusetts Medical School Center for Mindfulness, .\n\n. National Cancer Institute, _Smoking and Tobacco Control Monograph Series #15: Those Who Continue to Smoke_ (Washington, DC: National Institutes of Health, 2003), .\n\n. Sarah Bowen, Neha Chawla, and G. Alan Marlatt, _Mindfulness-Based Relapse Prevention for Addictive Behaviors: A Clinician's Guide_ (New York: Guilford, 2011).\n\n. Pavel Somov, _Eating the Moment: 141 Mindful Practices to Overcome Overeating One Meal at a Time_ (Oakland, CA: New Harbinger, 2008).\n\n. Abby Ellin, \"Fat and Thin Find Common Ground,\" _New York Times_ , October 10, 2013 .\n\n. Stanton Peele, \"Addiction in Society: Blinded by Biochemistry,\" _Psychology Today_ , September 1, 2010 .\n\n. Sarah Bowen et al., \"Mindfulness-Based Relapse Prevention for Substance Use Disorders: A Pilot Efficacy Trial,\" _Substance Abuse_ 30:205\u2013305, 2009.\n\nChapter 5\n\n. Maia Szalavitz, \"Being Ashamed of Drinking Prompts Relapse, Not Recovery,\" _Time_ , February 7, 2013, .\n\n. William L. White and William R. Miller, \"The Use of Confrontation in Addiction Treatment: History, Science and Time for Change,\" _Counselor_ 8(4): 12\u201330, 2007.\n\n. Alcoholics Anonymous World Organization, _Step One: \"We admitted we were powerless over alcohol_.\" New York: AA World Services, www.aa.org\/twelveandtwelve\/en_pdfs\/en_step1.pdf.\n\n. National Center for Mental Health Checkups, Columbia University, _Teens and Eating Disorders_ (New York: Columbia University, 2013), .\n\n. Ken Anderson, \"First Do No Harm,\" _The Fix_ , March 27, 2013, .\n\n. James Robert Milam and Katherine Ketchum, _Under the Influence_ (New York: Bantam, 1981).\n\n. Bob Egelko, \"Appeals Court Says Requirement to Attend AA Unconstitutional,\" _San Francisco Chronicle_ , September 7, 2007, .\n\n. Helen Y. Yang, Andrew S. Fox, Alexander J. Shackman et al., \"Compassion Training Alters Altruism and Neural Responses to Suffering,\" _Psychological Science_ , May 21, 2013, .\n\n. Kelly McGonigal, _The Willpower Instinct: How Self-Control Works, Why It Matters, and What You Can Do to Get More of It_ (New York: Penguin, 2012).\n\n. Alex Witchel, \"How Jeannette Walls Spins Good Stories Out of Bad Memories,\" _New York Times_ , May 24, 2013, www.nytimes.com\/2013\/05\/26\/magazine\/how-jeannette-walls-spins-good-stories-out-of-bad-memories.html.\n\nChapter 6\n\n. Roy F. Baumeister and John Tierney, _Willpower: Rediscovering the Greatest Human Strength_ (New York: Penguin Books, 2012). The book is filled with complicated brain, neurochemical, and evolutionary psychology analyses\u2014indeed, the book stands as an illustration of how speculative and unhelpful such notions are when applied to a common-sense idea.\n\n. James O. Prochaska and Carlo DiClemente, _The Transtheoretical Approach: Towards a Systematic Eclectic Framework_ (Homewood, IL: Dow Jones Irwin, 1984).\n\nChapter 7\n\n. G. Alan Marlatt and Dennis M. Donovan, _Relapse Prevention, Second Edition: Maintenance Strategies in the Treatment of Addictive Behaviors_ (New York: Guilford, 2005).\n\n. Roy F. Baumeister and John Tierney, _Willpower: Rediscovering the Greatest Human Strength_ (New York: Penguin Books, 2012).\n\n. John Tierney, \"Why You Won't Be the Person You Expect to Be,\" _New York Times_ , January 3, 2013, www.nytimes.com\/2013\/01\/04\/science\/study-in-science-shows-end-of-history-illusion.html.\n\n. Alex Copello, Jim Orford, Ray Hodgson et al., \"Social Behaviour and Network Therapy: Basic Principles and Early Experience,\" _Addictive Behaviors_ 27(3):345\u2013366, 2002.\n\n. In the interest of a spouse or loved one's not only getting out of the way, but being a support for overcoming addiction, PERFECT opposes current 12-step thinking. AA and its derivatives have complex differences in how they view spouses of alcoholics. Alanon is a group for spouses (nearly always meaning wives) of alcoholics that is famous for telling members it's the alcoholic's problem and the wife's only chance to survive is by understanding that her husband is diseased. \"You can't control your alcoholic spouse\" is the Alanon mantra. \"Don't try.\" By Alanon's lights, William should leave Sabrina to her own devices (meaning she had better go to AA) and look out for himself. More recently, however, has come the idea of codependence (distantly related to the idea of love addiction I have developed). Codependents\u2014again, _usually_ women\u2014have a disease just like the alcoholic or drug addict\u2014only the object of their disease is the addicted person. In codependence terms, Sabrina and William have equivalent, supporting diseases against which each of them must struggle by working the 12 steps!\n\n. The indexes for both _Tools_ and _Truth_ list a number of places where the community reinforcement approach (CRA)\u2014including reciprocity marital counseling\u2014is discussed.\n\n. Pavel Somov, _Present Perfect: A Mindfulness Approach to Letting Go of Perfectionism and the Need for Control_ (Oakland, CA: New Harbinger, 2010).\n\n. Susan Sontag, _Regarding the Pain of Others_ (New York: Picador, 2003).\n\n. Warren St. John, \"Sorrow So Sweet,\" _New York Times_ , August 24, 2002, www.nytimes.com\/2002\/08\/24\/arts\/sorrow-so-sweet-a-guilty-pleasure-in-another-s-woe.html.\n\n. William L. White and William R. Miller, \"The Use of Confrontation in Addiction Treatment: History, Science and Time for Change,\" _Counselor_ 8(4):12\u201330, 2007.\n\n. Maia Szalavitz, _Help at Any Cost: How the Troubled-Teen Industry Cons Parents and Hurts Kids_ (New York: Riverhead, 2006).\n\n. Robert J. Meyers and Brenda L. Wolfe, _Get Your Loved One Sober: Alternatives to Nagging, Pleading, and Threatening_ (Center City, MN: Hazelden, 2004).\n\n. Maia Szalavitz, \"Is Dr. Drew Too Dangerous for Prime Time?\" _The Fix_ , February 25, 2012, .\n\n. Stanton Peele and Alan Cudmore, \"Intervene This,\" _Huffington Post_ , January 23, 2012, .\n\n. William R. Miller, Robert J. Meyers, and J. Scott Tonigan, \"Engaging the Unmotivated in Treatment for Alcohol Problems: A Comparison of Three Strategies for Intervention Through Family Members,\" _Journal of Consulting and Clinical Psychology_ 67: 688\u201397, 1999.\n\n. William R. Miller and Stephen Rollnick, _Motivational Interviewing_ , _Third Edition: Helping People Change_ (New York: Guilford Press, 2013).\n\nChapter 8\n\n. Roy F. Baumeister and John Tierney, _Willpower: Rediscovering the Greatest Human Strength_ (New York: Penguin Books, 2012).\n\n. The best book about assessing potential addiction treatment facilities and therapists is Anne M. Fletcher, _Inside Rehab: The Surprising Truth About Addiction Treatment\u2014And How to Get Help That Works_ (New York: Viking, 2013).\n\n. G. Alan Marlatt, ed., _Harm Reduction: Pragmatic Strategies for Managing High-Risk Behaviors_ , 2nd ed. (New York: Guilford, 1998).\n\n. Stanton Peele and Bruce K. Alexander, \"Theories of Addiction,\" in Stanton Peele, _The Meaning of Addiction_ , 2nd ed. (San Francisco: Jossey-Bass, 1998), pp. 47\u201372; .\n\n. Sarah Bowen, Neha Chawla, and G. Alan Marlatt, _Mindfulness-Based Relapse Prevention for Addictive Behaviors: A Clinician's Guide_ (New York: Guilford, 2011).\n\n. There are now many books and programs on this topic. See Thich Nht Hanh and Lilian Cheung, _Savor: Mindful Eating, Mindful Life_ (New York: Harper, 2011).\n\nChapter 9\n\n. Maia Szalavitz, \"Being Ashamed of Drinking Prompts Relapse, Not Recovery,\" _Time_ , February 7, 2013, .\n\n. nonajordan.com\nIndex\n\nAbstinence\n\naddiction, free will, and, 58\u201361\n\nbasing treatment on, ,\n\nbreaking goal of, , , ,\n\nchoosing, 63\u201364\n\nmoderation vs., 64\u201369\n\nserving larger life goals,\n\nvalue of, 61\u201362\n\nAbuse models of addiction, 29\u201331\n\nAbusive relationships, 256\u2013258\n\nAccountability, ,\n\nAction stage, , 144\u2013145\n\nActivating free will, 59\u201361, 95\u201396\n\nAddiction. _See also_ Addiction models; Hitting bottom\n\napplying S.P.O.T. acronym to, 95\u201396\n\nartificial nature of, 39\u201340\n\nbenefits of, 134\u2013135\n\nboundary violations in,\n\ncombatting with mindfulness,\n\nat core of life,\n\ndefining, 13\u201315,\n\ndiscovering meaning beyond, 15\u201316\n\nas disease, xvi\n\ndopamine production and, 22\u201323\n\neffect of environments on, 38\u201339\n\nfilling one's life after, 55\u201356\n\nfinding reason to beat, , ,\n\nharm reduction for, 69\u201372\n\nhitting bottom, 88\u201389\n\nhow it appears in your life,\n\nlogic of, 39\u201340,\n\nmanifesting from trauma, 111\u2013115\n\nmapping DNA to,\n\nmore value in other things than,\n\nmyths about, 16\u201317\n\nnon-abstinent, 214\u2013215\n\noutgrowing, 14\u201315, 33\u201335,\n\novercoming, 36\u201337, 39\u201342, 107\u2013111,\n\noverriding,\n\nPERFECT program's approach to, xvi\u2013xviii, xix\n\npsychological sources of, 29\u201331\n\nrole of shame in quitting, 28\u201329\n\nRose's life of, 3\u20139\n\nsetting goals about,\n\nshifting balance in, 83\u201387\n\nStages of Change in, 142\u2013145\n\nsubstances and behaviors as symptom of,\n\ntemporary nature of, 17\u201318\n\ntreatment industry around,\n\ntypes of,\n\nwithdrawing from love, 57\u201358\n\nyou are not your, , 78\u201380\n\nAddiction models\n\naddiction as disease, xvii, 18\u201320,\n\nmindfulness in, xvi\u2013xvii\n\nneuroscientific, xvi, 12\u201313, ,\n\ntypes of, xv\u2013xvi\n\nAddiction Self-Assessment Questionnaire, 49\u201350\n\nAddictive urges\n\ndealing with, 241\u2013242\n\nmeditation suppressing cravings,\n\ntracking in journal,\n\ntriggering relapses, 211\u2013215\n\nusing S.P.O.T. exercise for, 95\u201396,\n\nAddicts. _See also_ Addictive urges\n\naligning with authentic self, , 78\u201380, 90\u201392\n\nchoosing abstinence, 61\u201364\n\nchoosing moderation, 64\u201369\n\ncomparing brains with siblings, 24\u201325\n\ndealing with decision making, 164\u2013166\n\ngetting straight, 195\u2013197\n\nhow people stop being, 27\u201329\n\nlearning to think like non-addict,\n\nmeeting addicted self,\n\nmyths about, 16\u201317\n\nnot your addiction, , 78\u201380\n\noverwhelm experienced by, xviii, , 252\u2013253\n\nredemptive narratives by,\n\nsearching for what's wrong, 111\u2013115\n\nthinking like, 12\u201313\n\nAdult Children of Alcoholics (ACoA), 114\u2013115\n\nAlcoholics Anonymous. _See_ 12-step programs\n\nAlcoholism, xvi, ,\n\nAllen, Woody,\n\nAmerican Board of Addiction Medicine (ABAM),\n\nAmerican Psychiatric Association,\n\nAnderson, Ken,\n\nAnorexia, 105\u2013107\n\nAnti-addiction skills\n\narranging social situations, 159\u2013162\n\nasking for help, 163\u2013164\n\nchanging routine,\n\ncounseling programs supporting, 162\u2013163\n\ncountering addictive triggers, 155\u2013156\n\nfinding reasons to quit,\n\nmeditating on discomfort, 156\u2013157\n\npermission for later addictive behavior, 158\u2013159\n\nself-acceptance as,\n\ntriggers for addictive behavior, 154\u2013155\n\nwriting out logical conclusions,\n\nAudio resources. _See_ Resources\n\nAuthentic self\n\naddiction not, , 78\u201380\n\naligning with, 90\u201392\n\nfinding with mindfulness, , 139\u2013141\n\nrediscovering integrity, xx, 140\u2013142\n\nBalance\n\nmaintaining,\n\nrelapses and, 207\u2013208\n\nshifting with mindfulness, 83\u201387\n\nBarrymore, Drew, 34\u201335,\n\nBaumeister, Roy, ,\n\nBeing present exercise, 190\u2013191\n\nBeliefs\n\nexamining negative,\n\nexercises for converting, ,\n\nshifting to positive, 110\u2013111\n\nBinge-eating, 63\u201364, 66\u201367\n\nBody imagery, 105\u2013106,\n\nBooks. _See_ Resources\n\nBoundary setting\n\nabusive relationships and,\n\naccepting people close to you,\n\nlearning, 176\u2013179\n\nrespecting others' boundaries, 226\u2013227\n\nviolations in addiction treatment,\n\nwhen helping others,\n\nBrach, Tara,\n\nBrain. _See_ Neuroscientific addiction model\n\n_Brainwashed_ (Satel and Lilienfeld),\n\nBreathing\n\ndifficulties focusing on,\n\nturning attention to, , 99\u2013100\n\nBrigati, Eddie,\n\nBrodsky, Archie, , , ,\n\nBrzezinski, Mika,\n\nBuddha,\n\nBuddhism\n\nforgiveness practice, 131\u2013132\n\nGod concept in, 119\u2013120\n\ntenet of loving kindness, 116\u2013117,\n\nCareer, 260\u2013262\n\nCavaliere, Felix,\n\nCelebrate (\"C\")\n\ncreating rituals, traditions, and celebrations, 227\u2013229\n\ndiscovering joy, 230\u2013233\n\nfinding rewards, 224\u2013225\n\ngoals for,\n\nhonoring accomplishments, xx, 221\u2013222\n\nhonoring what you value, 225\u2013227\n\nmaking changes, 233\u2013235\n\nreflecting on accomplishments, 218\u2013219\n\ntracking your progress, 219\u2013221\n\nunderstanding perfectionism, 223\u2013224\n\nCenter for Global Tobacco Control, 12\u201313\n\nChange. _See also_ Preparing for change\n\ncreating disillusionment, 135\u2013136\n\nembarking on, 192\u2013195\n\nfor everyone, 233\u2013235\n\nfounding on grace,\n\nhitting bottom vs. making, 89\u201390\n\nimplementing,\n\nreflection on,\n\nshaking up your routine,\n\nstages of, 142\u2013146\n\nstarting PERFECT program for,\n\ntracking, ,\n\n_Chemistry Between Us, The_ (Young),\n\nChildren, 29\u201331,\n\nCh\u00f6dron, Pema,\n\nCigarette smoking. _See_ Smoking\n\nCleary, Thomas,\n\n_Close to Home_ ,\n\nCognitive-behavior therapy (CBT), ,\n\nCommunicating boundaries, 177\u2013178\n\nCommunity. _See also_ CRA\n\ncreating, 197\u2013200\n\nimportance in recovery,\n\nlocating meetings with like-minded people,\n\nunplugging from online,\n\nCommunity reinforcement approach. _See_ CRA\n\nCompulsions. _See_ Addictive urges\n\nConnolly, Gregory N.,\n\nContacting creditors, 264\u2013265\n\nContemplation stage, ,\n\nContentment, 140\u2013141\n\nCoping. _See also_ Fortify\n\ndeveloping skill for, 169\u2013170\n\nduring detox,\n\nFortify as means of, xx\n\nsubstances and behaviors as symptoms of,\n\nCounseling\n\ndebt,\n\nescaping abusive relationships,\n\nfinding therapists, 258\u2013259\n\nreciprocity marital, 162\u2013163\n\nCRA (community reinforcement approach)\n\nCRAFT, , 181\u2013183\n\nreciprocity marital counseling in, 162\u2013163\n\nCravings. _See_ Addictive urges\n\nCuring road rage,\n\nDecision making\n\ndealing with, 164\u2013166\n\nopportunities for good,\n\nproblem solving and, 166\u2013167\n\nrole in recovery,\n\nDeflecting compliments, 108\u2013109\n\nDelaying gratification, 59\u201369\n\nDetoxing\n\nmedical supervision while,\n\npreparing for, , 51\u201356\n\n_Diagnostic and Statistical Manual of Mental Disorders, 5th edition (DSM-5)_ , , ,\n\n_Dietary Guidelines for Americans_ ,\n\nDisease model, xvi, 18\u201320,\n\nDisillusionment, 135\u2013139\n\nDonne, John,\n\nDonovan, Dennis,\n\nDopamine, 22\u201323,\n\nDrugs\n\nabuse by age, 37\u201338\n\nbrain scans for users of, 22\u201323\n\nconsuming without addiction to,\n\nenvironment and use of, 38\u201339\n\nharm reduction for users, 69\u201372\n\nmedia's portrayal of,\n\npercentage dependent on,\n\npreparing to quit,\n\nEating disorders\n\nabstaining from binge-eating, 63\u201364, 66\u201367\n\nanorexia and body imagery, 105\u2013107\n\navoiding relapse with, 214\u2013215\n\ncase study of, 105\u2013106\n\nfood addictions, , 17\u201318\n\npreparing for detox period,\n\ntemperance attitudes and,\n\nEducation and career, 200\u2013201, 260\u2013262\n\nEmbark (\"E\")\n\ncreating community and intimacy, 197\u2013200\n\neducation and work, 200\u2013201\n\nequilibrium with, xx\n\nfinancial skills, 201\u2013202\n\ngetting straight, 195\u2013197\n\ngoals for,\n\ninternal resources for recovery, 40\u201342\n\nleisure pursuits, 202\u2013203\n\nmaintaining balance,\n\nmental health, 203\u2013204\n\npreparing with self-knowledge, 188\u2013192\n\nreframing failure, 204\u2013206\n\nrelapse detours, 206\u2013215\n\nself-care,\n\nspiritual or humanitarian beliefs,\n\ntaking first steps, 192\u2013195\n\nEmbrace (\"E\")\n\naccentuating positive, 107\u2013111\n\ndeveloping self-acceptance, xx, xxi, 116\u2013120\n\neffect of self-negativity, 104\u2013107\n\ngoals of,\n\njournaling on forgiveness, 130\u2013131\n\nloving kindness meditation, 129\u2013130\n\nmisguided searching for what's wrong with you, 111\u2013115\n\nreducing harm with self-forgiveness, 126\u2013128\n\nself-forgiveness, 120\u2013122, 123\u2013128\n\nEmotional skills\n\nappreciating others' successes, 175\u2013176\n\nbeing true to yourself, 173\u2013175\n\ncountering feelings of unworthiness, 246\u2013247\n\ncuring road rage,\n\nmaintaining perspective, 53\u201354, 171\u2013172\n\nEnvironments\n\nmeditation, 47\u201348, 94\u201395\n\nrole in addiction, 38\u201339\n\nsetting up your domestic, 196\u2013197\n\nEvidence-based treatment,\n\nExercises\n\nacknowledging success,\n\ncollecting valuables as touchstone,\n\nconsidering effects to make change, 222\u2013223\n\nconverting negative beliefs, ,\n\ncreating rituals,\n\nduring withdrawal phase,\n\nfinding addictive triggers,\n\nfinding mindfulness,\n\ngrounding self with,\n\nhow others see you, 191\u2013192\n\njournaling on forgiveness, 130\u2013131\n\nlocating reason to quit,\n\npracticing listening,\n\nquestioning, 184\u2013185\n\nrelapse moments of truth,\n\nreviewing and pursuing values,\n\nreviewing social life,\n\nself-compassion, 117\u2013118\n\nself-knowledge, 190\u2013192\n\nshifting to positive perspective, ,\n\nS.O.B.E.R., 244\u2013245\n\nsorting personal values,\n\nExhausting willpower, , 158\u2013159\n\nFailure. _See also_ Relapses\n\nlack of resolve and, 134\u2013135\n\nreframing, 204\u2013206\n\nFamily\n\nabusive relationships in,\n\naccepting, ,\n\naddiction patterns in, 34\u201335\n\nallowing rights for, 178\u2013179\n\nappreciating successes of, 175\u2013176\n\nasking for help, 163\u2013164\n\ncommunicating boundaries to, 177\u2013178\n\nCRAFT approach with, , 181\u2013183\n\nhow others see you, 191\u2013192\n\nmotivational interviewing with, 183\u2013185\n\nsetting boundaries on helping,\n\nundermining addicts' gains, 161\u2013162\n\nFantasies about recovery, 135\u2013136,\n\nFinancial management, 201\u2013202, 262\u2013266\n\nFletcher, Anne,\n\nFlexibility in boundaries,\n\nFood. _See_ Eating disorders\n\nForgiveness. _See also_ Self-forgiveness\n\nhealing through, 125\u2013126\n\nloving kindness meditation on, 129\u2013130\n\nFortify (\"F\")\n\nanti-addiction skills, 154\u2013164\n\ncoping skills, xx, 169\u2013170\n\ndecision making, 164\u2013167\n\ndeveloping life skills, 152\u2013154\n\nemotional skills, 171\u2013176\n\ngoal setting, , 167\u2013169\n\nlistening, 170\u2013171,\n\nmotivational interviewing, 183\u2013185\n\nsetting boundaries, 176\u2013181\n\nusing CRAFT, , 181\u2013183\n\nFree will\n\nactivating, 59\u201361, 95\u201396\n\nexercising for recovery, 59\u201361\n\ngrace and, 80\u201383\n\nFriends\n\naccepting, ,\n\nappreciating successes of, 175\u2013176\n\nasking for help, 163\u2013164,\n\ncommunicating boundaries to, 177\u2013178\n\nhow they see you, 191\u2013192\n\nmaking, 198\u2013199\n\nmotivational interviewing with, 183\u2013185\n\nrespecting boundaries of, 178\u2013179, 226\u2013227\n\nsetting boundaries on helping,\n\nFrontal lobe theory\n\ndisproving,\n\nas source of self-control, 23\u201325,\n\nGambling, , 66\u201367\n\nGetting straight. _See also_ Embark; Preparing for change; Relapses\n\nabout,\n\neffective treatment for, 41\u201342\n\nfocusing on reasons for, ,\n\ngetting back on track, 209\u2013210\n\nhonoring commitments, 195\u2013196\n\nhow people stop being addicts, 27\u201329\n\nnavigating relapses, 211\u2013215\n\nonline accountability resources,\n\noutgrowing addiction, 14\u201315, 33\u201335,\n\novercoming addiction, 40\u201342\n\nrole of shame in, 28\u201329\n\nsetting up domestic spaces, 196\u2013197\n\ntracking your progress, 219\u2013221\n\nwriting your own script for, 267\u2013268\n\n_Getting Wasted_ (Vander Ven),\n\n_Glass Castle, The_ (Walls),\n\nGoals\n\nchoosing,\n\nimportance of, 136\u2013137\n\nlisting, , 194\u2013195\n\nsetting, 73\u201374, 167\u2013169,\n\ntracking,\n\nusing for change, 193\u2013195\n\nGoals Worksheet, 73\u201374, 168\u2013169\n\nGoing off the wagon, , , ,\n\nGrace\n\ncalling forth, 190\u2013191\n\nconnotations of,\n\njournaling about, 96\u201397\n\nrecognizing moments of, 80\u201383\n\nsparking motivation with moments of, 248\u2013249\n\nGuilt\n\nreducing effect of, 126\u2013128\n\nrole in relapse,\n\nstaying stuck in, 122\u2013123\n\nHahn, Thich Nhat,\n\nHarm reduction\n\ndefined,\n\nexercise supporting,\n\nresources for, 245\u2013246\n\nself-forgiveness as means of, 126\u2013128\n\nHarris, Richard, 74\u201375,\n\nHart, Carl, ,\n\nHaving a place,\n\nHazelden,\n\nHelp\n\nasking for, 163\u2013164,\n\nboundaries for giving,\n\ngetting detox,\n\nHitting bottom\n\nconcept of, 88\u201389\n\nmaking changes vs., 89\u201390\n\nmyth of,\n\nrelapses vs., ,\n\nRose's experience, 6\u20137\n\nHome environment, 196\u2013197\n\n\"How I Quit . . . \" (Lewis),\n\nHuman Genome Project,\n\nHumanitarian beliefs,\n\nHumiliation,\n\nHypersexual disorder,\n\nHypofrontalism,\n\n_I Ching_ (Cleary),\n\n_In the Realm of Hungry Ghosts_ (Mat\u00e9),\n\n_Inside Rehab_ (Fletcher),\n\nIntegrity, xx, 140\u2013142\n\niTunes podcasts,\n\nJaffe, Dr. Adi, , ,\n\nJoel, Billy, 65\u201366\n\nJolie, Angelina,\n\nJordan, Nona, 233\u2013235\n\nJournals\n\ndetailing strengths and vulnerabilities,\n\ndeveloping emotional skills with,\n\nexercise on forgiveness, 130\u2013131\n\ngetting,\n\nidentifying relapse triggers,\n\nlisting change goals, 194\u2013195\n\nlisting communities in, 197\u2013198\n\nmonitoring cravings in,\n\nnoting accomplishments in, ,\n\nPersonal and PERFECT,\n\nquestions about relapsing,\n\nreflecting on values in, 149\u2013150\n\nreframing failures,\n\nreviewing decision making,\n\ntracking changes in PERFECT, ,\n\nwriting about grace, 96\u201397\n\nJoy, 230\u2013233\n\nKern, Marc,\n\nLack of motivation, 247\u2013249\n\nLeDoux, Joseph,\n\nLeisure pursuits, 202\u2013203\n\nLeshner, Alan,\n\nLewis, Marc, ,\n\nLife skills\n\nanti-addiction skills, 154\u2013164\n\nboundary setting, 176\u2013181\n\ncoping skills, 169\u2013170\n\nCRAFT, , 181\u2013183\n\ndecision making, 164\u2013167\n\ndeveloping, 152\u2013154\n\neducation and work, 200\u2013201\n\nemotional skills, 171\u2013176\n\ngoal setting, 167\u2013169\n\nleisure pursuits, 202\u2013203\n\nlistening, 170\u2013171, ,\n\nmoney management, 201\u2013202\n\nmotivational interviewing, 183\u2013185\n\nself-care,\n\ntypes of,\n\nLilienfeld, Scott,\n\nListening\n\nto others' feedback,\n\npracticing, 170\u2013171,\n\n_Little Girl Lost_ (Barrymore),\n\nLoneliness, 250\u2013252\n\nLove\n\naddictions to, 17\u201318\n\navoiding relapse with, 214\u2013215\n\ndeveloping intimacy and, 199\u2013200\n\nescaping abusive relationships, 256\u2013258\n\nwithdrawal from, 57\u201358\n\n_Love and Addiction_ (Peele with Brodsky), , , ,\n\nLoving kindness\n\nabout, 116\u2013117\n\nmeditation on, 129\u2013130\n\npracticing,\n\nMaintaining perspective\n\non emotions, 53\u201354, 171\u2013172\n\nnavigating relapses, 211\u2013215\n\nusing mindfulness skills for,\n\nMaintenance stage, ,\n\nMaking amends,\n\nMaking friends, 198\u2013199\n\nMarital counseling, 162\u2013163\n\nMarlatt, Alan, , , , , 206\u2013207, 244\u2013245\n\nMat\u00e9, Gabor, 29\u201330\n\n_Meaning of Addiction, The_ (Peele),\n\nMedically supervised detox,\n\nMeditation\n\nbasic, 93\u201394, 98\u2013100\n\ndealing with abusive situations,\n\ndifficulties with, 239\u2013240\n\nforgiveness of others and self,\n\nguided, , , , , ,\n\nloving kindness, 129\u2013130,\n\nmeditating on discomfort, 156\u2013157\n\nmindfulness approach to, 93\u201394, 98\u2013100\n\noptions for, 100\u2013101\n\npreparing place for, 47\u201348,\n\nrediscovering values,\n\ntips for, 94\u201395\n\n_Memoirs of an Addicted Brain_ (Lewis),\n\nMental health, 203\u2013204\n\nMethamphetamines,\n\nMiller, Derek,\n\nMiller, William,\n\nMind-body programs,\n\nMindfulness. _See also_ Meditation; Mindfulness skills\n\nabout, xvi-xvii,\n\naligning with authentic self, 90\u201392\n\ncombatting addiction with, 92\u201393\n\ncuring road rage with,\n\ndefined,\n\nfinding true self, , 139\u2013141\n\ngrace and, 82\u201383\n\njoy in, 231\u2013233\n\nmeditation practices using, 98\u2013101\n\nmeeting addicted self,\n\nself-acceptance encouraged in, 41\u201342\n\nMindfulness skills, 92\u2013101. _See also_ Meditation\n\nactivating free will, 95\u201396\n\napproach to meditation, 93\u201394, 98\u2013100\n\njournal exercises, 96\u201397\n\nmaintaining perspective with,\n\nmeditation options checklist,\n\nmind-body programs developing,\n\nsupporting social situations with, 160\u2013162\n\nvariations on,\n\nyoga, 97\u201398\n\nMirroring,\n\nModeration, 64\u201369, 74\u201375\n\nMorality. _See also_ Religion and spirituality\n\nattitudes toward addictive substances,\n\nfinding humanitarian beliefs,\n\nTemperance Movement's, 18\u201319\n\nMotivational interviewing (MI), 183\u2013185\n\n_Moving Toward Balance_ (Yee),\n\nMoyers, Bill, 27\u201328\n\nNation, Carry A.,\n\nNational Cancer Institute,\n\nNational Epidemiologic Survey on Alcohol and Related Conditions (NESARC), 36\u201337\n\nNational Health Interview Survey (NHIS),\n\nNational Institute on Alcohol Abuse and Alcoholism (NIAAA), ,\n\nNational Institute on Drug Abuse (NIDA),\n\nNational Survey on Drug Use and Health,\n\nNeuromeme, ,\n\nNeuroscientific addiction model\n\nabuse models of addiction, 29\u201331\n\ndisproving frontal lobe theory,\n\ndopamine and pleasure receptors, 22\u201323,\n\nfrontal lobe theory, 23\u201325, ,\n\nlinking AA ideology with, ,\n\nneuroplasticity of brain, 31\u201333\n\npsychological sources of addiction, 29\u201331\n\nsearching for location of addiction, 20\u201321\n\nself-control and, 23\u201327\n\nself-defeating approach of, xvi\n\nsuccess rates with,\n\ntenet of powerlessness, xvi\n\nthinking like addict, 12\u201313\n\nNicotine replacement therapy (NRT), 12\u201313\n\nNon-abstinent addictions, 214\u2013215\n\nOnline communities,\n\nOvercoming addiction. _See_ Embark\n\nOverride (\"O\"),\n\nOverwhelm\n\nexperienced by addicts, xviii\n\novercoming,\n\ntriage when feeling, 252\u2013253\n\nPain, ,\n\nPause (\"P\"). _See also_ Mindfulness skills\n\naligning with authentic self, 90\u201392\n\ndeveloping mindfulness skills, 92\u2013101\n\ndistinguishing self from addiction, 78\u201380\n\ngoals and purpose for,\n\nhitting bottom, 88\u201390\n\nmindfulness found with, xx-xi\n\nrecognizing moments of grace, 80\u201383\n\nshifting balance with mindfulness, 83\u201387\n\nin S.P.O.T. acronym, 95\u201396\n\nPeele, Stanton, , , , , , ,\n\nPERFECT Program, The\n\nacronym for, xx-xxi\n\napproaches to addiction in, xvi\u2013xviii, 40\u201342\n\ncreating recovery goals within, 60\u201361\n\ndemystifying addiction, xvi-xviii, xix\n\nforgiveness practice in, 131\u2013132\n\nfounding change on grace,\n\nreframing self-control,\n\nrestoring quality of life with, 67\u201368\n\nself-acceptance in, xxi, 104\u2013107, 118\u2013120\n\nshifting perspective with, 109\u2013111\n\nPerfectionism, 223\u2013224\n\nPersonal empowerment,\n\nPinsky, Dr. Drew, , ,\n\nPositive values\n\nfinding, 107\u2013111, ,\n\nnoting in journal,\n\nPowerlessness\n\nas potential cause of addiction,\n\nreinforced by 12 steps, xviii, , , 16\u201317,\n\nPrecontemplation stage, ,\n\nPreparation stage, ,\n\nPreparing for change\n\nactivating self-control and free will, 59\u201361\n\ncaring for whole person, 54\u201355\n\ncase study in,\n\nconsidering abstinence, 61\u201364\n\nfilling one's life after addiction, 55\u201356\n\nharm reduction strategies when, 69\u201372\n\nhow addiction appears in your life,\n\njournals needed,\n\nmaintaining perspective when, 53\u201354\n\nmoderation as model, 64\u201369\n\nre-creating non-addicted life, 55\u201356\n\nseeking support,\n\ntracking in PERFECT Journal, ,\n\nunderstanding you are not an addict, , 78\u201380\n\nwithdrawing from love, 57\u201358\n\nProblem solving, 166\u2013167\n\nProhibition, ,\n\nPsychological issues\n\nleading to relapses, 54\u201355\n\nlogic of addiction, 39\u201340,\n\nas sources of addiction, 29\u201331\n\nPurpose, life, ,\n\nQuestioning exercise, 184\u2013185\n\nQuestionnaires\n\naddiction self-assessment, 49\u201350\n\nvalues, 50\u201351, ,\n\nQuinn, Christine, 63\u201364,\n\nQuitting. _See_ Getting straight\n\n_Radical Acceptance_ (Brach),\n\nRage-aholics, ,\n\nReciprocity marital counseling, 162\u2013163\n\nRecovery\n\nbuilding new life in, ,\n\ndeveloping self-acceptance, 116\u2013120\n\nexercising free will for, 59\u201361\n\nfinding goals for,\n\nharm reduction, 69\u201372\n\ninternal resources for, 40\u201342\n\nfrom methamphetamines,\n\nmoderation after, 64\u201369\n\nmoments of grace as core of, 80\u201383\n\nNESARC findings on, 36\u201337\n\nas normal part of experience, 13\u201314\n\nrole of shame in, 28\u201329, 104\u2013105\n\nRose's experience with, 3\u20139\n\nSAMSHA's definition of,\n\ntraditional views of,\n\ntruths about, 35\u201336\n\nwithdrawals during,\n\nRedefining boundaries,\n\nRedemptive narratives,\n\nRediscover (\"R\")\n\nbecoming your values, 134\u2013141\n\ncontinuing value assessments, 147\u2013149\n\nfinding contentment, 140\u2013141\n\nfocusing on your identity, 142\u2013145\n\ngoals for,\n\nintegrity with, xx, 140\u2013142\n\nreflection on change and acceptance,\n\nreturning to true purpose,\n\nReframing\n\nanxiety and depression,\n\nfailure, 204\u2013206\n\nrelapses, 208\u2013209\n\nRelapse prevention\n\ndeveloping skills for,\n\nmeditation practices in,\n\nmindfulness skills as bedrock of,\n\nresources for, 245\u2013246\n\nS.O.B.E.R. exercise for, 244\u2013245\n\n_Relapse Prevention_ (Marlatt), ,\n\nRelapses. _See also_ Relapse prevention; Triage\n\ndefined,\n\ndisillusionment and, 137\u2013139\n\nfailures in resolve, 134\u2013135\n\ngetting back on track, 209\u2013210\n\nimbalances triggering, 207\u2013208\n\nmanaging for non-abstinent addictions, 214\u2013215\n\noccurrence of vs. outgrowing addiction, 14\u201315\n\npredicting success through, xix\n\npsychological issues leading to, 54\u201355\n\nrates of,\n\nreframing, 204\u2013206, 208\u2013209\n\nreversing,\n\ntriage practices for, 243\u2013246\n\nReligion and spirituality\n\nforgiveness practice, 131\u2013132\n\nGod concept in Buddhism, 119\u2013120\n\nspiritual beliefs,\n\nspiritual dysmorphia,\n\ntenet of loving kindness, 116\u2013117,\n\nResources\n\ncoping with loneliness,\n\ndealing with abusive situations,\n\nfeeling overwhelmed, 253\u2013254\n\nfinding therapists,\n\nhandling addictive urges,\n\nhelping regain control,\n\nmanaging depression and anxiety, 255\u2013256\n\nmindfulness meditation,\n\npreventing relapse, 245\u2013246\n\nsparking motivation,\n\nsupporting self-worth,\n\nRestak, Richard,\n\nRewriting your story,\n\nRituals, 227\u2013229\n\nRobinson, Marnia,\n\nRodin, Auguste,\n\nRumi,\n\nSatel, Sally,\n\n_Schadenfreude_ ,\n\nSee (\"S\"), 95\u201396\n\nSelf-acceptance\n\naccepting family and,\n\nanti-addiction skills using,\n\nbeing true to yourself, 173\u2013175\n\nbody imagery and, 105\u2013106,\n\ncoping with shortcomings, 169\u2013170\n\ndeveloping, 116\u2013120\n\nfinding positive values, 107\u2013111, ,\n\nimportance of, xxi\n\nPERFECT program's emphasis on, xxi, 104\u2013107, 118\u2013120\n\nself-compassion exercises, 117\u2013118\n\nSelf-care,\n\nSelf-control\n\nactivating free will, 95\u201396\n\nexercised in harm reduction, 71\u201372\n\nexercising for recovery, 59\u201361\n\nexhausting willpower, , 158\u2013159\n\nfrontal lobe of brain and, 23\u201325\n\ngiving up porn addictions, 26\u201327\n\ninstilling in children,\n\nSelf-excuses, , 189\u2013190\n\nSelf-forgiveness\n\ndeveloping, 120\u2013122\n\nharm reduction and, 126\u2013128\n\njournaling on forgiveness, 130\u2013131\n\nself-excusing vs.,\n\nshifting from remorse to, 123\u2013128\n\nSelf-knowledge\n\nallowing self-excuses, 189\u2013190\n\ndefined,\n\ndiscovering motivations, 188\u2013190\n\nexercises for, 190\u2013192\n\njournaling on strengths and vulnerabilities,\n\nmoderation requiring,\n\nreframing relapses, 208\u2013209\n\nsharing your knowledge,\n\n_7 Tools to Beat Addiction_ (Peele),\n\nSexuality, 26\u201327, 67\u201368\n\nShame\n\nrole in quitting addictions, 28\u201329, 104\u2013105\n\nrole in relapse,\n\nSkills. _See_ Mindfulness skills; Life skills\n\nSMART recovery groups,\n\nSmith, Bob,\n\nSmoking\n\nquitting, , 77\u201378, 85\u201386\n\nrates of recovery in,\n\nvalue conflict in,\n\nS.O.B.E.R. exercise, 244\u2013245\n\nSobriety,\n\nSocial skills\n\narranging social situations, 159\u2013162\n\ncreating community and intimacy, 197\u2013200\n\ndeveloping intimacy and love, 199\u2013200\n\nmaking friends, 198\u2013199\n\nreviewing your social life,\n\nSorting\n\nbills and mail, 263\u2013264\n\npersonal values, 148\u2013149\n\nS.P.O.T. acronym, 95\u201396, ,\n\nStages of Change,\n\nStrengths and vulnerabilities,\n\nStress, 165\u2013166\n\nSubstance Abuse and Mental Health Services Administration (SAMHSA), ,\n\nSunday, Billy,\n\nSustaining recovery,\n\nSzalavitz, Maia, ,\n\nTemperance Movement, 18\u201319,\n\nTherapy\n\naddressing mental health with, 203\u2013204\n\ncognitive-behavior, ,\n\nescaping abusive relationships,\n\nfinding therapists, 258\u2013259\n\nnicotine replacement, 12\u201313\n\nreciprocity marital counseling, 162\u2013163\n\nresources on,\n\nseeking treatment from,\n\nThinking\n\nlike addict, 12\u201313\n\nlike non-addict,\n\nin meditation, ,\n\nnegative self-thoughts, 54\u201355\n\nThompson, Ilse,\n\n_Those Who Continue to Smoke_ (National Cancer Institute),\n\nTime\n\nfilling one's, 55\u201356\n\none day at a, , 158\u2013159\n\nTimer,\n\nTrack (\"T\"),\n\nTracking your progress, 219\u2013221\n\nTraumas, 111\u2013115\n\nTriage (\"T\")\n\nabusive relationships, 256\u2013258\n\naddictive urges, 241\u2013242\n\nanxiety or depression, 254\u2013256\n\ndifficulties with meditation, 239\u2013240\n\neducation and career, 260\u2013262\n\nfinancial management, 262\u2013266\n\nfinding therapists, 258\u2013259\n\ngoals for,\n\nlack of motivation, 247\u2013249\n\nloneliness, 250\u2013252\n\noverwhelm, 252\u2013253\n\nrealigning with, xx refocusing priorities,\n\nrelapse and harm reduction practices, 243\u2013246\n\nunworthiness, 246\u2013247\n\nTriggers\n\nidentifying, 154\u2013155, ,\n\nplans to counter, 155\u2013156\n\nrelapses and, 207\u2013208\n\n_Truth About Addiction and Recovery, The_ (Peele),\n\nTwain, Mark,\n\n12-step programs. _See also_ Alcoholics Anonymous\n\naddiction as disease, xvi\n\nappeal to divine intervention,\n\nbased on shame and humiliation, 104\u2013105\n\nmaking amends,\n\nmeaning of sobriety in, , ,\n\nneurochemical terms used to justify,\n\none day at a time in, 158\u2013159\n\npowerlessness reinforced by, xviii, , , 16\u201317,\n\nrelapse rates within,\n\nself-acceptance absent in, xxi, 104\u2013105\n\nself-will in, ,\n\nsense of powerlessness in, xvii, , , 16\u201317,\n\n3rd step,\n\nTzu, Lao,\n\nValues\n\nassessing your, 50\u201351, ,\n\nbasing recovery goals on, 60\u201361\n\ncreating values altar,\n\nfinding, 107\u2013111, , ,\n\ngrace illuminating core, 83\u201384\n\nhonoring your, 188\u2013190, 225\u2013227\n\nmaking changes based on, , 89\u201390, 128\u2013129\n\nValues Questionnaire, 50\u201351, ,\n\nVander Ven, Thomas, 33\u201334\n\nVietnam GIs,\n\nVolkow, Nora, , ,\n\nWalls, Jeannette,\n\nWebsite resources. _See_ Resources\n\nWillenbring, Dr. Mark,\n\nWillpower. _See_ Self-control\n\nWilson, Bill,\n\nWilson, Gary,\n\nWinehouse, Amy,\n\nWithdrawals, , 51\u201356\n\nYee, Rodney,\n\nYoga, 97\u201398\nAbout the Authors\n\n**Stanton Peele** has been a cutting-edge figure in the addiction field for four decades since the publication of _Love and Addiction_ in 1975. He has been a leader in opening up the field to an experiential, culturally and environmentally sensitive understanding of addiction and to practical, life-management approaches to treatment, harm reduction, and self-help. Along the way, Stanton has written twelve books (including _The Meaning of Addiction_ , _Diseasing of America_ , _The Truth About Addiction and Recovery_ , _7 Tools to Beat Addiction_ , and _Addiction-Proof Your Child_ ) and 250 professional articles, has won numerous awards (including from the _Journal of Studies on Alcohol and Drugs_ and the Drug Policy Alliance\u2014the leading drug policy reform organization in America), and has created the Life Process Program for addiction treatment, which continues to be utilized worldwide. Stanton also lectures on addiction around the world, writes the Addiction in Society Blog in _Psychology Today_ (), and blogs as an addiction expert for the Huffington Post (). He was named the best addiction blogger by All Treatment and one of the ten most influential figures in the addiction field by The Fix.\n\n**Ilse Thompson,** co-founder of the blog Stinkin-Thinkin: Muckraking the 12 Step Treatment Industry, is a writer and editor living in Portland, Oregon.\n","meta":{"redpajama_set_name":"RedPajamaBook"}} +{"text":"\nSELECTED FICTION WORKS \nBY L. RON HUBBARD\n\nFANTASY\n\nThe Case of the Friendly Corpse\n\nDeath's Deputy\n\nFear\n\nThe Ghoul\n\nThe Indigestible Triton\n\nSlaves of Sleep & The Masters of Sleep\n\nTypewriter in the Sky\n\nThe Ultimate Adventure\n\nSCIENCE FICTION\n\nBattlefield Earth\n\nThe Conquest of Space\n\nThe End Is Not Yet\n\nFinal Blackout\n\nThe Kilkenny Cats\n\nThe Kingslayer\n\nThe Mission Earth Dekalogy*\n\nOle Doc Methuselah\n\nTo the Stars\n\nADVENTURE\n\nThe Hell Job series\n\nWESTERN\n\nBuckskin Brigades\n\nEmpty Saddles\n\nGuns of Mark Jardine\n\nHot Lead Payoff\n\nA full list of L. Ron Hubbard's \nnovellas and short stories is provided at the back.\n\n*Dekalogy: a group of ten volumes\n\nPublished by \nGalaxy Press, LLC \n7051 Hollywood Boulevard, Suite 200 \nHollywood, CA 90028\n\n\u00a9 2014 L. Ron Hubbard Library. All rights reserved.\n\nAny unauthorized copying, translation, duplication, importation or distribution, in whole or in part, by any means, including electronic copying, storage or transmission, is a violation of applicable laws.\n\nMission Earth is a trademark owned by L. Ron Hubbard Library and is used with permission. Battlefield Earth is a trademark owned by Author Services, Inc. and is used with permission.\n\nHorsemen illustration from Western Story Magazine is \u00a9 and \u2122 Cond\u00e9 Nast Publications and is used with their permission. Fantasy, Far-Flung Adventure and Science Fiction illustrations: Unknown and Astounding Science Fiction copyright \u00a9 by Street & Smith Publications, Inc. Reprinted with permission of Penny Publications, LLC. Cover art: \u00a9 1935 Metropolitan Magazines, Inc. Reprinted with permission of Hachette Filipacchi Media.\n\nISBN 978-1-59212-563-0 EPUB version \nISBN 978-1-59212-756-6 Kindle version \nISBN 978-1-59212-272-1 print version \nISBN 978-1-59212-307-0 audiobook version\n\nLibrary of Congress Control Number: 2007903622\nContents\n\nFOREWORD\n\nFORBIDDEN GOLD\n\nCHAPTER ONE\n\nCHAPTER TWO\n\nCHAPTER THREE\n\nCHAPTER FOUR\n\nCHAPTER FIVE\n\nCHAPTER SIX\n\nCHAPTER SEVEN\n\nCHAPTER EIGHT\n\nCHAPTER NINE\n\nCHAPTER TEN\n\nCHAPTER ELEVEN\n\nCHAPTER TWELVE\n\nCHAPTER THIRTEEN\n\nSTORY PREVIEW\n\nMAN-KILLERS OF THE AIR\n\n[L. RON HUBBARD IN THE \nGOLDEN AGE OF \nPULP FICTION](BioTitle.xhtml#L.-Ron-Hubbard)\n\n[THE STORIES FROM THE \nGOLDEN AGE](BackMatter.xhtml#The-Stories-from-the--Golden-Age)\n\nGLOSSARY\nFOREWORD\n\nStories from \nPulp Fiction's \nGolden Age\n\nAND it was a golden age.\n\nThe 1930s and 1940s were a vibrant, seminal time for a gigantic audience of eager readers, probably the largest per capita audience of readers in American history. The magazine racks were chock-full of publications with ragged trims, garish cover art, cheap brown pulp paper, low cover prices\u2014and the most excitement you could hold in your hands.\n\n\"Pulp\" magazines, named for their rough-cut, pulpwood paper, were a vehicle for more amazing tales than Scheherazade could have told in a million and one nights. Set apart from higher-class \"slick\" magazines, printed on fancy glossy paper with quality artwork and superior production values, the pulps were for the \"rest of us,\" adventure story after adventure story for people who liked to read. Pulp fiction authors were no-holds-barred entertainers\u2014real storytellers. They were more interested in a thrilling plot twist, a horrific villain or a white-knuckle adventure than they were in lavish prose or convoluted metaphors.\n\nThe sheer volume of tales released during this wondrous golden age remains unmatched in any other period of literary history\u2014hundreds of thousands of published stories in over nine hundred different magazines. Some titles lasted only an issue or two; many magazines succumbed to paper shortages during World War II, while others endured for decades yet. Pulp fiction remains as a treasure trove of stories you can read, stories you can love, stories you can remember. The stories were driven by plot and character, with grand heroes, terrible villains, beautiful damsels (often in distress), diabolical plots, amazing places, breathless romances. The readers wanted to be taken beyond the mundane, to live adventures far removed from their ordinary lives\u2014and the pulps rarely failed to deliver.\n\nIn that regard, pulp fiction stands in the tradition of all memorable literature. For as history has shown, good stories are much more than fancy prose. William Shakespeare, Charles Dickens, Jules Verne, Alexandre Dumas\u2014many of the greatest literary figures wrote their fiction for the readers, not simply literary colleagues and academic admirers. And writers for pulp magazines were no exception. These publications reached an audience that dwarfed the circulations of today's short story magazines. Issues of the pulps were scooped up and read by over thirty million avid readers each month.\n\nBecause pulp fiction writers were often paid no more than a cent a word, they had to become prolific or starve. They also had to write aggressively. As Richard Kyle, publisher and editor of Argosy, the first and most long-lived of the pulps, so pointedly explained: \"The pulp magazine writers, the best of them, worked for markets that did not write for critics or attempt to satisfy timid advertisers. Not having to answer to anyone other than their readers, they wrote about human beings on the edges of the unknown, in those new lands the future would explore. They wrote for what we would become, not for what we had already been.\"\n\nSome of the more lasting names that graced the pulps include H. P. Lovecraft, Edgar Rice Burroughs, Robert E. Howard, Max Brand, Louis L'Amour, Elmore Leonard, Dashiell Hammett, Raymond Chandler, Erle Stanley Gardner, John D. MacDonald, Ray Bradbury, Isaac Asimov, Robert Heinlein\u2014and, of course, L. Ron Hubbard.\n\nIn a word, he was among the most prolific and popular writers of the era. He was also the most enduring\u2014hence this series\u2014and certainly among the most legendary. It all began only months after he first tried his hand at fiction, with L. Ron Hubbard tales appearing in Thrilling Adventures, Argosy, Five-Novels Monthly, Detective Fiction Weekly, Top-Notch, Texas Ranger, War Birds, Western Stories, even Romantic Range. He could write on any subject, in any genre, from jungle explorers to deep-sea divers, from G-men and gangsters, cowboys and flying aces to mountain climbers, hard-boiled detectives and spies. But he really began to shine when he turned his talent to science fiction and fantasy of which he authored nearly fifty novels or novelettes to forever change the shape of those genres.\n\nFollowing in the tradition of such famed authors as Herman Melville, Mark Twain, Jack London and Ernest Hemingway, Ron Hubbard actually lived adventures that his own characters would have admired\u2014as an ethnologist among primitive tribes, as prospector and engineer in hostile climes, as a captain of vessels on four oceans. He even wrote a series of articles for Argosy, called \"Hell Job,\" in which he lived and told of the most dangerous professions a man could put his hand to.\n\nFinally, and just for good measure, he was also an accomplished photographer, artist, filmmaker, musician and educator. But he was first and foremost a writer, and that's the L. Ron Hubbard we come to know through the pages of this volume.\n\nThis library of Stories from the Golden Age presents the best of L. Ron Hubbard's fiction from the heyday of storytelling, the Golden Age of the pulp magazines. In these eighty volumes, readers are treated to a full banquet of 153 stories, a kaleidoscope of tales representing every imaginable genre: science fiction, fantasy, western, mystery, thriller, horror, even romance\u2014action of all kinds and in all places.\n\nBecause the pulps themselves were printed on such inexpensive paper with high acid content, issues were not meant to endure. As the years go by, the original issues of every pulp from Argosy through Zeppelin Stories continue crumbling into brittle, brown dust. This library preserves the L. Ron Hubbard tales from that era, presented with a distinctive look that brings back the nostalgic flavor of those times.\n\nL. Ron Hubbard's Stories from the Golden Age has something for every taste, every reader. These tales will return you to a time when fiction was good clean entertainment and the most fun a kid could have on a rainy afternoon or the best thing an adult could enjoy after a long day at work.\n\nPick up a volume, and remember what reading is supposed to be all about. Remember curling up with a great story.\n\n\u2014Kevin J. Anderson\n\nKEVIN J. ANDERSON is the author of more than ninety critically acclaimed works of speculative fiction, including The Saga of Seven Suns, the continuation of the Dune Chronicles with Brian Herbert, and his New York Times bestselling novelization of L. Ron Hubbard's Ai! Pedrito! \nForbidden Gold\nChapter One\n\nTHAT'S all you have to do, Mr. Reid. Just match this gold nugget and old Nathan Reid's money is yours.\" Kimmelmeyer looked legally at Kurt Reid and rolled the nugget in question about in his soft, plump hand.\n\nKurt Reid cocked his head a little on one side and took a long drag at a cigarette. Then he crossed his long legs and exhaled the smoke in a blue cloud which enveloped the desk.\n\nKimmelmeyer coughed, but his eyes remained very fatherly and legal. Compared to Kurt, Kimmelmeyer was small. Kimmelmeyer's head was bald, shining as though newly burnished with furniture polish. Kimmelmeyer's ears were elfinly pointed. His chin was sunk far down in a wing collar, giving his face a half-moon appearance.\n\n\"That's all I have to do,\" said Kurt with a twisty grin. \"What's the matter, Kimmelmeyer, don't you like me any better than Nathan Reid did?\"\n\n\"Like you?\" gaped Kimmelmeyer, missing the point.\n\n\"You act as if I were about to go on a Sunday School picnic instead of a gold hunt in Yucat\u00e1n. What if I don't want to go, huh?\"\n\nThe legal look vanished. Kimmelmeyer stared amazed at Kurt. He did not feel at all at ease with this young man. Something in Kurt's attitude was vaguely insolent. The man's poise was too astounding. No, Kimmelmeyer did not understand Kurt Reid. They were too many character miles apart. Gangly, good-humored Kurt, on his part, understood Kimmelmeyer a little too well.\n\n\"But Mr. Reid!\" said Kimmelmeyer. \"Have you no sense of proportion at all? Here I have just offered you a chance at four million dollars and a town house and a country house and what do you do? You sit there and ask me foolish questions about whether I like you or not.\"\n\n\"I knew old Nathan Reid,\" said Kurt, dragging at his smoke. \"And as certain as I'm his grandson, he didn't intend to do any good by me through you. Besides, when you're running through soup and you're out of gas and you see a landing field, it's ten to one the thing's a bog and you'll get killed anyway.\"\n\n\"Ai! Don't be so pessimistic. I thought all pilots were optimists.\"\n\n\"I'm alive,\" said Kurt. \"Optimistic pilots are all dead.\"\n\n\"But what can be wrong? See here, I bring you here at my own expense\u2014\"\n\n\"At Nathan's,\" corrected Kurt.\n\n\"I bring you here to show you the contents of his will and you aren't even glad about it. He says right here, paragraph three, 'Whereas, if said Kurt Reid sees fit to match this gold nugget in Yucat\u00e1n, I designate further that he be given my entire estate.' Now what you want, eh? You want I should just sign these papers over to you now?\"\n\n\"That wouldn't be a bad idea,\" said Kurt. \"But come along. Let's stop arguing about this thing. Does he say where this gold is down there in Yucat\u00e1n?\"\n\n\"No.\"\n\n\"Any bet he only gives me a month to find the stuff.\"\n\n\"That's right.\"\n\n\"And he makes no provision for getting me to Yucat\u00e1n.\"\n\n\"What you want, eh?\" cried Kimmelmeyer. \"Can't you invest a couple thousand in return for four million?\"\n\n\"Sure, but I haven't got a penny. Look here.\" Kurt raised his brown oxford so that Kimmelmeyer could see the sole. A hole was there, backed by a white piece of paper. \"That paper is the letter you sent me,\" said Kurt.\n\n\"But I thought you had a good job on a transport line, eh?\"\n\n\"I had one until two weeks ago. I stunted a trimotor when I was feeling good and the company didn't like it at all. In fact, they fired me. I'm flat and you'll have to give me the dough to go down there.\"\n\nThe request was rather sudden. Kimmelmeyer took several seconds to answer. \"I... I'm sorry, Mr. Reid, but you see things are sort of slack and I thought...\"\n\n\"I thought you were so hot to get me down there,\" said Kurt.\n\n\"Oh, I am! I am! I mean... er... should I not want to see you get all this money instead of hospitals and things maybe?\"\n\n\"I don't know what the game is, Kimmelmeyer,\" said Kurt, squinting through the smoke, his silver-gray eyes studious. \"Old Nathan Reid was my grandfather, yes, but he never liked me. He wanted me to study and follow in his footsteps, but I ran off and learned to fly. Furthermore, I was often sassy and I seem to remember telling him to go to hell once or twice. He never appreciated that, someway.\n\n\"He hated me first because I was my father's son. He hated Dad because Dad went into the Navy and Nathan Reid was once thrown off the president's chair in Nicaragua by the United States Navy. He's got me all mixed up.\n\n\"Nathan Reid knew he could never get anything on me while he was alive. Now he's trying to do it after he's dead. He never had any scruples as a filibuster. He made enemies more than friends. After his Central American misadventures he tried to run everything by the same yardstick.\n\n\"You're just his mouthpiece, that's all. You don't know these things. I do. Nathan Reid wants to see me dead and I know damned well that a trap is waiting for me in Yucat\u00e1n if I go down there looking for this gold. That pretty nugget you've got there still retains some of its quartz. That's rose quartz. The ledge is jewelry rock. Oh, I know my gold mining. If it's there, I can find it. Give me time.\n\n\"But here's something that you've never heard about. There's a saying about Yucat\u00e1n and gold. The fact is known all around the Caribbean. You can look for gold in Yucat\u00e1n. Gold comes out of Yucat\u00e1n, brought by the Indians there. But no white man that ever found gold in Yucat\u00e1n ever got out alive except filibuster Nathan Reid.\"\n\n\"My God,\" whispered Kimmelmeyer.\n\n\"Nathan Reid hated me and now that he's dead he's trying to kill me. He knew that I'd go, and I'm going. I'm broke, but I'll make it someway. I know where he traveled in Yucat\u00e1n. Somehow I'll get a plane and fly over his old routes there until I find the place. I'm going to beat him at his own game.\"\n\nThe finality and earnestness of Kurt's last remark jarred Kimmelmeyer. In many ways, Kurt was like Nathan Reid. There was a certain positiveness about him, a certain gleam to his silver-gray eyes, a certain set to his lean, almost swarthy face.\n\nKimmelmeyer nodded. He had dropped the gold nugget on the polished surface of his desk. He had dropped it as though it had been hot. Kurt picked it up, studied it and handed it back.\n\nKurt stood up. \"I'm going now. In a month\u2014on the eighth of October\u2014I'll be back here with a mate for that gold.\"\n\n\"Wait, wait,\" said Kimmelmeyer, once more efficient and legal. For a moment he had been transported to the seared plains of Yucat\u00e1n, but now he was right back in New York with a solid chair under him, a newspaper and a big dinner waiting for him in an hour or two.\n\nKimmelmeyer picked up a copy of the Eastern Pilot, opened it and handed it to Kurt. \"I was looking for your address and I got a copy of this,\" said Kimmelmeyer. \"Look here, I just thought...\"\n\nKurt read the advertisement in its neat little box. It said:\n\nWANTED: A transport pilot, a radio operator and a mechanic for long flight. Two planes will be used, the duration of the trip will be six weeks or thereabouts. Destination: Yucat\u00e1n.\n\nKimmelmeyer was eager, \"There's your chance.\"\n\nKurt studied the man, grinned a little and then nodded. \"Yes, here's my chance.\" He stuffed the magazine into the pocket of his tweed jacket and went out, slamming the door behind him.\n\nKimmelmeyer mopped his forehead and muttered, \"Ai, but that was easy. Easy!\"\nChapter Two\n\nKURT went to the address mentioned in the advertisement. The place was on First Avenue, close under the El. Shabbily dressed, sad-faced people loitered on the doorsteps, their voices drowned in the surflike roar of the El. Children scrambled in the gutters, pinch-faced and ragged. A huckster bawled a string of indefinite syllables in an assured tone and clanged his brass bell.\n\nKurt felt ill at ease, anxious to be away. People turned and looked at him as he passed. He did not belong here. He felt a sullen ill will toward him.\n\nThe door which bore the right number was painted green, sandwiched between a fruit stand and a scrap iron shop. A sign creaked overhead in the hot wind stating that apartments were to be had there by the day, the week or the month.\n\nKurt pushed the buzzer and the door rasped and clicked until he opened it. Then after he had passed, it still rattled. The man upstairs must be impatient.\n\nThree flights up, Kurt found an open door. A man was standing in it looking at him. The man wore a vest which bore the signs of many hasty meals. He was unshaven, greasy of face and hands. The trousers he wore were peg-topped, flashily cut. The face also had the air of past flashiness, now worn through. The eyes were bulging, of indefinite color; the mouth was warped and cynical.\n\n\"Who the hell do you want?\" he demanded.\n\nKurt stopped before the door and very carefully looked the man up and back down to the scarred shoes. He let several uneasy seconds elapse before he answered and then he said, \"Who the hell wants to know?\"\n\n\"Name o' Sloan,\" muttered the other, his poise gone.\n\nKurt took out the magazine and thrust it into Sloan's hands, pointing to the ad. \"Have I got the wrong address? I'm thinking that I have at that.\"\n\n\"Oh, no, no. This is right. You a mechanic or a pilot or what?\"\n\n\"I'm a pilot. I'm Kurt Reid. Shall we go in and sit down or shall we tell all to the neighbors?\"\n\n\"Come in, come in,\" said Sloan, suddenly cordial. He led the way into a room blued with cigarette smoke. Two other men immediately bounced to their feet. A third person, smaller than the others, remained seated, watching with amused eyes.\n\nSloan did the introducing in an offhand way. \"The fat guy is Bruce. This here guy is Bill Connelly. And that guy there I don't know. This here guy is Kurt Reid. He says he's a pilot.\"\n\nBruce took a quick step forward. His eyes were rather hazy behind silver-rimmed glasses. His shirt was well cut and the cuffs were stiffly starched and unbuttoned. His face was rather soft and sunburned. His hair was standing erect like combed steel wool. He was a foot shorter than Kurt.\n\nBruce offered his hand. \"A pilot? Reid, you say? Very glad to know you, very glad to know you. I suppose you've come to see about that position, eh?\"\n\nKurt looked the three over. The fourth person definitely did not belong. A kid, decided Kurt, and a rather handsome kid at that.\n\n\"No,\" said Kurt, \"I came down here because I like to walk. What's offered?\"\n\n\"We're going to Yucat\u00e1n,\" said Bruce.\n\nBill Connelly nervously blinked his eyes and said, \"Yeah, Yucat\u00e1n.\"\n\n\"That's right,\" agreed Sloan. \"Yucat\u00e1n.\"\n\nKurt grinned. \"Oh, Yucat\u00e1n.\"\n\nSolemnly, the three nodded in unison. The kid in the corner smiled.\n\n\"Arch... archayologee,\" explained Bruce, wrestling with the word.\n\n\"Oh,\" said Kurt. \"From some university, eh? You're professors, that it?\"\n\nOnce more they all nodded. The kid in the corner laughed outright and they turned to stare. When their eyes came back to Kurt, Kurt knew that they knew he was laughing at them.\n\nBruce, after a moment's thought, evidently decided to let it ride. His hand came out of his right hip pocket. \"Yes, we're going down in the interests of science. We have two planes, both of them very good, very fast, but we have only one pilot. That's Bill Connelly there.\"\n\nConnelly's eyes were twitching. He swallowed a couple times, making his Adam's apple leap convulsively.\n\n\"The pay?\" said Kurt.\n\nBruce looked at Sloan. Sloan's bulging eyes rocked toward Kurt and came back to Bruce.\n\n\"It's good,\" said Bruce. \"A thousand dollars for the trip. And if you're the guy I think you are, then that ought to mean somethin' to you just now. You'll get it when you come back.\"\n\n\"While I'm down there,\" said Kurt, \"I may want some time off to myself.\"\n\n\"That's okay,\" said Bruce. \"You can even borrow one of our planes.\"\n\n\"And now how about me?\" said the kid in the corner.\n\n\"He wants the job as radio operator,\" Bruce explained to Kurt. \"Says he's pretty good. But I say he's too damned young.\"\n\nKurt looked fixedly at the kid in the corner. Young was the right word for it, unless... Kurt's silver-gray eyes were almost closed. A smile flickered on his mouth.\n\n\"Where's your papers?\" demanded Bruce. \"I gotta see your papers.\"\n\n\"I haven't got any, but if you'll take me to a key, I'll show you that I know my business.\"\n\n\"Where'd you get your experience?\" said Bruce.\n\n\"I... uh... I was airline operator for TAT for... for three years.\"\n\nBruce snorted. \"Nuts! You can't get a job by lying to me. You ain't old enough! Get out!\"\n\nThe kid stood up and shot Kurt an appealing glance. \"Maybe this gentleman could verify... see here, I've got a slip which shows...\" The kid reached into a jacket pocket and brought forth a bundle of envelopes. Something silver flashed down to the floor, rolled halfway across the rug and stopped, spinning.\n\nA compact.\n\nBruce stared at the thing, then at the kid. Kurt knew the answer instantly. This was no boy, but a girl. The face was more pretty than handsome. The voice was too fine for even a youngster.\n\nBruce loosed a muffled snarl. \"You damned spy! Who sent you here? Who sent you?\"\n\nBruce took two steps, feline steps. His hand gripped the girl's shoulder so hard that she winced. Bruce shook her, showing his teeth. \"Who sent you here?\" he roared.\n\nThe girl tried to answer, but the fingers hurt too much. She sagged forward, tears welled up in her eyes.\n\nKurt stepped easily to Bruce's side. He yanked Bruce around. No one saw the fist move, but the next instant, Bruce crashed into a chair clear across the room. Bill Connelly's jaw sagged.\n\nSloan yelped. His bulging eyes looked red. He stepped into Kurt with both hands clenched and swinging. Kurt weaved back and Sloan followed Bruce into the chair.\n\nBill Connelly was undecided. Kurt made up the man's mind. Bill Connelly crumpled up, a red welt appearing on his neck and jaw.\n\nThe three men were stacked against the shambles of the chair like a collapsed Indian tepee. They shifted, as though afraid to get up.\n\nKurt smiled at them. \"I guess we'll get along, boys. I guess we'll get along.\"\n\nKurt turned to the girl, \"Now, ma'am, let's let these fellows show us their planes and their radios. Time is speeding.\"\n\nShe rubbed her shoulder and then looked up at Kurt. Suddenly she laughed.\nChapter Three\n\nSEVERAL hours later, a sedan drew up before the Newark Airport Restaurant. Kurt Reid stepped out and Bruce handed him a five-dollar bill. The girl gave Bruce a questioning glance and then alighted at Kurt's side.\n\n\"I gotta arrange for the ships to be rolled out,\" said Bruce, now all complacent with the past incident apparently forgotten. \"You stay here until we come around for you.\"\n\nSloan and Bill Connelly nodded politely and the sedan drove off across the highway toward the brown-and-white modernistic operations office.\n\nThe girl found herself ushered through the door and to a black-topped table on the right of the oblong mahogany-and-brass interior. She carried a small bag in her hand\u2014a rather tattered bag from which she had produced a sport dress which she now wore.\n\nKurt looked at her hands. Capable hands they were, well trained, but right now they were shaking. The girl had a certain gray pallor in her cheeks, a certain listlessness in her dark blue eyes.\n\nWithout asking any questions, Kurt ordered a cup of black coffee for her. When she looked askance at him, he said, \"You haven't eaten for the last couple days, have you?\"\n\nShe lowered her eyes and nodded. Presently the coffee came and when she lifted it to her lips the ebon fluid ran down the sides of the thick white cup. Kurt took a sudden interest in the black-and-mahogany panels of the wall and ceiling.\n\nHer eyes thanked him and she drank the coffee down. After that a little color came into her face and her eyes were less tired.\n\n\"Looks like we've hired ourselves a job,\" said Kurt. \"What do you know about it?\"\n\nA platinum waitress hovered near, taking their orders. When she had gone, the girl said, \"Very little. I saw the ad in the Eastern Pilot and I got down to First Avenue just before you did.\"\n\n\"Why are you taking a chance at it?\" said Kurt.\n\nShe smiled; her mouth was tired. \"Broke. Luck running against me.\"\n\n\"You really are a radio operator?\"\n\n\"Yes, I really am. Six months ago I was the lead attraction for a flying circus. I turned a plane inside out every day for the crowds. A year ago I was copiloting a transport plane. Two years ago I was an airline hostess anxious to know all the ins and outs of a very mysterious, infinitely dangerous game. I know them now.\"\n\n\"You didn't tell me your name.\"\n\n\"It wouldn't mean anything to you. Nothing at all. I've heard of you, but...\"\n\n\"That isn't telling me your name.\"\n\n\"All right, if you insist on the real thing: Joyce Sutherland. Joy Sutherland.\"\n\n\"I read about you someplace,\" said Kurt.\n\n\"You read that I crashed six months ago. They expected the old crate to hold together for ever and ever and when it went they told me I was a hoodoo. An airliner crashed with me in it. A parachute jumper was killed diving off my plane. And now with that on my name and with things as they are, there isn't very much chance of my coming back. It was a swift career, wasn't it?\"\n\n\"And so you're perfectly willing to cast your lot in with Bruce and Sloan and Connelly.\"\n\n\"Funny thing about life,\" said Joy Sutherland. \"If you don't work you don't eat.\"\n\nKurt did not smile. The tragedy of this girl was too deep. He knew what it was to be considered a hoodoo. No game is more superstitious than flying. Her name had gone before her. Hospital bills, left in a strange town, no friends.\n\n\"You come from the West, don't you?\" said Kurt.\n\n\"Yes, San Francisco. How did you know?\"\n\n\"The way you talk.\"\n\n\"You haven't told me anything about yourself, Mr. Reid.\" Her dark blue eyes were studying him. In a swift appraisal she knew him. He was a headlong chap with very little regard for the opinions of others. He was violent and gentle all in one. He was as tough as a drill sergeant and as soft as a girl. He was typical of a hard-eyed breed who had come into being with flight. Steady contact with danger, closeness of eternity, had given him a careless attitude toward life. He knew things for what they were worth. Joy Sutherland knew and understood.\n\n\"I want to see Yucat\u00e1n,\" said Kurt. \"I never happened to have the chance to go there, and now that I'm on my uppers and my controls are kind of loose, I intend to give the country a squint.\"\n\n\"That's funny,\" said Joy Sutherland, staring at the two unwinking yellow eyes of her fried eggs. \"Old Nathan Reid used to stamp around down there. I read it in the story of his death. You aren't by any chance...?\"\n\n\"His grandson,\" said Kurt, a little bitterly.\n\nShe took her cue from his tone. \"I've heard about him before. Once the president of Nicaragua, unseated by the Navy, soldier of fortune, gold hunter, conquistador. From what they say he was a rather cruel individual.\"\n\n\"That doesn't describe him. He tried to break my father's heart and ended up by hating him because Dad went into the Navy. Now he's trying to...\"\n\n\"But he's dead,\" reminded the girl. \"Why speak of him in present tense?\"\n\n\"Nathan Reid will never be wholly dead. He left his mark too deep in Central America.\"\n\nShe was plainly puzzled now. \"But he was wealthy when he died. Why should his grandson have to take a rotten offer like this?\"\n\n\"Grandfathers and flying circuses are a lot alike,\" said Kurt. \"You and I are on the last lap of the flying trail. Perhaps I have a little more hope ahead than you, but unless I fly for sport I fly no more. Nathan Reid hated me. Down in Yucat\u00e1n...\"\n\nShe listened to his somewhat disjointed sentences, feeling something of the struggle inside him. When he left the explanation hanging in midair she did not press him further.\n\nBruce came, smoking a cigar, looking puffy and elated. \"They're on the line. Come on out, Mr. Reid, and we'll see what kind of pilot you are. If the ships are all right and if you're all right, we'll start in the morning.\"\n\nKurt stood up and drew back the girl's chair for her. The three went across the highway to the hangars, walking silently, their gaze fixed on the two planes which idled on the runway.\n\nOne was a two-motored cabin job apparently capable of high speed. Her sides were gray and dull with long exposure. Her engines sounded well enough. She looked like a huge bug sprawled on the concrete, sunning itself.\n\nThe other plane was also a cabin job. It was yellow with a swayback and spatted wheels. Kurt knew the type well. Racy and compact, built for speed over long distances.\n\nBruce pointed to the smaller ship. \"We'll take that one up, Mr. Reid, so you can show me how good you are. You'll probably pilot the bigger one and Connelly will have this one, I dunno. Anyway we'll see how good you are.\"\n\nKurt jackknifed himself and slid in under the control wheel of the plane. The ship had seen much service. Its panel was dented from a crash or two and some of the instruments were broken. However, Kurt had piloted worse in his time. He gave Bruce a grin.\n\n\"What am I supposed to do?\" said Kurt.\n\n\"Just show me you can fly it, that's all.\"\n\n\"Transport license doesn't count for much with you, does it?\" said Kurt.\n\n\"Take her off.\"\n\nKurt slammed the small ship down the runway. The bright disc of the spinning prop blurred the factory chimneys in the distance. The spatted wheels went light and came off. Kurt leveled out, gathering speed, and then sent the plane rocketing skyward in a steep climb. A glance sideways told him that Bruce was far from nervous.\n\nBruce kept his hands well away from the dual control wheel before him as though the thing might bite. He turned sideways and yelled in Kurt's ear, \"Someday I'm gonna learn to fly one of these things. Then I won't need extra pilots for my expeditions.\"\n\nThe yellow ship banked and went around like a top, its under wing seeming to remain stationary in the sky below. Kurt whipped out of that and did a swift figure eight. He climbed and dived again. Through it all, Bruce's expression did not change in the least.\n\nThey were out over water now, with the waves looking crisscross and small below. Tugs and even steamers were mere chips in the water.\n\nWithout any warning, Kurt thrust the control column away from him. The monoplane nosed over, the engine began to scream as it revved up. Wires took on a whining note and the world loomed suddenly big through their down-pointed prop. A smile was flickering around Kurt's mouth.\n\nThe tugs grew larger. Men could be seen on their decks. Then the men had faces and finally hands and the yellow plane was yowling down at three hundred miles an hour less than five hundred feet above the waves.\n\nIt was a moment for swift action, but instead, Kurt took both hands off, both feet off and carelessly yawned.\n\nBruce screamed unheard into the din. For him death was a fraction of an inch away. His pudgy hands snapped out and gripped his dual control column. He eased back, his feet found the rudders and the plane fishtailed to kill speed. The nose came up, up, up until the wheels were rapping parallel to the waves, almost in them. Bruce, mouth compressed, eyes watery behind his glasses, began to build altitude. The yellow ship started up again with an easy glide.\n\nWhen the altimeter was bobbing at a thousand feet, Bruce suddenly realized what he was doing. The plane wobbled and fell off on one wing. He overcontrolled. His eyes went beseechingly to Kurt's face.\n\nWith a very small smile, Kurt took his own controls and the ship slipped down to a smooth landing at Newark.\n\nWhen he had cut the gas and the switch, Kurt turned easily in his seat and said, \"Very nice work.\"\n\nBruce fidgeted with his belt, finally casting it off. \"Anybody can do that if they're scared enough,\" he growled sullenly. He edged out of the cabin.\n\n\"And Mr. Sloan,\" said Kurt, \"can he fly too?\" Then he laughed loudly as Bruce scurried away.\n\nJoy came to the step and looked up, questioningly. \"What's up?\"\n\n\"Bruce,\" said Kurt. \"Something's wrong here. Very wrong. Bruce can fly. He's a natural. Connelly can fly. Maybe Sloan can fly. And yet they have to hire another pilot. Whatever these fools are up to, it's shady.\"\n\n\"You have to eat, don't you?\" said Joy, amused.\n\n\"Sure, just as long as I don't have to eat too many bullets, I'm satisfied.\"\n\nSloan came over, his bulging, watery eyes very sad. \"We leave in the morning, wise guy. Here's a ten-dollar bill. Be on time, get it? Six o'clock.\"\nChapter Four\n\nTHE airport was cloaked in gray darkness. The two-motored ship idled sluggishly, thinly seen across the runway. Gas was gurgling into the auxiliary tanks of the yellow plane. Sloan stood by watching, his face hidden in the collar of his extreme cut topcoat.\n\nBruce was hunched down in the cabin of the twin-motored plane, trying to keep warm. Bill Connelly was under the controls, his eyes batting, his fingers shaking. Bill Connelly nodded at the engines and climbed down, approaching the yellow ship.\n\nA hand reached out of the grayness and detained him. Kurt Reid smiled and shook his head. \"You're taking the big one out. I'm taking the little one.\"\n\nBill Connelly opened and shut his mouth like a landed fish. Then without a word he went back to the larger plane and conversed with Bruce in low, jerky tones.\n\nJoy Sutherland, wrapped in a man's trench coat, came up to Kurt's side. \"Good morning, Black Knight. I called your room when I woke up but you'd already gone.\"\n\n\"Had any breakfast?\" said Kurt.\n\n\"I... I never eat any breakfast.\"\n\n\"But I gave you two bucks for chow,\" protested Kurt.\n\n\"I... I got me a permanent wave and a... a compact. I had to have them, Kurt.\"\n\n\"Never mind,\" he said with a grin, \"I've got a hot thermos of coffee and some sandwiches in my grip.\"\n\n\"Which plane are you going to fly?\"\n\n\"The little one. I couldn't stand to look at Sloan.\"\n\nBruce loomed out of the pea soup. \"You're flying the big one, Mr. Reid. Them's orders.\"\n\nKurt turned around very slowly. \"Your error, Bruce.\"\n\n\"My error, hell! Who's in charge around here anyway?\"\n\n\"I'm flying the little ship.\"\n\nBruce sputtered and then saw the girl. \"And we're not taking you. We decided we won't need any radio communication.\"\n\n\"The radio outfit is in the smaller plane,\" said Kurt. \"She's going in that crate with me.\"\n\nSloan edged up, his hands deep in his pockets, his bulging eyes darting from Bruce to Kurt as though awaiting orders.\n\n\"No,\" said Bruce to Sloan, irritably.\n\nBill Connelly, batting his eyes, his mouth twitching, came over.\n\n\"She's going,\" said Kurt. \"And I'm flying the smaller ship.\" His inky eyes went narrow with speculation. Then he added, \"Or neither of us go at all.\"\n\n\"You mean you'll run out on us?\" snapped Bruce.\n\n\"That's what I mean,\" said Kurt.\n\nSloan's hand in his pocket was moving up. \"Put the gun away,\" ordered Kurt. \"You can't do anything here on the runway and you're too yellow to do anything anyway. I see red when anybody pulls a gun on me. And if you shot me and I found out about it I'd really get sore.\"\n\n\"Aw, let him have his own way,\" growled Bruce. \"Let him ride with the dame. But I'd like to know how the hell I can send messages with her in the other ship.\"\n\n\"Wig-wag 'em across with your ears,\" said Kurt.\n\nThe tension wore off a little. Bill Connelly edged toward the twin-motored plane and Sloan followed him. Bruce underwent a change and smiled.\n\n\"Okay, Mr. Reid, I was just joking anyway. Of course you can fly the small job. We stop in New York, Richmond, Atlanta and New Orleans. We spend the night there and then hop across the Gulf to Progreso, Yucat\u00e1n\u2014a distance of six hundred miles.\" He smiled uncertainly.\n\nKurt opened the door of the yellow ship and helped Joy in. Bruce departed for the transport plane. But as Kurt came around the nose he met another man he had not seen before. The fellow was dressed in mufti but there was something professional, even militant about him.\n\nHis words were few. \"Watch them guys, buddy. You ain't one of them, I can tell that. But watch 'em close. They just missed getting a ten-year stretch at Leavenworth for kiting chinks across the border.\"\n\nThen the fellow was gone, leaving Kurt to scowl through the gray mist after him.\n\nKurt climbed under the controls. The transport ship took off and Kurt followed, sending the yellow two-seater boring upstairs to greet the murky dawn.\n\nJoy Sutherland had little to say. She had already discovered everything there was to know about the shortwave radio. She tuned in on the beam and connected the lights on the panel. Kurt felt a twinge of pride at her efficiency. He was more than glad to have her there, happy that he did not have to ride with the three.\n\nHe was not exactly sure of his position but he knew that he was somehow vital to the party. They weren't really afraid of him, not those fellows.\n\n\"She's riding kind of heavy,\" said Joy above the motor's full cry.\n\nKurt bobbed his head in agreement. Even an extra load of gas shouldn't make that difference. Joy did not weigh a hundred and ten pounds and his weight was less than a hundred and fifty.\n\nJoy twisted around in her seat, unfastening her safety belt. A small space was behind the two seats and it was covered with a strip of dirty canvas. She pulled it aside, staring down in surprise. She tugged Kurt's sleeve, pointing.\n\nTwo light machine guns were there, their loaded belts coiled like a den of snakes all white and brassy. Kurt frowned. He saw something else. A sample pick, a shovel, a metal gold pan.\n\nThere was the extra hundred pounds. Looking up at the cowl, Kurt saw the slots and mountings for the first time. He felt a chill of uneasiness. Just what were they walking into? Machine guns, a gold pan...\n\nThat fact he had told Kimmelmeyer rose up again: You could dig gold in Yucat\u00e1n but you couldn't take it away from there because of the Indians. Were the three going to try anyway? With planes and machine guns?\n\nThat was coincidence if he had ever seen it. Maybe too much coincidence. Something was wrong and amiss here someplace. He felt as though he were on the brink of a solution which he couldn't quite grasp.\n\nJoy was wide-eyed. A flush of excitement was on her cheeks. Her mouth was slightly open, moist and pearly and scarlet. Kurt smiled her an assurance he did not feel.\n\nFirst a dead man's trap and now a crazy gold expedition. In truth, all hell was waiting for him in Yucat\u00e1n.\nChapter Five\n\nRICHMOND, Atlanta and then New Orleans. All through the day Joy kept the beam coming in strong. Too far left for an N, too far right for an A, but most of the time Kurt slid down the invisible static highway with the signal coming in blurred and staccato, true on his course.\n\nIt was pleasant, skittering on top of the world at the level of the sparse white clouds. The fields were an immense checkerboard and the houses were dollhouses peopled by ants. The rivers were threads of silver on a minutely worked green tapestry. The mountains were frowning bumps, slashed and hacked and piled in long lines.\n\nOver the Appalachians they struck a local thundershower which washed their wings and made them shine when the sun came out again.\n\nBut always drifting ghostlike beside them came the transport plane, a gray shadow, impersonal and detached.\n\nAnd always with Kurt there remained the thought of Nathan Reid, filibuster, now dead. Nathan Reid who had carried the standard of a rabble army against the military autocracies known as republics in the ardent southland. And when he thought too long about it, Kurt's mouth would settle into a thin gash across his face\u2014just as Nathan Reid's mouth had set those many years past when the going was rough and when an ambush was ahead.\n\nKurt retained no illusions about the romance of his grandfather. He had been young when he had first read Nathan Reid's journals. He had found them one day in the musty old attic lumped and forgotten in a corner of a field trunk. They had been bound with the Great Seal of Nicaragua\u2014an over-ornate thing of comical rather than grand proportions.\n\nHe had read them, volumes held on his knickerbockered legs, with his grubby, small boy hands grimed with the dust of decades. The journals were too many for one reading and he had stolen back time after time to finally complete them. It had not been the romance which had made Kurt read those tomes. It had been sheer horror that had held him. Each time he read his stomach would twist uneasily within him and his dark eyes would grow large and afraid. He had marched in imagination with that rabble of Nathan Reid's and Nathan Reid had stinted nothing in setting down the chilly terror of the facts.\n\nThis man dead with gangrene, that one shot for theft, another murdered by his fellows. And the thick, oozing decay of the jungles running like a trail of slime through it all. Nathan Reid had dreamed empire and like so many men who have since become haloed saints in history, Nathan Reid had played his part\u2014that of a brutal, single-purposed, egotistical bully.\n\nThis man he had shot with his own hand. This native he had tortured for information. This town he had burned through military necessity\u2014and that pallid excuse for savage excess was painted well in the smeared, aging pages.\n\nYoung Kurt's back had smarted many times\u2014too many times. Young Kurt had absorbed the bitterness of his father toward a military martinet, a despot who knew nothing save his own will, whose world was black save for that section which became illumined by the fire of his ego.\n\nAnd now Nathan Reid was dead\u2014as dead as that rabble he had led into the southland. But Nathan Reid could not abide death and here, weeks after the clattering fingers had taken him, he was still holding court over Kurt's destiny. The thought was gruesome. Nathan Reid was laid out nicely in a black frock coat in an exclusive cemetery, in an ornate mausoleum. But as far as Kurt was concerned the man still barked his imperious orders and glared with his inky, brittle eyes.\n\nHad it not been for the presence of Joy, Kurt would have become very melancholy, following the ups and violent downs of his temperament. But Joy was seated serenely on his right, her eyes suddenly sparkling with interest at some sight below.\n\nHer sport suit had seen better days, but it was far from shabby. Rather it had an air of respectable dignity. The color was blue, matching her eyes and the open-throated shirt was buff, matching her hair.\n\nJoy was not beautiful in a fragile, insipid way. Her face was firm and round and frank and her mouth was made for laughter rather than pouts.\n\nWhen evening came, Kurt was tiring. Without question, Joy took the dual control and flew with a graceful ease and unconscious smoothness which made Kurt wonder at her inability to get a job. But then, Kurt had always said that the greatest danger in aviation was starvation, and Joy had become branded as a hoodoo\u2014as Jonah had been branded as a Jonah but had been nonetheless saintly for it.\n\nThe Mississippi curved over the horizon, a dozen twisting slashes of gold across a flat, brown world. Lake Pontchartrain shimmered under the slanted rays of the sun as big as an ocean decked with curving prows and fluttering sails.\n\nThe transport ship came down and circled the square field and then slid in for a cautious, almost stealthy landing.\n\nKurt sent the yellow ship down in a hissing sideslip which straightened out only when twenty feet separated them from the earth. The two-seater whistled just above the ground, floating, losing speed, to suddenly crunch down for a precise but somehow devil-may-care three-point.\n\nBruce was at the side of the yellow ship almost before it had stopped rolling. He opened the door and peered anxiously in. But the canvas appeared not to have been disturbed, nor did either Joy or Kurt mention the discovery of the machine guns.\n\nBruce smiled up as far as his flat, bulbous nose. There the smile stopped. \"I'll attend to the hangaring of the ships, Mr. Reid. You and the dame... I mean Miss Sutherland can go uptown. Report back here about six tomorrow morning.\"\n\nKurt slid out of the cabin, stretching his long length and flexing his arms. \"What'll I do for money? I'd like to have a hundred on account, Bruce. I've got to get some clothes.\"\n\nBruce scowled. \"I can't...\"\n\n\"Then,\" said Kurt, stifling a wide yawn, \"I'll have to withdraw from your entourage, I'm afraid.\"\n\nGrudgingly, Bruce drew out his wallet and counted a hundred in tens into Kurt's hand. Once more Kurt was surprised at this evidence that he was wanted very badly in the party. He wondered just how far this sort of thing would go.\n\n\"And Miss Sutherland would like an advance on her pay, too,\" said Kurt. \"She ought to get about three hundred for this trip. You can let her have seventy-five now.\"\n\nSloan was slipping up toward Bruce's elbow. He shot a meaning glance at his boss and then licked his lips nervously.\n\nBruce tried to stare Kurt down. He saw the threat in Kurt's eyes. Not only the threat of leaving.\n\nBruce counted out seventy-five. Kurt laughed out loud at the slowness of the man's movements. Joy smiled and took the money.\n\nThen without looking back, the two climbed into a taxi and headed off toward New Orleans.\n\n\"You've got him scared,\" said Joy.\n\n\"I wish I was certain that was it.\"\n\nThe cab deposited them on Canal Street and they stood for a few moments at the curb looking up and down the straight thoroughfare as though undecided where to go. Finally Kurt led the way to a store which was still open.\n\nThey separated at the entrance with a promise to meet there in half an hour. Kurt made his way to the men's clothing department and made known his wants.\n\nThe items he bought were of the greatest need: a pair of high, soft lace boots, a pair of light whipcord breeches, a broad-brimmed gray felt hat and a pair of light shirts.\n\nWalking down the counter past the sporting goods section, he saw guns on display inside the shining case. He stopped, struck by a sudden idea.\n\n\"That Colt .45,\" he said to the clerk. \"Can I have it now?\"\n\n\"Well, it's a little irregular, but...\"\n\n\"Give me a box of shells and five extra clips.\" Then with the gun bulging under his coat, he felt somehow safer. One never knew what would happen. Nathan Reid, Bruce...\n\nJoy was waiting for him, giggling like a very small girl. \"Tonight,\" she said, \"you're going to take me to dinner, and then we're going someplace and dance. I just couldn't resist a dress I saw although I know I'll just throw it away after tonight.\"\n\nKurt looked at her, slightly amazed.\n\nShe stopped laughing, something like tears came up in her eyes. \"It's... it's not often I'm happy, Kurt, and tomorrow you and I are going south across the Gulf to Yucat\u00e1n\u2014to God knows what. I... I have a hunch, Kurt, that... that we're never coming back.\"\n\nThe chilly statement sent a shiver down Kurt's straight spine. He forced a smile. \"Forget it, Joy. Forget it. Tonight we'll find a place where there's music and good things to eat and maybe moonlight and we'll forget all about everything, huh? Just you and I.\"\n\nShe brightened, remembered her dress and began to chatter with him about small but interesting things. Kurt walked silently beside her, listening to her voice, shouldering their way through the crowds. The Colt .45 banged against his ribs with every step.\nChapter Six\n\nPROGRESO, Yucat\u00e1n, in the later Empire of the Mayans might conceivably have lived up to its name, but through the sleepy passage of centuries it had grown more and more dormant until at last it represented a typical Central American village living only for its afternoon siesta.\n\nIt is situated between two long lines of sea sand dunes, built on sand. To the north lies the restless blue of the Caribbean and to the south lies the low tableland\u2014and all the forgotten mystery of the Mayans, all the sullen danger of untamed tropics.\n\nThe two ships landed on a smooth strip of beach and were immediately surrounded by crowds of natives dressed in abbreviated cotton shorts, white cotton jackets and Mexican straw headgear.\n\nBruce, alighting with nervous haste, brushed the crowds aside and went stamping down the beach, leaving dents in the sand with his heels. Bill Connelly batted his eyes and remained under the wheel of the transport. Sloan thoughtfully roved his eyes over the hybrid assembly about the planes.\n\nJoy looked at the people and found kindness in their faces. Bananas, pineapples, strange green fruits with pulpy orange centers\u2014the carelessly slung baskets presented a lure for her. She climbed down and spoke to a yellow-skinned native in Spanish.\n\nKurt was surprised at the fluidness of her speech. He knew something of Spanish; he had always prided himself upon his knowledge of it. But Joy was talking like a native.\n\nThe natives understood quite a little of her speech. Their own language was a crisscross patois of Indian, Spanish and Mexican. But what they did not understand in her words, they took from the tone of her voice\u2014a quality of language plundered by the printed page, a universal passport no matter what language is spoken. They also understood her eyes.\n\nMany baskets were offered. These people had seen one or two planes before; they had seen a few white women; they had seen enough of life along this tropic strand to understand much they could not put into words. They sheered away from the transport plane and centered their attention on the sleek yellow ship. It was as though the gray bimotored job had smelled bad.\n\nA man in a small flat-topped straw hat carrying a cane and stroking a flowing white mustache came up to Joy with a bow. His words were in the purest of Castiliano.\n\n\"You go far into the interior?\" he asked.\n\n\"I don't know,\" replied Joy with a quick smile.\n\n\"Perhaps you go to Quintana Roo, eh? I ask because I have seen others go before.\"\n\n\"What is the matter with Quintana Roo? What is Quintana Roo?\"\n\n\"The southern portion of the peninsula,\" replied the Spaniard. \"It is an unknown fastness. I do not know just why it should attract the people of the north\u2014except perhaps for the gold. I beg your pardon for asking in idle curiosity.\"\n\n\"No, no,\" said Joy quickly. \"I am pleased that you interest yourself. What about Quintana Roo?\"\n\n\"Oh,\" vaguely, \"many have gone, few have ever come back. It is the last stronghold of the Ancients. The Indians there for long dwelled in this more equitable section, but when the Spanish crushed their revolts time after time, the Indians moved back away and out of sight, losing themselves forever in the jungle and on the plateau.\n\n\"You know of the early Spanish, yes? They tried to penetrate Quintana Roo and found it impossible. The Indians live there in peace\u2014or perhaps their idea of peace. Ave Maria, se\u00f1orita, but they went to long odds to obtain that peace. How they use it we do not know. But there is gold there. Sometimes it comes out. Sometimes we see huge nuggets brought by Indians.\n\n\"But we who live on this barren coast have grown cautious. We no longer try to push back into a territory which will not have us. We leave that for the people of the north. People such as that great filibustero Nathan Reid.\"\n\n\"You know of him?\" said Kurt with quick interest.\n\n\"Know of him? By all the saints, se\u00f1or, you must be joking. He is a legend here. Why, once he anchored in this very harbor. He saw a nugget from across the peninsula and he disappeared with a dozen of his men. Weeks later he came back, alone. But he had a nugget with him. A piece of gold studded with rose quartz as though he had ripped it from the vein. I was a little boy then, but I remember.\"\n\nKurt experienced a queer wave of unreality. He had seen that same piece of quartz on the desk of a bald-headed shyster as carelessly handled as a paperweight. That bit of sun metal had cost the lives of a dozen men. And it might well cost the lives of thirteen.\n\nHe was about to say something about it when Bruce came back. Bruce was sweating and fuming, nerves raw with the indolence of the place. White men like Bruce had experienced the same fever for centuries. They had raved and fumed and had soothed themselves with alcohol and then had ceased to care even when the tropics finally got them.\n\n\"The dumb so-and-sos,\" rapped Bruce. \"We can't get gas until morning! We'll have to stay here overnight.\"\n\n\"How long do we fly tomorrow?\" said Kurt.\n\n\"It's a hundred miles to Quintana Roo,\" growled Bruce. \"We could have made it tonight. I'm sick of this damned job. The sooner it's over the better.\" He stamped over to the transport plane and explained things to Sloan and Connelly.\n\nThe Spanish gentleman looked askance at the squat Bruce and then\u2014perhaps it was because Joy smiled\u2014he did that thing which Spaniards are always supposed to do and don't. He offered Kurt and Joy the hospitality of his house for the night.\n\nThey left the yellow plane under the guard of a ragtag, bobtailed soldiery who had come yawning from their barracks and who stood in the shade of the wings, rifles held awry, feet spread wide, splayed bare toes gripping the sand like a monkey's.\n\nThe Spaniard's hospitality was excellent, his house was beautiful, his wife was complacently plump, smoothly gracious. Joy and Kurt were driven out to their ship in the small hours of the coming day, greatly refreshed, feeling for the first time a sparkle of adventure. Perhaps that came from the awe in which the Spaniard held them.\n\nAfter all, they did look like a romantic pair. Joy's shopping in New Orleans had netted her laced boots and a riding skirt of white piqu\u00e9, a broadcloth shirt, and a white hat which looked immensely impractical but which was not.\n\nThe tanks were being filled when they arrived and Kurt kept well away from the three self-styled scientists. He didn't wish to break the tranquility of the moment, the illusion that everything was well. Somehow contact with the three made him feel cheap.\n\nHe filled in a few minutes by removing the glass from the doors and side windows of the yellow ship's cabin. \"It's too hot,\" he explained to the Spaniard. But to do this, he had to sacrifice the comfort of his gray felt hat. From his small bag he took a helmet and a pair of goggles.\n\nJoy exclaimed her pleasure at the sight of the helmet. \"It's funny! Where did you get that thing?\"\n\nKurt smiled. \"You ought to know. It came from your beloved California. Chinese, I guess. I received it from an aged fellow who used to take my plane every few trips.\"\n\nHe held the helmet out so that she could see it better. It was made of heavy material, soft as kangaroo hide. Embroidered and painted along the crest of it, so that the tails came down to twine about the ear pads, was a great fire-spitting dragon.\n\nIt was one of those things a pilot likes to acquire as an offering to the dangerousness of his trade.\n\n\"It's good luck,\" said Kurt, and was then instantly sorry.\n\nJoy's gaze was averted. She pretended to take an interest in the natives who were straggling out of their huts in the early dawn. Kurt had reminded her that she was supposed to be a hoodoo. It was painful\u2014this seriousness in superstition\u2014as adolescent as the profession of flying itself.\n\nThey took off in a blasting cloud of sand. The transport ship was leading the way now, flying low and fast as though anxious to reach its destination without any more loss of valuable time.\n\nThey flew for an hour. On the ground it would have been a trek of a week's duration, perhaps more. But here in the clear blue air they devoured miles in the breath of seconds.\n\nHenequen fields, acres of bayonet-pointed plants, fled away under their downreaching wheels. Roads gave way to ox trails and then there was nothing but blank ground, verdant expanse, tangled and meaningless.\n\nThey came to a high plain, flat as a table, an admirable landing field. The transport ship headed down and landed in a geyser of dust. The yellow ship followed and came to a stop a dozen feet from the stretching wings of the giant.\n\nKurt got down. It was hot with a shriveling heat. It was windless and depressing. The silence of empty miles closed in upon them, ringing in their ears.\n\nSloan came out of the big ship first. His bulging eyes were fishy but his trap mouth was set. Bruce followed him, walking stiff-legged like a stalking wolf. Connelly sat under the controls, waiting.\n\nKurt had not had time to realize what was up. He had no warning whatever. A blue, ugly gun glinted in Sloan's grimy fist and the muzzle was unwaveringly centered on Kurt's chest.\n\n\"If he yipes,\" said Bruce, \"give it to him.\"\n\n\"What the hell...?\" began Kurt.\n\nJoy gasped, one foot still in the fuselage stirrup, blue eyes wide with fear for Kurt.\n\n\"Okay, Reid,\" said Bruce. \"We're here. We're in the most deserted section of Quintana Roo. If you want to yell, yell. It won't do you no good. You asked for all this and you're going to get it.\" He waited for that to sink in. His glasses were flashing in the sun, his shirt clung to his back with sweat.\n\n\"You're Nathan Reid's grandson. You're down here to find a ledge of gold ore. I know all about you\u2014all about you. Now spit it out and quick. Where is that ledge?\"\n\n\"Tell Sloan to put that thing away,\" ordered Kurt, eyes as black as ebony, as hard as obsidian. His mouth was closed to a thin line and he spat his words through his teeth. \"If you want information from me, you can go bark for it. Did it ever occur to you that I didn't know anything about this ledge?\"\n\nBruce snorted in derision. \"Turn around.\"\n\nInstead, Kurt advanced a pace, straight at the gun. Sloan slanted a questioning glance at Bruce but the muzzle didn't waver.\n\nBruce also advanced. He shook his arm up and down and a leather-jacketed sap slid out like a stubby snake to hang by its wrist thong against his hand. Bruce juggled it. Kurt came on.\n\n\"Don't!\" cried Joy. \"Kurt! Come back! They'll kill you!\"\n\nBruce sidestepped with a quick motion. The sap moaned through the air, missing Kurt by a fraction of an inch.\n\nSloan's face was completely dead as though he had never felt an emotion in his life. His bulging, codfish eyes were utterly impersonal. He aimed at the fleshy part of Kurt's thigh and fired.\n\nThe impact of the bullet turned Kurt half around. His leg crumpled. He went down, swearing, with a coil of powder smoke drifting about his gaily helmeted head.\nChapter Seven\n\nJOY ran swiftly to Kurt, afraid that he was dead. She was not reasoning logically in that she gave no thought to what her own fate would be with Kurt out of the race.\n\nThe dry dust was swirling in a cloud about the fallen man and for a moment no one realized that Kurt was rolling over and over, plunging sideways from Sloan's gun.\n\nAbruptly a stab of white lightning ripped out of the tan fog. Sloan's automatic leaped back away from bloodied fingers and landed with a small thump on the ground. The blast of Kurt's shot was deafening, but the voice which followed it was more like the thunder accompanying the lightning flash.\n\n\"Keep away from your guns!\" roared Kurt. \"Damn you, stand still!\"\n\nSloan was backing swiftly. He stopped, shaking his hand to rid it of the pain, sending a fine spatter of blood over the sand. Bruce, goggle-eyed and gasping, stayed where he was. Connelly, unseen by Kurt, twisted about in his seat in the transport plane and fumbled nervously through the pile of dunnage.\n\nKurt came cautiously to his feet, still holding the .45. Joy was there beside him, holding him up. They backed slowly toward the yellow ship. Sloan, whimpering, watched them go without protest. Bruce's lips were moving in a slow monotonous fashion, cursing them.\n\nJoy mounted the stirrup and helped Kurt into the ship after her. She flipped the booster and the engine started with a mounting whine.\n\nConnelly found what he was seeking. It came up blue and shining.\n\n\"Hey, you!\" cried Connelly. \"Stop!\"\n\nThe command went unheard in the blast of the yellow plane's engine. With Joy at the controls, the ship was already moving forward.\n\nThe light sub-Thompson in Connelly's hands began to chatter. Bits of dust flecked away from under the belly of the ship. Fabric vibrated under the onslaught of lead. The rudder slammed hard over, hammered there. The yellow ship careened into a right-angle turn.\n\nThe dust which arose from the skidding tail partially obscured the ship for a moment, but when Connelly saw it again it was flying free, headed up into the wind, wheels turning idly under the past momentum of the ground.\n\nThey were gone.\n\nBruce whirled about, his face red and furious. \"Don't stand there like a fool. Spot the direction of their course.\"\n\n\"They got the machine guns,\" protested Sloan, nursing his hand.\n\n\"They... they what?\" stormed Bruce.\n\n\"The two machine guns you said to put in that ship.\"\n\n\"I told you to take them out!\" Bruce roared.\n\n\"I tried to, but I was afraid a customs man would see me or something. Honest-to-God, Bruce... oh, my hand!\"\n\nKurt was engaged in an inspection of his leg. He could feel a trickle of blood going down his thigh. With a pocket knife he slit away the cloth over the wound. Then he smiled.\n\n\"Nicked, that's all,\" said Kurt.\n\nJoy looked relieved. She was jockeying the plane through buffeting hammers of heat lift, gaining altitude as swiftly as possible.\n\n\"Where away?\" said Joy.\n\n\"I don't know exactly.\" Kurt found a roll of bandage in the dunnage and in spite of the close confines he was making fair progress with the dressing. The iodine was making him wince as he covered up the graze.\n\nThat done he looked out across the endless land, gathering his wits. Back in his knickerbocker days he had read something in those old records of Nathan Reid's. Something about a lake of great size, two mountains like a gunsight, and a country slashed by deep ravines. Something about gold. He wished he could remember exactly where those mountains were. But the thought was hazy and incomplete. Nathan Reid's adventures in this locale had been harrowing enough.\n\nHe resorted to a map of the country. The surveyors had guessed at many things, using the things they had heard rather than seen. Quintana Roo seven or eight centuries after the Later Mayan Empire was still a lost world.\n\nBut he found the lake marked in blue and he found two marks like asterisks which meant mountains. He was elated, though he was far from sure that these markings would lead him to anything like a gold vein.\n\nHe was glad of this break with Sloan and Connelly and Bruce. It had given him the excuse he wanted. It had been a shock to hear that they were after Nathan's gold, and he knew they would hardly let the matter drop where it was, but he was glad all the same. Of course, he'd hear from them later.\n\n\"Course due east,\" he told Joy, pointing at the black compass bowl.\n\n\"Aren't you going back to Progreso?\" said Joy, yelling in his ear to make herself heard above the drumming engine.\n\n\"No, I'll explain later.\"\n\nFor a plane it was a small country. On foot it was huge. In a matter of minutes they had sighted a mountain. Joy sliced toward the peak.\n\nKurt sat eagerly forward, watching ahead. There should be another mountain there, close beside the first. And below them he should find a lake.\n\nAnd there it was. Two mountains. He sighted the ground about them, watching for a glint of blue. This was too easy, too easy. The lake was spread out like a sheet of beaten metal, quiet and serene and completely forgotten\u2014or so it appeared.\n\nHe took the controls then, forgetting his leg in the excitement of the discovery. His eyes were sparkling and alive and his mouth was drawn into a tight smile. Nathan Reid had not counted upon such ease. Of that Kurt was sure. Nathan Reid had wanted him to slog across the jungles in painful search.\n\nThe yellow ship cruised over the lake while Kurt inspected the terrain below. He frowned as he saw something which looked like a human habitation. He had heard much about these Indians. About their revolts and their wild return to the land and cities of the forefathers in Quintana Roo.\n\nThe thing he saw looked like a pyramid\u2014was a pyramid with its sides ascending in steps to a square structure on the very top. Mayan architecture. Heavy stone statues of the feathered serpent. He noted that the stone appeared worn and that trailing vines were absent.\n\nBut then that might be some trick of growth rather than an indication of habitation.\n\nJoy was staring down with parted lips, astonished at the structure, completely forgetting the present in the favor of that long-gone past. She remembered what she had heard of the Later Mayan Empire. Human sacrifice, terrible rites, the cruelty of the jaguar.\n\nKurt was interested in the place only as a landmark. There were other buildings down there, partially hidden by the brush, solid and blocky. This had once been a thriving city but now\u2014or so it appeared\u2014it was reclaimed by jungle.\n\nThe yellow ship spiraled lower and lower toward the top of the pyramid.\n\nSuddenly Kurt yelled. Joy stiffened, brought back too swiftly from her imaginings.\n\nKurt was pointing down at the structure. The yellow plane went round and round, one wing motionless, spinning without losing altitude.\n\nA streak of yellow had shined briefly there.\n\nKurt cut the engine. \"There's gold! That means there's a ledge of it around here someplace. They wouldn't carry it far. That means we're right!\"\n\nJoy didn't have the slightest idea of what was behind all this but the thought of yellow metal thrilled her.\n\nKurt shot the power on again and the ship went hurtling back into the blue. Kurt looked around, watching for a black speck in their element which would proclaim the coming of the transport plane.\n\nThen he dived in once more upon the pyramid. The lake had left a sandy stretch of beach beside it which might conceivably be used as a landing field in a pinch, but Kurt passed it by. Something was warning him not to land.\n\n\"If I could only get some of that,\" he muttered, looking at the yellow flecks of sunlight down in the temple. \"It might be the same gold.\"\n\nThe plane went around in a tight bank, almost touching the top of the pyramid with its left wing. Kurt stared at the structure which was whizzing by so swiftly. He reached out his hand as though he could breach the gulf and take the temple away with him.\n\nThen he looked at Joy. She was regarding him with a wide-eyed stare as though she thought him completely insane.\n\nKurt leveled off and drove upward again to the altitude of a thousand feet. Several miles away he could see a clear stretch of sand. He would land on that and look the country over. Certainly the vein was here somewhere. He would have to match that nugget in Kimmelmeyer's office\u2014that nugget with its identifying streaks of rose quartz still imbedded in it.\n\nThe country was slashed by a hundred ravines, deep and dark as though hiding their contents from the morning sun.\n\nThe yellow ship went swiftly in for a landing. The ledge had looked wide from afar but here it was apparent that it was flanked by two ravines which left only thirty feet between them. A thirty-foot runway is sufficient if it is long enough, but as he neared the spot it became obvious that the landing would be a tricky affair. The hot and cold summits and depths were making a shambles of the air currents. The wind was rocketing away from cliffs and shooting straight up or ramming straight down again.\n\nThe ship was bounced like a rubber ball. Joy watched the runway below as Kurt came in.\n\nThe wheels seemed to fumble for the ground. Kurt fought the controls, right, left, right, forward and back, trying to maintain a balance.\n\nIt was crosswind and they kept drifting over the edge. Kurt went around and came back again, eyes very hard with the effort.\n\nSuddenly he sent the plane down in a quick pass at the ground. The wheels struck, bounced and struck again. The edge was almost within reach of their fingertips. Kurt held them on the runway with his motor and his rudder.\n\nAt last they stopped rolling, one wing over the ravine. Kurt climbed out, flexing his stiff leg, looking about him. Joy remained in the ship, feeling weak after the effort at getting down.\n\n\"What's this all about?\" demanded Joy.\n\nKurt realized then that he had told her nothing of all this even though she was embroiled tightly within it. He came back to the stirrup and smiled at her.\n\nIn a few tense words he told her about Nathan Reid, about the gold nugget that had to be matched.\n\n\"But,\" she protested, \"there was gold on that pyramid. I saw it. Why not get some of that?\"\n\n\"I don't think it's from the vein,\" said Kurt. \"I've got to find a gold nugget with the rock still clinging to it. Otherwise I miss out on four million, a town house, a country house, and God knows how much more. It's worth the try.\"\n\n\"I should say it is,\" she said, dazzled.\n\n\"Well, then, let's be up and doing. I've only got about twenty-eight days in which to find this thing. And by the shades of Nathan Reid, I'm certainly going to find it.\"\nChapter Eight\n\nTHE country might have looked small while they were aloft, but now that they started down a ravine with the terrifying solid height of the canyon walls, they began to have some conception of this silent immensity. They spoke little going now, partly through the precariousness of their descent, partly through the solemnity of the tomblike silence which was relieved only by the dismal moan of the wind finding its way through the giant gray boulders and the clattering harsh green leaves of strange trees.\n\nKurt, in his excitement, had forgotten the gray hat. He wore the helmet, that talisman presented to him in Joy's native state. Halfway down he stopped on a ledge, uncoiling a long piece of rope he had brought with him from the plane. When he had it secured to a niche in the sheer wall, he absently shifted his .45 from his pocket to his belt. The gesture was not missed by Joy and she began to stare up and down the canyon floor below them as though expecting all sorts of horrible things to leap forth.\n\nHe fastened the rope carefully about her slim waist. \"Hang on,\" he commanded and began to lower her over sixty feet of space. Swinging there, going slowly down, Joy saw the wing of the plane over them like the protecting hand of a saint.\n\n\"How... how will we get back up?\" she called.\n\n\"I'll manage it,\" Kurt promised.\n\nShe came to rest on a ledge below and Kurt came down like a descending bomb. When he had dropped beside her he released the rope from his grasp and let it hang. Fifty feet still remained between their ledge and the bottom, but the slope was not severe, and they had little difficulty in traversing it.\n\n\"What are we going to do now?\" asked Joy.\n\nKurt produced the sharp pointed sample pick from his belt. \"A ledge such as the one Nathan Reid must have found here is certain to be in evidence. We'll scout some of these ravines.\"\n\nHe had added the gold pan to his equipment for testing the wandering stream which brawled down through the ravine. His eyes held a far light and his mouth was set in a half smile which was more determination than humor.\n\n\"Later,\" said Kurt, \"we'll visit the Maya city. I'd like to take a look at that big pyramid just for luck. I remember something about it from the journals. Gradually everything I read is coming back. Gee,\" he cried boyishly, \"wouldn't it be swell to walk in on Kimmelmeyer before the eighth and slap an identical nugget on that desk of his!\"\n\nSome of his enthusiasm began to infect her. It was strange, this wish to defeat a dead man. At first the thought had been gruesome to her. But the dead man had hated Kurt Reid and something in that was helping her to understand, to want Kurt to succeed, to wish for victory for Kurt's sake.\n\nThey walked along the side of the brook, parting the small bushes which grew there, disturbing clouds of insects which rose angrily like hostile fleets of planes to jab sharp stingers into their fair skins.\n\nKurt stopped from time to time, taking up dirt from the creek and placing it in the big flat metal pan. He washed it with a swinging, rotating motion, picking out the larger rocks, doing his work carefully until only a little black sand remained in the bottom. Sometimes the sand contained flecks of bright yellow gold.\n\n\"See that color!\" cried Kurt each time. \"There's a vein along here, up above here. See there's more this time than there was last. We're getting closer and closer!\"\n\nLate in the afternoon, having dined upon a pocketful of raisins and a flinty biscuit apiece, they came upon the source of the creek. They were not far from the plane as they had not progressed swiftly, but it seemed a long way to Joy.\n\nSuddenly Kurt gave a shout. He was pointing up at a streak of white rock. \"Ore! That's gold up there!\"\n\nHe scrambled ahead without watching his footing. Forgotten was his wound. He mounted high above Joy and began to hammer at the white quartz.\n\nThen he stopped and came down. His face was so melancholy that Joy laughed at him.\n\n\"That's not it,\" said Kurt. \"That's white quartz. Gold ore, yes, but I've got to get a piece with rose quartz in it. Come on, we're going back to the plane. Tomorrow's another day.\"\n\nTiredly she followed him through the approaching dusk. The brook was their trail part of the time and they slogged along, silent again, hemmed in by space and the depressing quietness of the place.\n\nKurt stopped so quickly that Joy bumped into his back. A sound had come up to them. The crackling of brush. The whisper of voices. A chilly fear ran through Joy like a rapier. She was unable to breathe, sensing danger, not from the sound but from Kurt's alert posture, from the quiver of his thin nostrils as though he could scent the air and discover the danger as cave men had discovered danger a million years before them.\n\nJoy felt her heart swelling up, pounding inside her breast like a hammer, suffocating her.\n\nAgain the sound reached them, closer now. Two men with coppery skins emerged from the brush ahead, walking with their gaze on the ground as though reading a message there. They were trackers. Mayans!\n\nKurt did not move. The man in the lead, his black hair drawn down tight with a metal band, stopped, also sensing danger. His black eyes reached up, caught sight of Kurt and stared. The man's companion bumped him and glanced across the small clearing.\n\nA yell more shrill than anything Joy had ever heard before rasped through the air. A cry of warning from the second Indian.\n\nThe first darted into the bushes, pulling an arrow from his quiver. Kurt heard the whistle of the feathered shaft. He drew the Colt .45 as though he were on a target range.\n\nFlame ripped across the thick dusk. The Indian screamed and fell forward. His companion was running swiftly away. Kurt, unwilling to shoot a man in the back, let him go.\n\nJoy's throat pulsed. She moaned a little, leaning heavily against Kurt, trying not to look at the last agonies of the dying man.\n\nThe brush was suddenly filled with cries and the crash of broken bushes. There were others, many others coming toward the sound of alarm and the shot. Kurt backed up, pushing Joy along with him. He looked anxiously about him for a barricade, something behind which they could hide and defend themselves. He found nothing.\n\n\"Run,\" he said and his voice was harsh.\n\n\"And... and leave you?\"\n\n\"Run! I can't. My leg won't let me. If you get free, if they can't find you, then you can take the plane and perhaps help me. Go quickly. Damn it, run!\"\n\nJoy saw the logic behind the order. She did not question the rightfulness of it. Every instinct made her want to stay with Kurt but he had ordered her to do a thing and somehow he was not to be questioned.\n\nIn an instant she was gone. Kurt turned about and faced the clearing again. Men were pouring up through the trees, dimly seen except for the flashes of copper skin. The Mayans stopped when they came to the clearing edge. Kurt was waiting for them, waiting for them to make the first aggressive move.\n\nA copper-tipped spear carved air in a flash of brilliance against the leaden hue of the dusk. When it struck a tree behind Kurt its shaft hummed.\n\nAn arrow sang shrilly in his ear and then an avalanche of feathered color came at him. Despair welled inside him. The .45 rapped again and again. Sparks streaked out far before him. Men thrashed about in the underbrush.\n\nOne clip gone, Kurt hastily began to load. But they would not grant him time for that. Like yellow-skinned tigers they ran across the intervening space, yowling and brandishing war clubs.\n\nNo time to reload. The sample pick was in Kurt's belt. He whipped it out. Its hand was a foot and a half long. One end of it was a hammer, the other was a wicked sharp point. Let them come.\n\nThe attack of the first man knocked Kurt back with its violence. The sample pick buried its point in the Indian's skull, coming away dripping.\n\nThe pack closed in. Kurt was borne to earth under a writhing blanket of unwashed greasy bodies. Hard edges hammered him. Nails tore at him. He fought back as best he could using every hold he knew.\n\nBut the end was certain, there before Kurt knew it. They held him inert under them, gripping his arms, punching him to see if he were dead. Then convinced that he was only half unconscious they dragged him along over the ground as though he were a sack of maize.\n\nThe grass was turned red as he passed, but through his half-closed eyes he saw five men who would never move again. He had paid his score in full.\n\nThey had forgotten Joy, perhaps. He could not see. The trail was long and when he reached the end of it he was slumped like an empty burlap bag.\n\nNathan Reid had known the trap he had set. Perhaps Nathan Reid's restless ghost was somewhere about, smiling with that cruel thin smile with which he had taken a rabble army to its death.\nChapter Nine\n\nHOW long he had been there he did not know. Many dawns had come and gone. Many hot afternoons had passed by, melting into the cool of evening.\n\nFever hits hard on the heels of physical injury and the wounds were almost healed before Kurt Reid lost the lethargy of delirium and high temperature.\n\nOne day he sat up with a start, knowing where he was and why he was there, remembering Nathan Reid and Bruce and the Mayans. It was like awaking from a bad dream to find that it was so after all.\n\nHe was in an oblong room built of dirty limestone. The ceiling came together above him in steps, its architecture that of the Later Mayan Empire because of its false arch. The Mayans had never learned to make an arch.\n\nDried lake reeds went to make his hard bed. A square window, a mere hole in the thick rock walls, showed a section of blue sky and the drifting segment of a white cloud. The place was silent save for the drone of flies in the room.\n\nTen minutes of sitting up made him realize how weak he was. He lay back with a weary sigh, looking up at the smoky, stepped ceiling.\n\nHow in the name of God had he gotten there? Where was he? Why was he still alive?\n\nThat last fact made him wonder the most. It did not seem reasonable that he would be attacked, that he could kill five and still live himself. Something was wrong. And then when he thought about it hard a tugging thought made him shiver.\n\nWere they keeping him for some terrible purpose?\n\nHe slept after that and dreamed of shifting horrors, of flames and pain and death.\n\nThe next day he was awakened by the entrance of an aged woman. She was fat and greasy. Her hair was braided and she was dressed in a dirty white cotton singlet. When she saw that he was conscious she stood staring at him a long time. Then she went out and returned with a copper bowl filled with maize and a heavy bread. Her study was disconcerting\u2014she looked at him as one looks at a pig before slaughtering time.\n\nKurt sat up again. He was suddenly possessed with a restless warning, a nervousness. It was as though a dynamo had started up inside him, filling him with tingling electricity. How many days had passed? How close was it to the eighth of October? He was due back in New York. Otherwise Nathan Reid would win after all.\n\nAnd what had happened to Joy? Had she gone with the ship? And where were Bruce and Sloan and Connelly?\n\nHe ate the maize with the ravenous appetite of past fever. When he had scraped the shining copper bowl of all it had held he found that its smooth bottom was a perfect mirror. A gaunt yellow face stared back at him. The eyes were sunken, a stubble of black beard had come out on his chin.\n\nFrom the length of the beard he knew that he had been there many, many days. Weeks perhaps. Why had they kept him?\n\nHis helmet had gone, his pockets were empty. The remains of bandages clung loosely to his arms and shoulders. He did not recognize his own identity. He was filled with the strange idea that it was not Kurt Reid.\n\nAnd then voices drifted to him from the front of the hut. Men were speaking in Spanish out there. And one voice had the guttural American intonation he would have recognized anyplace.\n\nBruce!\n\nThe other man spoke slowly and clearly as though he were very old. \"Now that the black devil is again awake, you are forced to wait no longer. You may be rewarded for bringing him here to us by witnessing his death. Perhaps we shall find other ways of rewarding you.\"\n\n\"The more speed the better,\" replied Bruce. \"I'm sick of hanging around this place. I've done you a favor, now you can do one for me by speeding it up. To me, time is valuable.\"\n\n\"But how well I understand. However, there is such a thing as decorum. In the light of the full moon the rites shall be carried out. We have waited too long for this to be in a hurry.\"\n\n\"Waited too long?\" said Bruce.\n\n\"How not? Perhaps fifty years. I myself scarcely remember the time. But I remember his face. He has not changed, he cannot age. Until he is devoured by flame, he will return twice each century to take his toll of our people. He is an avenging spirit and it is necessary that we kill him.\"\n\n\"Oh, certainly,\" agreed Bruce. \"He's the one all right. What did he do the time before?\"\n\n\"He came with a dozen men, all of them wild of eye and armed with weapons we thought strange and godlike. At first we accepted him, but when we refused to give what he wanted, he killed like a wolf that knows no satiation. We slaughtered the twelve, but him we could not kill. Perhaps our gods were against it, who knows?\"\n\n\"He's the one,\" said Bruce. \"I came far to tell you and to bring him to you. Perhaps I shall want a reward a little more definite than witnessing his death.\"\n\n\"Your service has been great. The three of you shall not want of our goods.\"\n\nThe voices faded away, still talking, leaving Kurt in the grip of a cold sweat. His staring eyes were filled with the knowledge of the Mayans' error.\n\nHe knew now why Nathan Reid had made him come down here. He looked a little like Nathan. Generally, anyway. Black hair, dark eyes, stringy figure. He had come booted, with a gun flaming in his hand.\n\nThey had known Nathan Reid would come back and Nathan Reid had sent him. They had waited for fifty years! The gruesomeness of such patience made Kurt shiver.\n\nNathan Reid had sent him into a trap and Bruce had clinched it. But how did Bruce tie up with all this?\n\nHe slept again and when he awoke it was late afternoon. The sun was on the wrong side of the building and it was very dark within. But in spite of the darkness, a square of light danced restlessly on the ceiling.\n\nKurt studied the square. It went back and forth, back and forth, sometimes quickly, sometimes slowly. Someone was carrying something shiny outside. In a moment the light would stop.\n\nBut the light did not stop. It went on and on for minutes. Curiosity made Kurt arise. He stumbled to the window and supported himself on the narrow ledge with his elbows, looking out.\n\nThe source of the light came from a small hut across a shallow ravine. It flashed with varying length.\n\nThen Kurt knew exactly what it was. Talking sunlight ! Coming from a window, using international Morse code.\n\nDash, dash, dot, dash. Dot, dot, dot. Dash.\n\nThat would be QST. \"Calling, calling.\"\n\nFlash, flash, flip, flash. Flip, flip, flip. Flash. \"Calling.\"\n\nFor a moment Kurt was puzzled. Who would want to get in touch with him? Who would be here besides Bruce and Connelly and Sloan?\n\nJoy!\n\nIt was like a shower of ice water. Kurt looked back at the room and saw the bright pan. It would be impossible to signal. He had no sunlight in his direction. He was forced to stand there and watch, powerless to answer.\n\nHe did not sleep well that night. With returning strength he was growing restless. No one of his vitality could remain down so very long. He awoke just as the sky was graying. He spent an hour trying to clean himself up, using the copper bucket of water which had been left inside the hut. It was a painful task, ridding himself of that stubbly chin growth, but he managed it.\n\nHe took off the now useless bandages and bathed himself. He felt better after that, almost well again.\n\nWhen the sun came swinging out of the horizon he began the construction of a heliograph. He took the morning bread and placed it on the sill. Then he notched it with sights like those of a rifle. Finally he sunk the copper plate into the far end, making a hole in its center so that he could direct the beam with his improvised sight.\n\nHe tried his QST several times that morning and he began to be tormented by the fear that Joy had been taken away. Then at noon he received an answer.\n\nFlip, flip, flip, flip. Flip. Dot, dash, dot, dot. Dot, dash, dot, dot. Dash, dash, dash. \"HELLO,\" said Joy.\n\nKurt applied himself to his heliograph. \"How did you get here?\"\n\n\"They found me and brought me in.\"\n\n\"What are they going to do with you?\" demanded Kurt.\n\n\"Nothing that I can see. They treat me with every courtesy but they won't let me walk outside.\"\n\nTwo stabs of sunlight flashing across the ravine. A silent conversation which went unnoticed by the village.\n\n\"Bruce is here.\"\n\n\"I know. He landed days ago,\" said Joy.\n\n\"Won't they do anything to him?\"\n\n\"I guess not. They let him wander through the town without a guard. I can see the transport plane down on the strip of beach.\"\n\nFor an hour they talked on and then footsteps sounded outside Kurt's door and he was forced to hide his crude instrument.\n\nThe door opened and Bruce thrust his face inside. Bruce was tattered and unwashed. He had not shaved and even his glasses were smudged. Behind him stood an old man and two young warriors leaning on their copper-tipped spears. In that glimpse of the outside, Kurt saw the pyramid.\n\nThe old man with Bruce was dressed in a flowing robe. His eyes were steady and serene, his face was wrinkled and wise, but there was about him a certain streak of savageness which Kurt could feel rather than see.\n\n\"Hello, wise guy,\" said Bruce. \"How are you getting on? Enjoying yourself, I hear.\"\n\nKurt looked steadily at him without answering.\n\n\"We came in just in time,\" said Bruce. \"The natives were discussing whether or not you could be Nathan Reid. So we stood up for you. Yes, sir, we stood up for you. We said you were Nathan Reid. We said we was after you but that as a special favor we'd let them have the fun of killing you.\"\n\n\"Thanks,\" said Kurt, hands in his pockets, eyes very dark.\n\n\"It's a laugh on you,\" continued Bruce. \"Your granddaddy raised hell down here, and you look enough like him to stir up their memories. They been waiting for this for fifty years. How do you like that?\"\n\n\"Fine,\" said Kurt. \"Fine.\"\n\n\"And they're setting up all the pins in the alley,\" said Bruce, rocking on his heels, overflowing with triumph. \"You're an easy mark. You're dumb. You was a pushover, big boy. A pushover. And now besides a good chunk of pay, the three of us are going to collect some lucre in the form of gold.\"\n\n\"Had all this planned, did you?\" said Kurt. There was something in his voice like the mutter of distant thunder.\n\n\"Sure we did. And you fell for it. Old Kimmelmeyer was sweating for a while. He was scared you'd have dough enough to come down here by yourself.\"\n\n\"Kimmelmeyer behind this?\"\n\n\"Sure he is. He hired us three to bring you down here. He put that ad in the Eastern Pilot himself and made sure you saw it. You don't think a shyster like Kimmelmeyer would pass up four millions and property, do you? Not on your life. He's got it all fixed. Old Nathan Reid didn't leave a good will. He let Kimmelmeyer draw it up. And now Kimmelmeyer can take the works himself without a squawk. 'Course he's going to be mighty surprised when we start the old bleed on him, but he'll still have plenty.\"\n\n\"So he wanted to make sure I'd die down here,\" said Kurt.\n\n\"Sure. We were going to just plain kill you after we found your granddaddy's gold, but this is better. I don't like straight murder.\"\n\n\"Of course you've got your scruples,\" replied Kurt.\n\n\"Oh, sure. And I'm going to get the dinero without having to bump you off. Diga,\" he said to the old man, reverting to Spanish, \"tell him.\"\n\nThe old man's eyes lit up with a gleam of pleasure. \"Tonight, devil though you are, you are going to die by fire. Prepare yourself, exhort your gods. They can do nothing for you against ours. Before you came for gold. Before you came for gold with fire.\n\n\"Now you're going to get gold!\"\n\nThe Old One hitched his robe about him and went out. Bruce, with a lopsided smile, followed him.\n\nKurt sank down on the edge of the straw bed and stared at the wall.\n\nNathan Reid had taken another trick.\nChapter Ten\n\nTHE pungent odor of woodsmoke drifted into the dark room shortly after darkness had fallen. Kurt sniffed at it uneasily. He felt very like a trapped animal, unable to do anything about his circumstances. His strength, in this emergency, had returned to him.\n\nHe stopped in his pacing at the window. A fire was somewhere in the front of the building. He could see its reflected glare on the houses opposite the window. The black night was drawn down tight as a net over the village.\n\nThe wish to defeat Nathan Reid had carried him to this. But then, if he hadn't tried, he never would have met Joy. That seemed very vital to him and he felt himself standing in fear of the fact that he would have missed being with her.\n\nWhat would happen to her now? She was dangerous to Bruce and therefore Bruce could hardly be expected to take her away. She was certainly no use to these Indians and they would therefore kill her as they were going to kill him.\n\nHe thought about her a little while. Her blue eyes, laughing. Her hair with its golden lights. Joy hadn't been afraid.\n\nIf only he could get to his plane somehow. But then, of course, they'd found the yellow ship. It wouldn't be there anymore.\n\nHis musings were interrupted by the sounds of men outside. The door was flung back. Straight Mayans were standing there, led by the old man in the robe. Their glistening bodies were silhouetted against the fires on top of the huge pyramid.\n\nKurt began to understand now. He'd come for gold, he was going to get gold.\n\nHe stepped out into the center of the military file. Coppery spears, coppery skins. Dark eyes which did not even look at him. These Mayans had remembered something of their ancient mercenaries, the Toltecs. They marched on either side of him, in two lines, in step.\n\nThe pyramid looked bigger than it was in the flaring light of the smoking fires at its top. Kurt became aware of a horde of people standing about the front of the base. Faces were turned exultantly, wonderingly, cruelly, in his direction.\n\nThis show was for the devil who had returned after fifty years. For the killer who had come for gold. And now they were going to give him the gold he wanted. They were going to give him death besides in spite of his charmed existence and his talisman.\n\nKurt held his head erect, neither looking to the left or right. He wouldn't give them the pleasure of seeing that he was afraid anyway. He marched like the soldiers and their copper spears. His boots rang above the sounds of bare feet on the stone pavements.\n\nThey reached the base of the pyramid. A ripple of sound went over the assembly like a wave. It died as Kurt started the ascent toward the narrow top.\n\nThe moon was shining now, clear and yellow, sparkling on the surface of the lake. Great stone statues stood out in all their grotesque hideousness.\n\nA shaft of memory came to Kurt's aid. Nathan Reid had described all this. A reversion from Christianity, a throwback to the savage paganism of their ancestors. The last grasp of a people to its past glory.\n\nThis was the temple of Kukulc\u00e1n\u2014a god who was represented by a man with bird and snake attributes. The great feathered serpent of the Aztec and the Toltec had originally been this Kukulc\u00e1n. Mexican influence had brought in sacrifice, even cannibalism insofar as the witnesses of the rites were oftentimes required to partake of the flesh of the victim.\n\nKurt Reid, as he went up the stairway on the front of the pyramid, was climbing back through centuries to a decayed and warped survival of the cruelest religious customs. As he came closer to the top he saw that fires had been built all about the square blocks above\u2014had been built in a rectangle which enclosed the images of deities.\n\nAt first it was apparent that no opening had been left in the flames and then he saw that the two front lines were at variant depth so that a man could turn from his course and go through unscathed. This was part of the magic mummery with which the priests held their restless people.\n\nPassing between the scorching fires, Kurt first saw the image of the death god. It was a repulsive thing, this fancied likeness of death. It was a great stone skull with grinning teeth and clasped bony hands. Under it was seated a man incredibly like the stone image. The priest of death seemed to be drugged as he did not look up when Kurt entered the square.\n\nAnd then Kurt received a shock. The carved stone image of Kukulc\u00e1n had been done in such a way that it left a seat between the two outstretched, clawlike hands. And on that seat, arrayed in a feathered robe, sat Joy.\n\nShe did not look down. She stared straight ahead, unblinking. No motion of her lips or hands was apparent. She was obviously under the influence of some drug, thought Kurt.\n\nGod, what a fate to leave her to. Her golden hair had done the trick. Bruce had not wanted to identify himself with her and he had let the Mayans draw their own conclusions. The priests had not been slow in recognizing her potentialities. She would be held there, living embodiment of the sun until she died\u2014or was killed because her usefulness was ended. True, she would be inviolate. No man would dare touch her. Such had been the reaction of the Mayans to the first blond white woman they had ever seen.\n\nThe men with the spears distributed themselves about the square, their shining backs to the fire, their eyes impassive. Kurt felt his arms grasped from behind.\n\nThe Ancient One approached, muttering a chant. He addressed Kurt in Spanish. \"You came again. The Mayans are a hospitable people. You shall have your gold.\" He chanted again and then said, \"So many warriors have you killed, so much damage have you done. So have you changed the seasons and blighted our crops. Your deviltry has brought plagues and famine. You are responsible for all we have suffered for fifty years.\n\n\"Now you are offered to Kukulc\u00e1n, god of the sun, god of the sun metal, gold. Your own magic can avail you nothing against his, for he has sent a powerful servant down from the skies to help us.\" He pointed dramatically to Joy.\n\nShe did not move. She was holding the heavy staff of the feathered serpent stiffly upright beside her. Her robe was shining, made of golden feathers of tropic birds. Her blond hair curled down near her shoulders, sparkling in the light.\n\nKurt saw her bewitched stare and mourned that she would not give him just one sign. It would have made it easier for him.\n\nHe let his gaze roam about. Through the fires he could see the vague outline of the big plane on the beach. Bruce was somewhere in the crowd with Connelly and Sloan.\n\nA crude metal crane was erected over a makeshift forge. These people had worked in metal years before the Spaniards came. From the crane was suspended a pot. A man was working at the bellows. The contents of the cauldron were bubbling and hissing.\n\nMolten gold! Liquid fire! One thousand and sixty three degrees centigrade! Yes, they were going to give him gold.\n\nHe staggered back as though already feeling the sting of it. The men behind him held hard, muscles rippling on their naked backs.\n\nAgain Kurt looked at Joy. She was still staring straight before her, unmoving.\n\nHis eyes caught sight of something else. How could he have missed it before? The altar about the base of Kukulc\u00e1n was made of gold, pure gold cemented together in irregular lumps. And in that gold were flecks of rose quartz.\n\nMy God, no wonder they hated Nathan Reid. He had stolen a part of their altar! A spot was empty near the tip, apparently chipped away. That would be the spot Nathan Reid had found that nugget Kimmelmeyer had balanced so carelessly in his hand.\n\nSo near to success and yet so far from it. The Ancient One was addressing the people below, flecks of foam on his lips as he spoke. A wild light was in his eyes. He was bringing something from the folds of his robe: Kurt's helmet with its goggles and its emblazoned dragon. They thought it was Kurt's idol. The Old One was mocking it, shaking it and making the goggles sparkle in the flames.\n\nThe Old One turned and came to Kurt. He jammed the helmet on Kurt's head with such ferocity that the goggles were shaken down until they covered Kurt's eyes.\n\nThe lenses gave him relief from the stinging, swirling smoke. The Old One had unconsciously done him a favor in mocking that poor Asiatic dragon.\n\nThe crane began to swing away from the fire now. It was precariously balanced, spilling some of its precious liquid on the stones where it spattered like beams of sunlight, exploding as it struck.\n\nThe men behind Kurt flexed their naked shoulders. They forced him to his knees. He was so near Joy he could have touched the skirt of her robe. Still she did not look at him.\n\nThe crane swung closer so that its heat scorched Kurt's face. The Old One and the ring of younger, naked priests were chanting in a high monotone, their breech clouts swinging back and forth as they gave up their bodies to the rhythm of the song.\n\nMy God, they were going to pour molten gold down his throat!\n\nKurt felt himself turn sick. He tried to struggle back to his feet and the hands closed hard about his arms, holding him. The crane swung nearer and nearer. In a matter of seconds he'd be dead!\n\nFascinated he watched the slow approach of the balanced cauldron. He tried to reach out with his booted foot and kick it away, but they prevented that. Even so, he touched the edge and spilled a full pint of the sizzling liquid.\n\nHe closed his eyes, gritting his teeth. The Old One was yelling more loudly. The crane was so fixed that a delicate mechanism could tip it without any actual physical touch.\n\nThe chant grew louder and louder, drowning the crackle of the flames.\n\nHow Nathan Reid's ghost must be laughing! How Bruce must be reveling in this. And Kimmelmeyer had sent him here, knowing all about it.\n\nHe resigned himself to his death before the hot breath of the cauldron. Joy was drugged, thought Kurt, that was well. She would not have to watch this.\n\nSuddenly he caught a blur of motion. The chant broke. Men screamed and shrank quickly away. The feathered staff Joy had held came down in a blurred arc. Its heavy head struck the mechanism which tipped the cauldron.\n\nA shower of flaming gold leaped up into the air. It came down instantly in a fine spray, scalding. Kurt cried out as drops struck his unprotected cheek. He felt his helmet scorch under the rain of flame. The lenses to his goggles were instantly bubbled where the gold had touched.\n\nBut the Mayans were almost naked. They wore no such protection as clothes and helmets and goggles. They screamed, some of them blinded forever. The rank odor of burning flesh was in the air. A crazed guard stumbled into the fire and was instantly a tower of flame, burning but still alive.\n\nKurt's mind acted swiftly. He was on his feet before all the gold had come down. He cried, \"Come on, Joy!\"\n\n\"Run to the plane!\" she shouted, eyes alight. \"I'll hinder you. Come back for me!\"\n\nKurt knew that time would not allow an argument. He sprinted across the bodies toward the entrance. A swelling roar of the mob came up to him. Men were running up the steps on the front of the pyramid.\n\nFlames were to the rear. Kurt knew it was either that or nothing. He seized a spear of a blinded guard. Men stood between him and the rear. He charged them. The spear bit deeply, snapped off. The target fell aside.\n\nKurt dived through the fire. Long steps were before him. He catapulted down them. The mob was streaming around the sides to intercept him. The jungle was still far away. He ran faster, each landing jarring his teeth.\n\nA runner, faster than the others, was there waiting for him. Kurt sent the shaft of the spear before him like an arrow. It caught the Mayan in the forehead and drove him down. His body fell alongside Kurt's descent for several steps.\n\nA gun flashed. That would be Bruce. Or Sloan or Connelly. Kurt reached the bottom just ahead of the crowd. He ran toward the jungle edge, toward the place he had left the yellow plane, hoping against hope that the ship would still be there. Without it he could do nothing.\n\nShots sounded again, closer to him. He looked back into the mob, saw their open mouths, their angry eyes. He doubled his speed. He seemed tireless, exhilarated by the escape, bolstered up by his determination to lick Nathan Reid after all, driven onward by the necessity of pulling Joy out of the city.\n\nHe reached the edge of the jungle and flashed through the opening to a path. The moonlight was streaky before him, lighting his way.\nChapter Eleven\n\nTHE restless pattern of the streaks of light was sufficient for Kurt's passage. Once in a while he checked his headlong run to dodge as some fancied ambush seemed to loom through the shadows.\n\nBehind him the searching parties were spreading out, covering every conceivable trail. Once Kurt heard men running close behind him and he doubled his speed, placing as much distance between himself and his pursuers as possible.\n\nAfter that he heard nothing. The silence should have made him easier, but it did not. He could fancy now that they were waiting silently for him at every turn of the path.\n\nHe came out into a clearing and saw the mountains there. In truth they were a gunsight, and he was instantly aware of his exact position. He had only to follow down, keeping that cleft in sight to arrive at the ravine where he had left the plane. If he could only be certain that the plane was still there!\n\nMaybe they would kill the girl instantly for her treachery. All manner of doubts began to seep into Kurt's confidence, eventually shattering it.\n\nFor minutes he ran without stopping. Then he would pause and listen. On he would go, scanning the shadows. His boots made a terrific amount of noise on this soft turf\u2014or so it seemed to him. Would he never reach that ravine?\n\nHe sprinted through a canopy of leaves, all in darkness for a moment. The bottom fell out from under him. He crashed down into the ravine. The drop was only ten feet but it jarred him. He stood up dizzily, faltering in his stride. Then he saw the gunsight again and his vigor returned.\n\nHe came to a fork in the trail. Two ravines met here to diverge again at a narrow angle. He was undecided and then chose the right-hand trail.\n\nA flicker of light came from behind. He stopped and looked at it. The thing was bobbing up and down, back and forth. A man walking, carrying a torch. They were close on him again.\n\nHe began to run, avoiding the mighty boulders all about him. He was not quite sure which ridge held the plane. Nor was he certain that the plane was still there. Things looked different in the moonlight, but he had thought he could see the wing.\n\nShouts rose up far back of him. He stood clearly outlined in the moonlight, standing on barren white sand with the cliffs like gray ghosts on either side of him. Where was the rope he had left there?\n\nThe truth was slow in coming. He was in the wrong channel! He was one ravine up from the one he had climbed down. Nevertheless, if he could only scale this high cliff, he could get to the ship from the opposite side.\n\nHe had no rope, no sample pick to help him, but he started up. A fissure had been left in the porous rock, a chimney open at one side. By placing his back to one side and his feet against the other he was able to inch himself upward a little at a time. But the cliff was better than a hundred and fifty feet high and he saw too late that the chimney did not continue all the way.\n\nA chorus of cries reached him. Torches bobbed like fireflies down the ravine. Men were coming up, running at full speed. They had found his trail, and in a moment they would discover him on the wall.\n\nKurt moved faster. He had to get himself out of the range of arrows and spears.\n\nIf Bruce or Sloan or Connelly were in that mob, he'd be shot down instantly.\n\nThen they saw him. They stopped for a moment, lifting their torches up above their heads as though to shed their light higher. The moon was bright, sending ripples of light off their shoulders. The sparks from the torches fell unnoticed on bare backs.\n\nWith a bellowing concert of discovery, they closed in on the bottom of the cliff.\n\nAn arrow sang close by Kurt's hand. With a metallic ping it bent its copper point against the rock and fell back. Kurt went faster than before.\n\nHe had run miles already and he was tiring fast. He had forgotten his past sickness but he was remembering it now.\n\nJust as his hands closed over the ledge thirty feet from the top, just as he left the chimney, the thought struck him that nothing prevented the Indians from climbing up the other side to get him.\n\nAnd the wall above was sheer, too steep to climb. He needed a rope and he had none. He was trapped, unable to go either up or down.\n\nArrows were coming with greater regularity. He leaned back from the edge, watching the gleaming points pass up and turn back on themselves for a swift descent vertical.\n\nAn occasional arrow came over the edge with just enough momentum to fall at Kurt's feet. He picked up a handful. They wouldn't be able to shoot them again anyway.\n\nAnd then Kurt was obsessed with a coldblooded thought. Those Mayans were used to climbing. Maybe he saw a way out of it.\n\nCupping his hands, his dark eyes glittering, he yelled, \"\u00a1Ven aca! \u00a1Ven aca, carajos! Come up and get me!\"\n\nA shrill chorus greeted the dare. Kurt, crouching on the ledge, his helmet straps flapping in the brisk wind, cried, \"You yellow snails, \u00a1ven aca!\"\n\nHe did not show too much of his head. Bruce or Sloan or Connelly might be waiting down there for him.\n\nA scratching sound reached him after a long silence. Sure enough the men were coming. Looking down the fissure of rock he could see their bronzed shoulders moving. There were three in a row.\n\nKurt's mouth tightened to a slit. He felt like laughing and knew how close he was to hysteria\u2014as near as a man of Kurt's temperament can get.\n\n\"Come on!\" he cried almost joyfully. \"Come on and get me!\"\n\nThe first in the line looked up with startled surprise at the nearness of the voice. Then he climbed faster. One hand clutched a knife between two fingers.\n\nKurt waited. When the Indian was within three feet of the top, Kurt very deliberately reached down and took the knife wrist in his powerful grasp. He pulled up. The Indian, surprised at such tactics, could do nothing but use the aid to his climbing.\n\nAround the Mayan's shoulder was coiled a rope. The Mayans had been the first to so use sisal hemp, carrying rope everywhere with them. This fellow, to his own danger, was obeying the custom.\n\nKurt pulled until he could reach the rope with his free hand. Then he suddenly released his grasp. With a startled shout, the Mayan fell back, unable to keep his holds, leaving the hemp in Kurt's hands.\n\nThe two others in the chimney were knocked loose. Their screams rose in a terrified discord as they turned over and over through space. The thuds of their bodies striking the rocks below came dully up to Kurt.\n\nKurt lost no time. He had what he needed now. He tied the bundle of arrows together. They were heavy and strong, making a good weight. Then, like a sailor throwing a lead line to sound depth, he started to swing his rope back and forth along the cliff side.\n\nEach time it swung, it gathered momentum, until it was reaching horizontal with every swing. At last he had it spinning in a mighty circle. He released his hold suddenly. The arrows shot upward. Kurt held his breath. The bundle landed between two big rocks. Cautiously he tested it. It held!\n\nAfter that there was no stopping him. He went up the line like a human elevator. He reached out and snatched at the top, holding the edge, dragging himself further upward.\n\nA shadow loomed over him, monstrous against the moon. He saw something gleam an instant. He dodged, instinctively throwing himself to solid ground over the edge.\n\nA bullet snapped close by his head. He sprang up. The twitching eyes of Connelly met his. Connelly had come up from the other side!\n\nKurt dived in for the gun. Connelly had hesitated for an instant and that instant had meant his death.\n\nKurt twisted the man about in a half circle. Grasping the gun, Kurt threw Connelly away from him. Connelly shrieked in terror. His feet fought to keep the edge. His grip, moistened by sweat, came loose from the gun.\n\nConnelly plunged downward through a hundred and fifty feet, his cry cut off short as he struck.\n\nThe plane was sitting where he had left it. Kurt, with a shout, darted toward it. Other men were moving along the sandy ridge. They were briefly glimpsed.\n\nKurt reached the plane. Running feet were behind him. He whirled and took a quick aim with Connelly's gun. Without waiting to see whether he had hit his mark, he jumped into the cabin and reached for the throttles and booster.\n\nThe engine started with a blasting roar, making the ship quiver. Disregarding the perils of taking off with a cold engine, thrust beyond the reach of all caution, Kurt jammed the throttle all the way down and came about on the ground.\n\nMen snatched at his wings. He shot twice from the cockpit. The ship was suddenly free. Fighting it to keep it on the narrow runway, he slammed along the sand, engine bellowing, wings fighting to take the air.\n\nAnd then he was away and free. A man below was staring up with a white face, firing with an automatic.\n\nKurt, exhilarated and unafraid, leaned out over Bruce and disdainfully thumbed his nose.\nChapter Twelve\n\nTHE lake was a sheet of beaten silver in the moonlight. High above it, traveling fast in his own element, Kurt could see the altar fires still smoldering on the pyramid. Now if nothing had happened to Joy...\n\nThe streak of white down there was the landing place the transport plane had used. The transport was still there, great wings spread unattended.\n\nWithout waiting to look the scene over, Kurt shot down for a fast landing. Sand flew up under his wheels. He cut the engine to idling speed as he coasted to a stop.\n\nThe village had been silent a moment before. Now it seemed that a thousand men came out of nowhere to run toward the plane. They came from the huts, from the pyramid, just as though they had been waiting for this move. The leaves of the trees blocked away the moonlight in spots, making the charging throng appear and disappear as though wafted onward by magic rather than human feet.\n\nKurt reached behind him. He knew what was there, knew how to use them. A light machine gun came up in his hands. He pulled back the loading handle and dropped to the ground. Let them try for him now. He was ready and waiting.\n\nThe first rank came within a hundred feet of him. He pulled the trigger. The belt began to eat through the breech. A stream of hot sparks fled out from the muzzle, lighting up the sand for yards. The chattering howl of the gun was deafening.\n\nThe first rank melted, the second stopped. The gun raved on, eating its way through the Mayans with leaden teeth.\n\nWith a scream of terror the Indians fled. Kurt cradled the smoking hot gun under his arm and ran in the direction of the hut he knew had once contained Joy. He did not know that she would be there, but something magnetic was drawing him toward the spot.\n\nArrows whistled about him, but he paid them no heed. Once started he could not be stopped. He no longer felt vulnerable. If they had done anything to Joy he would clean up this ruined town as fire cleans an ant hill.\n\nA voice was calling to him. Joy!\n\n\"Here I am! Here I am, Kurt!\"\n\nHe sprinted on toward the hut. The door was closed, barred and locked with numerous barriers. Kurt beat his fists against them. \"Coming, Joy.\"\n\nBut the barriers would not give way. Men were lining up on the beach, waiting for his return. He called out, \"Get into the corner behind something. I'm going to shoot the door down!\"\n\n\"Fire, Gridley!\" cried Joy.\n\nThe machine gun chattered again. Splinters flew from the panels. Smoke wreathed up as the wood burned under the onslaught of sparks.\n\nKurt slammed his boot heel against it. It caved in. Joy was suddenly there, gripping his arm, looking at him with starry eyes.\n\n\"I knew you'd come,\" she said.\n\nGone were the feathered robes. In their place she had put her own trim clothes, now torn. But she still carried the staff of the feathered serpent.\n\n\"They were going to kill you and me together when they found you,\" she said.\n\nKurt turned on the beach. He had had it in mind to destroy the transport plane. Now he saw that it was far away from the yellow ship. He did not dare wait that long.\n\nHe knew he had to get away. Already he might be too late in getting back to New York.\n\nThey ran down to the waiting, idling ship. Kurt stopped within a few feet of it. His way was blocked again. The light machine gun started up. The flashes of powder were so close together that they appeared like one great flare.\n\nThe Mayans scattered again. Kurt thrust Joy into the cabin and followed her. His machine gun was empty, and he tossed it in back. The plane came around with a blast from its hot exhaust stacks.\n\nThe Indians, brave again, tried to close upon it. A single pistol shot came out from under the wing of the transport ship.\n\nThen the yellow plane was up and over the lake, beating the ground with the thunder of its motor.\n\n\"I should have destroyed their crate,\" shouted Kurt. \"They'll follow us.\" Then he stared at Joy aghast. \"My God, I forgot the gold nugget!\"\n\nJoy smiled. Her hand went into the pocket of her skirt and came forth holding a glinting, shining thing. \"I thought,\" said Joy, \"that you might be in a hurry when you came back and I brought a nugget with me. They didn't notice in all the fuss of your getting away.\"\n\nThe plane wobbled for a moment on its course and then, its attention no longer to be ignored, Kurt discontinued the kiss.\n\nIn the morning they landed at Progreso, scanning the skies behind them for pursuit.\n\nThe old Spaniard appeared magically on the beach, smiling, genuinely glad to see them again.\n\n\"I had thought you would never come back,\" he said.\n\n\"But we did,\" replied Kurt with a grin. \"Please, se\u00f1or, those others are behind us, following us. We must have gas and quickly.\"\n\n\"Gas it will be,\" said the Spaniard and went off to procure it.\n\nA half-hour later, when the fluid was gurgling into the tanks, a low mutter came out of the south. Presently a speck could be seen just above the horizon. The transport plane.\n\n\"Quick,\" said Kurt, starting the motor and pressing a few bills upon the Spaniard at the same time. \"What is the date?\"\n\n\"The seventh... I think. Puede ser but that it is the eighth? Si, yo creo... The eighth, se\u00f1or. The eighth it is!\"\n\n\"The eighth,\" moaned Kurt. \"And I have to be in New York before midnight tonight!\"\n\n\"But it's only seven o'clock now,\" said Joy, hopefully. \"That's nineteen hours.... Goodbye, se\u00f1or.\"\n\nThe yellow plane lashed down the strip of sand and took the air again. The Spaniard waved behind them and then jerked up his head at the sound of other motors in the sky. The transport plane was not stopping at Progreso. It would first see the finish of Kurt Reid.\n\nTwo shadows fled across the surface of the Caribbean. At first they were far apart and then gradually the distance began to close between them. The transport plane was miles an hour faster than the other and its light load of gas and equipment was even increasing the advantage.\n\nJoy's glance was restless as she looked back. She saw the set of Kurt's mouth, saw the little drops of gold which had clung to the bizarre helmet. Each time she saw Kurt's eyes she dismissed her fears. They'd win out somehow.\n\nShe began to suspect that they should have stayed at Progreso, but then the time limit would not allow that. They were now far from land. While they had been in Progreso, Bruce could have tried nothing.\n\nShe could fancy his smudged glasses, his coarse mouth, his anger as he drove the transport plane after them. Sloan would be with him, his bulging eyes ready to squint down the sights of a machine gun.\n\nKurt turned back and looked. \"They're gaining. Get that machine gun out. The loaded one.\"\n\nSwallowing hard, Joy obeyed him. He let go the controls and she took them. A glow of happiness came over her. He trusted her, had confidence in her. Then she remembered the coming hail of lead and swallowed again.\n\n\"Bank and go back past them,\" ordered Kurt.\n\nShe put the ship about in a heart-stopping vertical, placing Kurt on the side next to the transport.\n\nThe big plane veered off, but not quickly enough. Kurt raised the machine gun, sighted at a spot in advance of the twin propellers and let drive.\n\nBruce dived out of range. Sloan's face was visible for an instant through an open window. Sloan had a dead pan, the same lack of expression he had used when he had first shot Kurt. His codfish mouth was working, he was talking to Bruce.\n\nThe yellow ship followed down. Suddenly the transport plane stabbed its props upward. White flame ripped out of a window. Fabric ripped away from the yellow wings. The slugs were taking effect.\n\nJoy, trying to stay cool, let the yellow ship dive past. She heard Kurt's gun start up. Its incessant hammering seemed to obscure her vision. She caught a brief glimpse of the other ship. For an instant it was hanging on its props, about to stall out of the position, but while it was there it made an excellent target.\n\nKurt shouted. Joy saw flames. She banked again. They were down close to the waves now, flying almost with their wheels in the white caps.\n\nThe transport plane fell out of its stall. One wing was down and it curved away in a great arc. Joy saw the smoke it trailed behind it. Then she knew that it was hit. Hit and burning.\n\nA man leaped through the swinging door. He had no chute. He went whirling through space like a bomb, striking the water long before the transport. Sloan.\n\nBruce rode the flaming coffin down. When it hit it seemed to explode. Steam shot skyward, mingled with spray.\n\nAfter that there was nothing but scraps of floating wreckage. Joy circled as though unable to drag her eyes away from the sight.\n\nKurt shook the controls, took them and headed the plane toward the north. Joy, suddenly very weak from reaction, slumped back in her seat and wondered, for Kurt's sake, if they would be in time.\nChapter Thirteen\n\nAT eleven-thirty that night, Kimmelmeyer prepared himself for bed. His immense bedroom was dwarfed by the four-poster he had purchased from an antique dealer and the carpet was very soft. The lights were subdued, but even then they reflected themselves upon his black-fringed pate.\n\nKimmelmeyer, dressed in purple pajamas, threw back the sheets and slid within. He lay there for some time without covering himself up. He gave himself over wholeheartedly to the dreams in which he had dared to indulge during the last month.\n\nWhat would he do with Nathan Reid's millions? What wouldn't he do! Big cars, a bigger house, beautiful women.\n\nPraise the day that crazy old fool had come into his office, sent by a legal friend. He had stamped up and down the room while dictating the conditions of his will. He had stamped and stormed and had loosed fragments of his wrath against the world at large.\n\nHe was Nathan Reid, thwarted in everything but the disgusting accumulation of money. And who did he have to leave the money to? No one. No one at all but a fool who had disobeyed him at every turn. A man who had made an aerial chauffeur out of himself instead of a military hero.\n\nSon of his son, perhaps, but then Nathan Reid's son had not been so much in Nathan Reid's eyes. He had run away to Annapolis, that's what he had done, ungrateful pup. Joined the Navy just because he knew it would make his father mad. And the Navy? Damn the Navy. Hadn't they stolen Nicaragua from him?\n\nStamping and storming and damning the world at large. He wasn't going to leave his wealth to a disobedient pup. Not he! Let the yellow belly suffer some of the things Nathan Reid had suffered, let him go down and rot in the tropics. Good riddance. Let the name Reid die with Nathan.\n\nKimmelmeyer chuckled to himself and covered his fat body. Oh yes, he'd agreed with the old fool. He'd told him he was doing right. So Nathan Reid's legal advisors wouldn't hear of such a plan, eh? Well, the plan was perfectly just. Perfectly just. Yes, he'd draw the will. Glad to do it for the friend of a friend. Perfectly legal will.\n\nAnd suppose this Kurt Reid came back with the ore?\n\nNathan Reid had laughed. That ore was part of a Mayan altar and the Mayan men were still there to guard it. The pup didn't have any chance of getting it. Let Kurt Reid have the directions if he wanted them. He wouldn't come back.\n\nBut suppose he did?\n\nThen send the damned money to charity. Any charity. Those legal wolves of his wouldn't get it. Name any outfit that was reliable and the trick was done.\n\nWhat? Was the job finished already? Fine. Splendid. That was capital! Very good work, Kimmelmeyer.\n\nAgain Kimmelmeyer smiled, squirming into a softer portion of the mattress. The charity had been his own thought. He'd already handled their trustees. A few greased palms and everything was for Kimmelmeyer.\n\nAt this late hour, nothing could have slipped up. He should have received a radio from them. He'd wanted to know the instant Kurt Reid died. Too bad they couldn't have gotten a decent operator. A woman, they'd said, and Kurt had insisted. Oh, well, they'd probably had to kill her too. Some worthless tramp, no doubt.\n\nHow he'd spend those millions!\n\nA soft footfall reached him. Was it possible that a servant was still awake at this hour? Kimmelmeyer turned on a lamp beside his bed. It threw shadows grotesquely upon the walls.\n\nThe door creaked, came open. Kimmelmeyer shrieked. He hunched himself back to the top of the bed as though trying to escape. He threw up his fat arm and hid his eyes.\n\nThe gaunt apparition must be a ghost, come back to haunt him. It could be nothing else. Kurt Reid was dead in the jungles of Yucat\u00e1n!\n\nAnd still the apparition advanced across the room. Another was following it. A smaller, slighter person with a merry light in her eyes.\n\n\"Get on a bathrobe,\" snapped Kurt.\n\nKimmelmeyer quivered like gelatin. \"Where... where is Bruce...?\"\n\n\"Dead at the bottom of the Caribbean. Sloan's dead, Connelly's dead. It's twenty minutes to twelve. We've still got time to compare this ore. Where are the papers?\"\n\n\"They... they're here, in my desk.... I...\" Kimmelmeyer was fighting to regain his poise. He mustn't let on the part he had played in this. He must put up a front. This Kurt Reid was real, altogether too real. Big and threatening.\n\n\"Don't kill him here,\" said Joy, maliciously. \"I'd hate to see this rug all dirtied up.\" She winked at Kurt, trying to keep a straight face.\n\nKurt scowled like a thundercloud and his voice was like a thunderclap. \"Get those papers!\"\n\nKimmelmeyer, struggling into a purple robe, was quick to obey. He had everything right there, he said. Only a second. Only a second. He threw the legal sheets out on the desk, brought forth the nugget he had been hiding there.\n\nKurt placed his own piece of ore beside it. They matched perfectly.\n\n\"I hope... hope you'll remember everything I've done for you,\" choked Kimmelmeyer with a sick smile. \"Here, sign this, and this and this.... But I need a witness.\"\n\n\"You'll do,\" said Kurt to Joy. \"And ahoy outside there. Come on in.\"\n\nA blue coat and brass buttons loomed through the entrance. It was the cop on the beat, his ruddy face very straight. \"I guess, sor, that ye're not akidding me after all. I heard him ask for this feller Bruce, just like you told me to listen for.\"\n\n\"Good going. Have you got the warrant I swore out? Then present it after I've signed this and you've witnessed them.\"\n\nThe business was done in a matter of seconds. The officer witnessed the signature and the transaction with tongue twisted painfully between his lips.\n\nJoy signed with a flourish. Everything was done now. A court would place the stamp of approval upon it later, but they didn't have to wait for that.\n\nKimmelmeyer, shrinking away from the officer, was ordered to get into his clothes. Protesting, he was led away, out of the house and to the waiting police car. He would soon be standing trial for the unanswerable crime of attempted murder and attempted fraud.\n\nJoy and Kurt went outside. Joy was gay, tired out but not willing to admit it even to herself.\n\n\"And thus it ends,\" she said, leaning on the staff of the feathered serpent.\n\nKurt looked at her for a moment and then frowned. That remark wasn't refusal, it was an invitation. He bounced the two nuggets in his hand and his smile broadened. \"Ah, yes, thus it ends. By the way, do you prefer a plain gold band from this nugget or a fancy one from this?\"\n\nShe saw that he meant it and stood close to him. A minute or so later they heard the taxi driver who had brought them say, \"Where next, boss?\"\n\n\"The town house,\" replied Kurt with a lordly air. \"Ah, yes, the town house with all despatch.\"\n\n\"And jump a couple of red lights,\" said Joy, \"I feel adventurous.\"\n\nThe taillight of the cab was lost down the dark street like the glowing end of a cigar butt... or perhaps the last embers of an altar fire in far-off Yucat\u00e1n.\n\nStory Preview\n\nNOW that you've just ventured through one of the captivating tales in the Stories from the Golden Age collection by L. Ron Hubbard, turn the page and enjoy a preview of Man-Killers of the Air. Join Smoke Burnham, a colorful daredevil pilot who's gone broke creating a new fighter plane. With his principal financier hot on his tail to recoup his investment, Smoke enters an international race that will take him into the skies of Central America, over the Andes and across the Brazilian jungle\u2014with only death as his copilot.\nMan-Killers of the Air\n\nGIRARD was standing with both feet solidly planted, both hands shoved into the pockets of a pure camel's-hair overcoat. Girard's face looked as though someone had started to mold it from soggy putty and had then become bored with the job.\n\nGirard was a big man\u2014knew it, said it and acted it. He could afford to be a big man. He was one of the greatest newspaper publishers in the United States, one of the greatest exponents of that fourth stage of the newspaper, yellow journalism. He had once tipped a waiter a thousand-dollar bill, and the next day he had fired a legman for being twenty-five cents over on his swindle sheet.\n\nGirard was surrounded by his own men, but one never saw those. They were dressed plainly, looked plain, were plain, and always nodded eagerly, \"YES!\"\n\n\"Well, well, well!\" rumbled Girard. \"That was some record, my boy, some record! Hey, you over there with the movie camera, want my picture shaking Burnham's hand?\"\n\nThe movie man started to comply and then saw the look Smoke Burnham gave him. \"No,\" said Smoke. \"We aren't waving any flags. Not today. And I'm not shaking hands with you, Girard, any day!\"\n\nGirard was startled. \"But, my boy\u2014\"\n\n\"Save it,\" said Smoke. \"Let's get ahead with our business. You came up here to make me fork over the dough you lent me. And you've got the sheriff right there behind you, so don't deny it. You're foreclosing on Burnham Aeronautical Company, but you don't want to do it until the crowd goes.\"\n\nPatty looked at Girard and licked her feline lips. Girard stared at both pilot and cheetah.\n\n\"Who put you wise?\" he demanded.\n\n\"I did, mister. You haven't got a lease on all the brains in this country. You want this new fight-plane so you can turn it over to the government.\"\n\n\"But how\u2014\"\n\n\"I know what you're up to. You've got an air defense campaign underway, Girard. You're saying that the Japs are about to fly across San Francisco and wipe us out with bombers. And you're saying via a hundred newspapers that we haven't a single plane to withstand that offense.\n\n\"And, furthermore, you've challenged anyone to produce such a plane.\"\n\n\"You'd better watch out!\" cried Girard, as though he wielded a saber instead of a Malacca cane.\n\n\"And,\" rapped Smoke, \"you're going to foreclose on me, take the plans of this ship, the ship itself, and turn it over to the Army. That's patriotism! That's honor! You jump your ad rates on the resulting circulation and clean up.\"\n\nGirard still waved the cane. He might have struck Smoke, because there were plenty of men behind Girard. But the cheetah was still licking her lips, and Smoke's hand was loose on the leash.\n\nTwo fighters, identical with the one Smoke had just flown in, crouched in the hangar. Smoke pointed to them. \"Those two ships are company property. The one I used today belongs to Melanie King. I gave her the bill of sale. Now go ahead and serve your papers.\"\n\nThe sheriff, at Girard's nod, stepped up, skirting Patty's striking range. Although Patty had never struck anyone, people thought she did, and that was just as good.\n\nSmoke began to smile and then to grin. The effect through the grime was ghastly, but he meant it.\n\n\"If you'll come inside,\" said Smoke, \"I'll sign everything up and we'll all go have some lunch.\"\n\nGirard's face was puzzled. Smoke Burnham had more records than Girard had newspapers. A story about Smoke was worth a hundred-thousand circulation jump. But that was no sign Smoke was an open book. Warily, Girard stepped into the hangar in Smoke's wake.\n\nSmoke indicated some folding chairs at the back, \"Sit yourself down, gentlemen. I haven't any cigars, but I see you've brought your own.\" He thrust a cigarette into his mouth at a climbing angle and lit up. Patty sat down in front of him, watching the curling blue wisps.\n\nGirard, far from trusting Smoke, seated himself. It was all that he could do.\n\nSmoke, still holding the burning match in spite of the mammoth sign: No Smoking! Fire Hazard! looked casually about him. Under the belly of the first pursuit ship there was a small puddle of gasoline, spilled at the last filling and not yet wholly evaporated.\n\nSmoke flipped the burning match into the puddle.\n\nA geyser of white flame shot up. A piece of cotton waste, soaked with oil, ignited with a crackling sound.\n\nGirard jumped to his feet. \"Fire! My God, fire!\"\n\nSmoke watched the flames engulf the shiny metal. A tongue slapped out and sideswiped the other ship. The heat rose from seventy to two hundred in a space of seconds.\n\nGirard's crowd charged toward the hangar's doors, shrieking. Patty bared her fangs and unsheathed her claws in fear. Acrid fumes leaped, black and greasy.\n\nOn the outside of the hangar the crowd surged, shouting advice, shouting prayers, shouting anything as long as they made noise.\n\nAlex ran wildly about crying, \"Anybody seen Burnham? Where's Smoke?\"\n\nNewspaper men were milling, bellowing, \"Where's Girard? Mr. Girard's in there!\"\n\nThe thickening smoke was heavy and hot, completely filling the hangar. It was thick enough to carve.\n\nA staggering man came out of the flame-seared maw. He was lugging another man.\n\nAlex cried, \"It's Smoke!\"\n\nThe reporters yelled, \"There's Girard!\"\n\nSmoke, stumbling and coughing, dropped his burden and then fell flat on his face. With a glance, Alex saw that Smoke was still all in one piece and that Girard was breathing.\n\nAlex suddenly confronted the reporters. \"There you are, boys! Get those pictures! Get this story! There you are!\"\n\n\"What happened?\" demanded a pale-faced newshawk.\n\nAlex waved his hands majestically. \"Girard accidentally threw a lighted cigar into a gasoline can and then Smoke stayed behind, searching for him. Looking through all that flaming hell. Fumbling under the ships, around already burning chairs. He heard a sound like coughing and crept nearer, not letting himself retreat from the searing, scorching heat. And then he found Girard. He found Girard, gentlemen, at the risk of his own life! And there's Girard, safe and sound. But he would be but a blackened corpse if Smoke Burnham had not\u2014\"\n\nGirard was sitting up. He saw the reporters running toward the phones. It was too late to stop them. And besides, circulation would soar instantly with those headlines. Money was in the making.\n\nBut that did not keep Girard from rolling closer to Smoke. The publisher's flame-stung face was the color of raw beef. His eyes were a sickly red.\n\n\"You win, Burnham. But I'll make you a bet. I'll bet this place rebuilt against that one last pursuit plane.\"\n\nSmoke grinned and lit a cigarette, as though he had not had enough smoke as it was. Patty, licking scorched fur, watched him with adoring eyes.\n\n\"Okay,\" said Smoke. \"What's the bet?\"\n\n\"That you can't win my transcontinental derby next month.\"\n\nSmoke nodded. \"Do you recall the other contest before that?\"\n\n\"Yes. You'll have to win that before you can get into the derby.\"\n\n\"Make it a place twice as big as this and you're on.\"\n\nGirard smiled, circulation figures dancing before his eyes.\n\n\"All right, Burnham. We'll have that put on paper.\"\n\nTo find out more about Man-Killers of the Air and how you can obtain your copy, go to www.goldenagestories.com.\nYour Next Ticket to Adventure\n\nUnleash All of the Thrills of Flight!\n\nTake a touch of Charles Lindbergh, mix in a dash of Evel Knievel, throw in one man-killing cat\u2014and you've got a recipe for adventure featuring the high-flying , hard-living Smoke Burnham. Now, he's in a life-and-death race in pursuit of big money ... and big trouble. Because one thing you can count on\u2014in the air, in a fight or in his girlfriend's arms\u2014where there's Smoke, there's fire.\n\nSet a course for the Andes and the Amazon as the audio version of Man-Killers of the Air takes you on a death-defying flight from heaven to hell and back again.\n\nGet\n\nMan-Killers of the Air\n\nCALL TOLL-FREE: 1-877-8GALAXY (1-877-842-5299) \nOR GO ONLINE TO www.goldenagestories.com\n\nGalaxy Press, 7051 Hollywood Blvd., Suite 200, Hollywood, CA 90028\nL. Ron Hubbard in the \nGolden Age of \nPulp Fiction\nIn writing an adventure story \na writer has to know that he is adventuring \nfor a lot of people who cannot. \nThe writer has to take them here and there \nabout the globe and show them \nexcitement and love and realism. \nAs long as that writer is living the part of an \nadventurer when he is hammering \nthe keys, he is succeeding with his story.\n\nAdventuring is a state of mind. \nIf you adventure through life, you have a \ngood chance to be a success on paper.\n\nAdventure doesn't mean globe-trotting, \nexactly, and it doesn't mean great deeds. \nAdventuring is like art. \nYou have to live it to make it real.\n\n\u2014 L. Ron Hubbard\nL. Ron Hubbard \nand American \nPulp Fiction\n\nBORN March 13, 1911, L. Ron Hubbard lived a life at least as expansive as the stories with which he enthralled a hundred million readers through a fifty-year career.\n\nOriginally hailing from Tilden, Nebraska, he spent his formative years in a classically rugged Montana, replete with the cowpunchers, lawmen and desperadoes who would later people his Wild West adventures. And lest anyone imagine those adventures were drawn from vicarious experience, he was not only breaking broncs at a tender age, he was also among the few whites ever admitted into Blackfoot society as a bona fide blood brother. While if only to round out an otherwise rough and tumble youth, his mother was that rarity of her time\u2014a thoroughly educated woman\u2014who introduced her son to the classics of Occidental literature even before his seventh birthday.\n\nBut as any dedicated L. Ron Hubbard reader will attest, his world extended far beyond Montana. In point of fact, and as the son of a United States naval officer, by the age of eighteen he had traveled over a quarter of a million miles. Included therein were three Pacific crossings to a then still mysterious Asia, where he ran with the likes of Her British Majesty's agent-in-place for North China, and the last in the line of Royal Magicians from the court of Kublai Khan. For the record, L. Ron Hubbard was also among the first Westerners to gain admittance to forbidden Tibetan monasteries below Manchuria, and his photographs of China's Great Wall long graced American geography texts.\n\nUpon his return to the United States and a hasty completion of his interrupted high school education, the young Ron Hubbard entered George Washington University. There, as fans of his aerial adventures may have heard, he earned his wings as a pioneering barnstormer at the dawn of American aviation. He also earned a place in free-flight record books for the longest sustained flight above Chicago. Moreover, as a roving reporter for Sportsman Pilot (featuring his first professionally penned articles), he further helped inspire a generation of pilots who would take America to world airpower.\n\nL. Ron Hubbard, left, at Congressional Airport, Washington, DC, 1931, with members of George Washington University flying club.\n\nImmediately beyond his sophomore year, Ron embarked on the first of his famed ethnological expeditions, initially to then untrammeled Caribbean shores (descriptions of which would later fill a whole series of West Indies mystery-thrillers). That the Puerto Rican interior would also figure into the future of Ron Hubbard stories was likewise no accident. For in addition to cultural studies of the island, a 1932\u201333 LRH expedition is rightly remembered as conducting the first complete mineralogical survey of a Puerto Rico under United States jurisdiction.\n\nThere was many another adventure along this vein: As a lifetime member of the famed Explorers Club, L. Ron Hubbard charted North Pacific waters with the first shipboard radio direction finder, and so pioneered a long-range navigation system universally employed until the late twentieth century. While not to put too fine an edge on it, he also held a rare Master Mariner's license to pilot any vessel, of any tonnage in any ocean.\n\nCapt. L. Ron Hubbard in Ketchikan, Alaska, 1940, on his Alaskan Radio Experimental Expedition, the first of three voyages conducted under the Explorers Club Flag.\n\nYet lest we stray too far afield, there is an LRH note at this juncture in his saga, and it reads in part:\n\n\"I started out writing for the pulps, writing the best I knew, writing for every mag on the stands, slanting as well as I could.\"\n\nTo which one might add: His earliest submissions date from the summer of 1934, and included tales drawn from true-to-life Asian adventures, with characters roughly modeled on British\/American intelligence operatives he had known in Shanghai. His early Westerns were similarly peppered with details drawn from personal experience. Although therein lay a first hard lesson from the often cruel world of the pulps. His first Westerns were soundly rejected as lacking the authenticity of a Max Brand yarn (a particularly frustrating comment given L. Ron Hubbard's Westerns came straight from his Montana homeland, while Max Brand was a mediocre New York poet named Frederick Schiller Faust, who turned out implausible six-shooter tales from the terrace of an Italian villa).\n\nNevertheless, and needless to say, L. Ron Hubbard persevered and soon earned a reputation as among the most publishable names in pulp fiction, with a ninety percent placement rate of first-draft manuscripts. He was also among the most prolific, averaging between seventy and a hundred thousand words a month. Hence the rumors that L. Ron Hubbard had redesigned a typewriter for faster keyboard action and pounded out manuscripts on a continuous roll of butcher paper to save the precious seconds it took to insert a single sheet of paper into manual typewriters of the day.\n\nL. Ron Hubbard, circa 1930, at the outset of a literary career that would span half a century.\n\nThat all L. Ron Hubbard stories did not run beneath said byline is yet another aspect of pulp fiction lore. That is, as publishers periodically rejected manuscripts from top-drawer authors if only to avoid paying top dollar, L. Ron Hubbard and company just as frequently replied with submissions under various pseudonyms. In Ron's case, the list included: Rene Lafayette, Captain Charles Gordon, Lt. Scott Morgan and the notorious Kurt von Rachen\u2014supposedly on the lam for a murder rap, while hammering out two-fisted prose in Argentina. The point: While L. Ron Hubbard as Ken Martin spun stories of Southeast Asian intrigue, LRH as Barry Randolph authored tales of romance on the Western range\u2014which, stretching between a dozen genres is how he came to stand among the two hundred elite authors providing close to a million tales through the glory days of American Pulp Fiction.\n\nA Man of Many Names\n\nBetween 1934 and 1950, L. Ron Hubbard authored more than fifteen million words of fiction in more than two hundred classic publications.\n\nTo supply his fans and editors with stories across an array of genres and pulp titles, he adopted fifteen pseudonyms in addition to his already renowned L. Ron Hubbard byline. \n______\n\nWinchester Remington Colt\n\nLt. Jonathan Daly\n\nCapt. Charles Gordon\n\nCapt. L. Ron Hubbard\n\nBernard Hubbel\n\nMichael Keith\n\nRene Lafayette\n\nLegionnaire 148\n\nLegionnaire 14830\n\nKen Martin\n\nScott Morgan\n\nLt. Scott Morgan\n\nKurt von Rachen\n\nBarry Randolph\n\nCapt. Humbert Reynolds\n\nIn evidence of exactly that, by 1936 L. Ron Hubbard was literally leading pulp fiction's elite as president of New York's American Fiction Guild. Members included a veritable pulp hall of fame: Lester \"Doc Savage\" Dent, Walter \"The Shadow\" Gibson, and the legendary Dashiell Hammett\u2014to cite but a few.\n\nAlso in evidence of just where L. Ron Hubbard stood within his first two years on the American pulp circuit: By the spring of 1937, he was ensconced in Hollywood, adopting a Caribbean thriller for Columbia Pictures, remembered today as The Secret of Treasure Island. Comprising fifteen thirty-minute episodes, the L. Ron Hubbard screenplay led to the most profitable matin\u00e9e serial in Hollywood history. In accord with Hollywood culture, he was thereafter continually called upon to rewrite\/doctor scripts\u2014most famously for long-time friend and fellow adventurer Clark Gable.\n\nThe 1937 Secret of Treasure Island, a fifteen-episode serial adapted for the screen by L. Ron Hubbard from his novel, Murder at Pirate Castle.\n\nIn the interim\u2014and herein lies another distinctive chapter of the L. Ron Hubbard story\u2014he continually worked to open Pulp Kingdom gates to up-and-coming authors. Or, for that matter, anyone who wished to write. It was a fairly unconventional stance, as markets were already thin and competition razor sharp. But the fact remains, it was an L. Ron Hubbard hallmark that he vehemently lobbied on behalf of young authors\u2014regularly supplying instructional articles to trade journals, guest-lecturing to short story classes at George Washington University and Harvard, and even founding his own creative writing competition. It was established in 1940, dubbed the Golden Pen, and guaranteed winners both New York representation and publication in Argosy.\n\nBut it was John W. Campbell Jr.'s Astounding Science Fiction that finally proved the most memorable LRH vehicle. While every fan of L. Ron Hubbard's galactic epics undoubtedly knows the story, it nonetheless bears repeating: By late 1938, the pulp publishing magnate of Street & Smith was determined to revamp Astounding Science Fiction for broader readership. In particular, senior editorial director F. Orlin Tremaine called for stories with a stronger human element. When acting editor John W. Campbell balked, preferring his spaceship-driven tales, Tremaine enlisted Hubbard. Hubbard, in turn, replied with the genre's first truly character-driven works, wherein heroes are pitted not against bug-eyed monsters but the mystery and majesty of deep space itself\u2014and thus was launched the Golden Age of Science Fiction.\n\nThe names alone are enough to quicken the pulse of any science fiction aficionado, including LRH friend and prot\u00e9g\u00e9, Robert Heinlein, Isaac Asimov, A. E. van Vogt and Ray Bradbury. Moreover, when coupled with LRH stories of fantasy, we further come to what's rightly been described as the foundation of every modern tale of horror: L. Ron Hubbard's immortal Fear. It was rightly proclaimed by Stephen King as one of the very few works to genuinely warrant that overworked term \"classic\"\u2014as in: \"This is a classic tale of creeping, surreal menace and horror.... This is one of the really, really good ones.\"\n\nL. Ron Hubbard, 1948, among fellow science fiction luminaries at the World Science Fiction Convention in Toronto.\n\nTo accommodate the greater body of L. Ron Hubbard fantasies, Street & Smith inaugurated Unknown\u2014a classic pulp if there ever was one, and wherein readers were soon thrilling to the likes of Typewriter in the Sky and Slaves of Sleep of which Frederik Pohl would declare: \"There are bits and pieces from Ron's work that became part of the language in ways that very few other writers managed.\"\n\nAnd, indeed, at J. W. Campbell Jr.'s insistence, Ron was regularly drawing on themes from the Arabian Nights and so introducing readers to a world of genies, jinn, Aladdin and Sinbad\u2014all of which, of course, continue to float through cultural mythology to this day.\n\nAt least as influential in terms of post-apocalypse stories was L. Ron Hubbard's 1940 Final Blackout. Generally acclaimed as the finest anti-war novel of the decade and among the ten best works of the genre ever authored\u2014here, too, was a tale that would live on in ways few other writers imagined. Hence, the later Robert Heinlein verdict: \"Final Blackout is as perfect a piece of science fiction as has ever been written.\"\n\nLike many another who both lived and wrote American pulp adventure, the war proved a tragic end to Ron's sojourn in the pulps. He served with distinction in four theaters and was highly decorated for commanding corvettes in the North Pacific. He was also grievously wounded in combat, lost many a close friend and colleague and thus resolved to say farewell to pulp fiction and devote himself to what it had supported these many years\u2014namely, his serious research.\n\nPortland, Oregon, 1943; L. Ron Hubbard, captain of the US Navy subchaser PC 815.\n\nBut in no way was the LRH literary saga at an end, for as he wrote some thirty years later, in 1980:\n\n\"Recently there came a period when I had little to do. This was novel in a life so crammed with busy years, and I decided to amuse myself by writing a novel that was pure science fiction.\"\n\nThat work was Battlefield Earth: A Saga of the Year 3000. It was an immediate New York Times bestseller and, in fact, the first international science fiction blockbuster in decades. It was not, however, L. Ron Hubbard's magnum opus, as that distinction is generally reserved for his next and final work: The 1.2 million word Mission Earth.\n\nHow he managed those 1.2 million words in just over twelve months is yet another piece of the L. Ron Hubbard legend. But the fact remains, he did indeed author a ten-volume dekalogy that lives in publishing history for the fact that each and every volume of the series was also a New York Times bestseller.\n\nMoreover, as subsequent generations discovered L. Ron Hubbard through republished works and novelizations of his screenplays, the mere fact of his name on a cover signaled an international bestseller.... Until, to date, sales of his works exceed hundreds of millions, and he otherwise remains among the most enduring and widely read authors in literary history. Although as a final word on the tales of L. Ron Hubbard, perhaps it's enough to simply reiterate what editors told readers in the glory days of American Pulp Fiction:\n\nHe writes the way he does, brothers, because he's been there, seen it and done it!\n\nTo find out more about L. Ron Hubbard, visit www.LRonHubbard.org\nThe Stories from the \nGolden Age\n\nYour ticket to adventure starts here with the Stories from the Golden Age collection by master storyteller L. Ron Hubbard. These gripping tales are set in a kaleidoscope of exotic locales and brim with fascinating characters, including some of the most vile villains, dangerous dames and brazen heroes you'll ever get to meet.\n\nThe entire collection of over one hundred and fifty stories is being released in a series of eighty books and audiobooks. For an up-to-date listing of available titles, go to www.goldenagestories.com.\n\nAIR ADVENTURE\n\nArctic Wings\n\nThe Battling Pilot\n\nBoomerang Bomber\n\nThe Crate Killer\n\nThe Dive Bomber\n\nForbidden Gold\n\nHurtling Wings\n\nThe Lieutenant Takes the Sky\n\nMan\u00ad-Killers of the Air\n\nOn Blazing Wings\n\nRed Death Over China\n\nSabotage in the Sky\n\nSky Birds Dare!\n\nThe Sky\u00ad-Crasher\n\nTrouble on His Wings\n\nWings Over Ethiopia\n\nFAR-FLUNG ADVENTURE\n\nThe Adventure of \"X\"\n\nAll Frontiers Are Jealous\n\nThe Barbarians\n\nThe Black Sultan\n\nBlack Towers to Danger\n\nThe Bold Dare All\n\nBuckley Plays a Hunch\n\nThe Cossack\n\nDestiny's Drum\n\nEscape for Three\n\nFifty-\u00adFifty O'Brien\n\nThe Headhunters\n\nHell's Legionnaire\n\nHe Walked to War\n\nHostage to Death\n\nHurricane\n\nThe Iron Duke\n\nMachine Gun 21,000\n\nMedals for Mahoney\n\nPrice of a Hat\n\nRed Sand\n\nThe Sky Devil\n\nThe Small Boss of Nunaloha\n\nThe Squad That Never Came Back\n\nStarch and Stripes\n\nTomb of the Ten Thousand Dead\n\nTrick Soldier\n\nWhile Bugles Blow!\n\nYukon Madness\n\nSEA ADVENTURE\n\nCargo of Coffins\n\nThe Drowned City\n\nFalse Cargo\n\nGrounded\n\nLoot of the Shanung\n\nMister Tidwell, Gunner\n\nThe Phantom Patrol\n\nSea Fangs\n\nSubmarine\n\nTwenty Fathoms Down\n\nUnder the Black Ensign\n\nTALES FROM THE ORIENT\n\nThe Devil\u2014With Wings\n\nThe Falcon Killer\n\nFive Mex for a Million\n\nGolden Hell\n\nThe Green God\n\nHurricane's Roar\n\nInky Odds\n\nOrders Is Orders\n\nPearl Pirate\n\nThe Red Dragon\n\nSpy Killer\n\nTah\n\nThe Trail of the Red Diamonds\n\nWind\u00ad-Gone-\u00adMad\n\nYellow Loot\n\nMYSTERY\n\nThe Blow Torch Murder\n\nBrass Keys to Murder\n\nCalling Squad Cars!\n\nThe Carnival of Death\n\nThe Chee\u00ad-Chalker\n\nDead Men Kill\n\nThe Death Flyer\n\nFlame City\n\nThe Grease Spot\n\nKiller Ape\n\nKiller's Law\n\nThe Mad Dog Murder\n\nMouthpiece\n\nMurder Afloat\n\nThe Slickers\n\nThey Killed Him Dead\n\nFANTASY\n\nBorrowed Glory\n\nThe Crossroads\n\nDanger in the Dark\n\nThe Devil's Rescue\n\nHe Didn't Like Cats\n\nIf I Were You\n\nThe Last Drop\n\nThe Room\n\nThe Tramp\n\nSCIENCE FICTION\n\nThe Automagic Horse\n\nBattle of Wizards\n\nBattling Bolto\n\nThe Beast\n\nBeyond All Weapons\n\nA Can of Vacuum\n\nThe Conroy Diary\n\nThe Dangerous Dimension\n\nFinal Enemy\n\nThe Great Secret\n\nGreed\n\nThe Invaders\n\nA Matter of Matter\n\nThe Obsolete Weapon\n\nOne Was Stubborn\n\nThe Planet Makers\n\nThe Professor Was a Thief\n\nThe Slaver\n\nSpace Can\n\nStrain\n\nTough Old Man\n\n240,000 Miles Straight Up\n\nWhen Shadows Fall\n\nWESTERN\n\nThe Baron of Coyote River\n\nBlood on His Spurs\n\nBoss of the Lazy B\n\nBranded Outlaw\n\nCattle King for a Day\n\nCome and Get It\n\nDeath Waits at Sundown\n\nDevil's Manhunt\n\nThe Ghost Town Gun\u00ad-Ghost\n\nGun Boss of Tumbleweed\n\nGunman!\n\nGunman's Tally\n\nThe Gunner from Gehenna\n\nHoss Tamer\n\nJohnny, the Town Tamer\n\nKing of the Gunmen\n\nThe Magic Quirt\n\nMan for Breakfast\n\nThe No-\u00adGun Gunhawk\n\nThe No\u00ad-Gun Man\n\nThe Ranch That No One Would Buy\n\nReign of the Gila Monster\n\nRide 'Em, Cowboy\n\nRuin at Rio Piedras\n\nShadows from Boot Hill\n\nSilent Pards\n\nSix\u00ad-Gun Caballero\n\nStacked Bullets\n\nStranger in Town\n\nTinhorn's Daughter\n\nThe Toughest Ranger\n\nUnder the Diehard Brand\n\nVengeance Is Mine!\n\nWhen Gilhooly Was in Flower\nJOIN THE PULP REVIVAL\n\nAmerica in the 1930s and 40s\n\nPulp fiction was in its heyday and 30 million readers were regularly riveted by the larger than life tales of master storyteller L. Ron Hubbard. For this was pulp fiction's golden age, when the writing was raw and every page packed a walloping punch.\n\nThat magic can now be yours. An evocative world of nefarious villains, exotic intrigues, courageous heroes and heroines\u2014a world that today's cinema has barely tapped for tales of adventure and swashbucklers.\n\nEnroll today in the Stories from the Golden Age Club and begin receiving your monthly feature edition selected from more than 150 stories in the collection.\n\nYou may choose to enjoy them as either a paperback or audiobook for the special membership price of $9.95 each month along with FREE shipping and handling.\n\nCall toll free: \n1-877-8GALAXY (1-877-842-5299)\n\nOr go online to \nwww.goldenagestories.com\n\nAnd become part of the pulp revival!\n\nPrices are set in US dollars only. For non-US residents, please call 1-323-466-7815 for pricing information. Free shipping available for US residents only. \nGalaxy Press, 7051 Hollywood Blvd., Suite 200, Hollywood, CA 90028\n\nGlossary\n\nSTORIES FROM THE GOLDEN AGE reflect the words and expressions used in the 1930s and 1940s, adding unique flavor and authenticity to the tales. While a character's speech may often reflect regional origins, it also can convey attitudes common in the day. So that readers can better grasp such cultural and historical terms, uncommon words or expressions of the era, the following glossary has been provided.\n\naltimeter: a gauge that measures altitude. [return to text]\n\nAnnapolis: the capital of Maryland and the site of the US Naval Academy, founded in 1845. [return to text]\n\nbeam: an early form of radio navigation using beacons to define navigational airways. A pilot flew for 100 miles guided by the beacon behind him and then tuned in the beacon ahead for the next 100 miles. The beacons transmitted two Morse code signals, the letter \"A\" and the letter \"N.\" When the aircraft was centered on the airway, these two signals merged into a steady, monotonous tone. If the aircraft drifted off course to one side, the Morse code for the letter \"A\" could be faintly heard. Straying to the opposite side produced the \"N\" Morse code signal. [return to text]\n\ncabin job: an airplane that has an enclosed section where passengers can sit or cargo is stored. [return to text]\n\nColt .45: a .45-caliber automatic pistol manufactured by the Colt Firearms Company of Hartford, Connecticut. Colt was founded in 1847 by Samuel Colt (1814\u20131862), who revolutionized the firearms industry. [return to text]\n\nconquistador: a Spanish conqueror or adventurer. [return to text]\n\ncowl: a removable metal covering for an engine, especially an aircraft engine. [return to text]\n\ncrate: an airplane. [return to text]\n\nEl: elevated railway. [return to text]\n\nfilibustero: (Spanish) filibuster; this term derived from the Spanish filibustero for \"pirate,\" \"buccaneer\" or \"freebooter,\" individuals who attack foreign lands or interests for financial gain without authority from their own government. It applied to Anglo-American adventurers in the mid-nineteenth century who tried to take control of various Caribbean, Mexican and Central American territories by force of arms. [return to text]\n\nfire, Gridley: refers to Charles Vernon Gridley (1844\u20131898); US naval officer who started the Battle of Manila Bay in the Spanish-American War with the order from his commanding officer, \"You may fire when you are ready, Gridley.\" The Spanish fleet was annihilated without the loss of a single American life. This dramatic victory eventually led to the US annexation of the Philippines. [return to text]\n\nG-men: government men; agents of the Federal Bureau of Investigation. [return to text]\n\ngreat seal: the principal seal of a government or state, with which official documents are stamped. [return to text]\n\nheliograph: a device for signaling by means of a movable mirror that reflects beams of light, especially sunlight, to a distance. [return to text]\n\nhenequen: a plant that has large thick fibrous leaves shaped like swords, the fiber from which is used in making rope and twine. Native to tropical America, chiefly the Yucat\u00e1n Peninsula of Mexico. [return to text]\n\nhoodoo: one that brings bad luck. [return to text]\n\nhuckster: a street peddler. [return to text]\n\njewelry rock: gold-bearing vein quartz. [return to text]\n\nJonah: somebody who brings bad luck. [return to text]\n\nkey: a hand-operated device used to transmit Morse code messages. [return to text]\n\nkiting: flying. [return to text]\n\nknickerbockered: clothed in loose-fitting pants gathered at the knee or calf. [return to text]\n\nLake Pontchartrain: a lake in southeastern Louisiana north of New Orleans. [return to text]\n\nLeavenworth: Fort Leavenworth; the site of a federal penitentiary in Kansas. [return to text]\n\nlegman: a reporter who gathers information by visiting news sources, or by being present at news events. [return to text]\n\nMalacca: the stem of a species of palm, brown in color and often mottled, used for making canes and umbrella handles; named after a town in western Malaysia. [return to text]\n\nmonoplane: an airplane with one sustaining surface or one set of wings. [return to text]\n\nmouthpiece: a lawyer, especially a criminal lawyer. [return to text]\n\nmufti: civilian clothes; ordinary clothes worn by somebody who usually wears a uniform. [return to text]\n\nmummery: a pretentious or hypocritical show or ceremony. [return to text]\n\nnewshawk: a newspaper reporter, especially one who is energetic and aggressive. [return to text]\n\npatois: a regional form of a language, especially of French, differing from the standard, literary form of the language. [return to text]\n\npeg-topped: describing pants that are full and gathered at the hips and narrow at the ankles. [return to text]\n\npuede ser: (Spanish) could be. [return to text]\n\nQST: radio signal meaning \"general call to all stations.\" The Q code is a standardized collection of three-letter message encodings, all starting with the letter \"Q\"; initially developed for commercial radiotelegraph communication and later adopted by other radio services. [return to text]\n\nrudders: devices used to steer aircraft. A rudder is a flat plane or sheet of material attached with hinges to the craft's stern or tail. In typical aircraft, pedals operate rudders via mechanical linkages. [return to text]\n\nsap: blackjack; a short, leather-covered club, consisting of a heavy head on a flexible handle, used as a weapon. [return to text]\n\nScheherazade: the female narrator of The Arabian Nights, who during one thousand and one adventurous nights saved her life by entertaining her husband, the king, with stories. [return to text]\n\nsideslip: (of an aircraft when excessively banked) to slide sideways, toward the center of the curve described in turning. [return to text]\n\nsisal: a strong fiber obtained from the leaves of a plant native to southern Mexico and now cultivated throughout the tropics, used for making rope, sacking, insulation, etc. [return to text]\n\nsoup: a thick fog. [return to text]\n\nspatted wheels: a structure around the top of the wheels of a fixed airplane landing gear. [return to text]\n\nsub-Thompson: a type of machine gun that fires short pistol rounds, named after its creator, John Taliaferro Thompson, who produced the first model in 1919. [return to text]\n\nTAT: Transcontinental Air Transport, airline founded in 1928. It was one of the first to be geared to passenger service at a time when most airlines focused on air mail. In 1930, it merged with Western Air Express to form what became TWA. [return to text]\n\nthree-point: three-point landing; an airplane landing in which the two main wheels and the nose wheel all touch the ground simultaneously. [return to text]\n\nToltecs: members of an Indian people living in central Mexico before the advent of the Aztecs and traditionally credited with laying the foundation of Aztec culture. [return to text]\n\nuppers, on my: on one's uppers; poor; in reduced circumstances. First recorded in 1886, this term alludes to having worn out the soles of one's shoes so badly that only the top portions remain. [return to text]\n\nwig-wag: a method of using flags or pennants to send signals. [return to text]\n\nwing collar: a shirt collar, used especially in men's formal clothing, in which the front edges are folded down in such a way as to resemble a pair of wings. [return to text]\n\nyo creo: (Spanish) I believe. [return to text]\n\nYucat\u00e1n: a peninsula mostly in southeastern Mexico between the Caribbean Sea and the Gulf of Mexico. [return to text]\n","meta":{"redpajama_set_name":"RedPajamaBook"}} +{"text":"\n\n\n\nProduced by sp1nd, Mary Meehan and the Online Distributed\nProofreading Team at http:\/\/www.pgdp.net (This file was\nproduced from images generously made available by The\nInternet Archive)\n\n\n\n\n\n\n\n\n\n\n\n ALAMO RANCH\n\n _A Story of New Mexico_\n\n BY SARAH WARNER BROOKS\n\n Author of \"My Fire Opal,\" \"The Search of Ceres,\" etc.\n\n CAMBRIDGE\n PRIVATELY PRINTED\n MCMIII\n\n UNIVERSITY PRESS . JOHN WILSON\n\n AND SON . CAMBRIDGE . U.S.A.\n\n\n TO LEON\n\n _Across the silence that between us stays,\n Speak! I should hear it from God's outmost sun,\n Above Earth's noise of idle blame and praise,--\n The longed-for whisper of thy dear \"Well done!\"_\n\n\n\n\n[Illustration: ALAMO RANCH]\n\n\n\n\nALAMO RANCH\n\n_A STORY OF NEW MEXICO_\n\n\n\n\nCHAPTER I\n\n\nIt is autumn; and the last week in November. In New Mexico, this land of\nsunshine, the season is now as kindly as in the early weeks of our\nNorthern September.\n\nTo-day the sky is one cloudless arch of sapphire! The light breeze\nscarce ruffles a leaf of the tall alamo, the name tree of this ranch.\nHere any holding bigger than a kitchen garden is known as a ranch. The\nalamo, Spanish for poplar, lends here and there its scant, stiff shade\nto this roomy adobe dwelling, with its warm southern frontage and\nhalf-detached wings. Behind the house irregular out-buildings are\nscattered about.\n\nA commodious corral, now the distinguished residence of six fine Jersey\ncows, lies between the house and the orchard,--a not over-flourishing\ncollection of peach, apricot, and plum trees.\n\nHere and there may be seen wide patches of kitchen garden, carefully\nintersected by irrigating ditches.\n\nNear and afar, wide alfalfa fields with their stiff aftermath stretch\naway to the very rim of the mesa, where the cotton-tail makes his home,\nand sage-brush and mesquite strike root in the meagre soil. Cones of\nalfalfa hay stacked here and there outline themselves like giant\nbeehives against the soft blue sky; and over all lies the sunny silence\nof a cloudless afternoon with its smiling westering sun.\n\nBasking in this grateful warmth, their splint arm-chairs idly tilted\nagainst the house-front, the boarders look with sated invalid eyes upon\nthis gracious landscape.\n\nAlamo Ranch is a health resort. In this thin, dry air of Mesilla Valley,\nhigh above the sea level, the consumptive finds his Eldorado. Hither,\nyear by year, come these foredoomed children of men to fight for breath,\nputting into this struggle more noble heroism and praiseworthy courage\nthan sometimes goes to victory in battle-fields.\n\nOf these combatants some are still buoyed by the hope of recovery;\nothers are but hopeless mortals, with the single sad choice of eking out\nexistence far from friends and home, or returning to native skies, there\nto throw up hands in despair and succumb to the foe.\n\nSixteen miles away the Organ Mountains--seeming, in this wonderfully\nclear atmosphere, within but a stone's throw--loom superbly against the\ncloudless sky; great hills of sand are these, surmounted by tall,\nserrated peaks of bare rock, and now taking on their afternoon array in\nthe ever-changing light, rare marvels of shifting color,--amethyst and\nviolet, rosy pink, creamy gold, and dusky purple.\n\nThe El Paso range rises sombrely on the gray distance, and on every hand\ndetached sugar-loaf peaks lend their magnificence to the grand\nmesa-range that cordons the Mesilla Valley.\n\nAnd now, out on the mesa, at first but a speck between the loungers on\nthe piazza and the distant mountain view, a single pedestrian, an\ninvalid sportsman, comes in sight. As he nears the ranch with the slowed\nstep of fatigue, he is heartening himself by the way with a song. When\nthe listeners hear the familiar tune,--it is \"Home, Sweet Home,\"--one of\nthem rallying his meagre wind whistles a faint accompaniment to the\nchorus. It is not a success; and with a mirthless laugh, the whistler\nabandons his poor attempt, and, with the big lump in his throat swelling\nto a sob, rises from his chair and goes dejectedly in. A sympathetic\nchord thrills along the tilted piazza chairs.\n\nThe discomfited whistler is but newly arrived at Alamo; and his feeble\nstep and weary, hollow cough predict that the poor fellow's journey will\nnot take him back to the \"Sweet Home\" of the song, but rather to the\nuncharted country.\n\nAnd now the invalid sportsman steps cheerily on the piazza.\n\n\"Here, you lazy folks,\" mocks he, holding high his well-filled game-bag,\n\"behold the pigeon stew for your supper!\" And good-naturedly hailing a\nMexican chore-boy, lazily propped by a neighboring poplar trunk, he\ncries, \"Catch!\" and deftly tossing him the game (pigeons from the mesa)\ngoes in to put away his gun. When later he returns to the piazza, bathed\nand refreshed, it is as if, in a room dim-lit by tallow candles, the gas\nhad suddenly been turned on to a big chandelier.\n\nSeating himself in the vacant arm-chair, he fills a briar-wood pipe.\nSome of the loungers do likewise; and now, while they smoke and chat,\nlook at the new-comer, Leonard Starr. Though not robust, he has the\nsubstantial mien and bearing of one who finds it good to live, and makes\nthose about him also find it good. It is not long before most of these\ndispirited loungers are laughing at his lively stories and sallies, and\ncheerily matching them with their own.\n\nWell is it for this troublous world of ours that some of its children\nare \"born to turn the sunny side of things to human eyes.\"\n\n\n\n\nCHAPTER II\n\n\nIt is the middle of December; the Alamo boarders are now well arrived.\n\nFirst and foremost, Mr. John Morehouse--the one lion of the ranch--makes\nhis bow. He is conspicuous for his able research in Archaeology, and\namong his fellow boarders is familiarly known as \"the Antiquary.\"\n\nMr. Morehouse has come to New Mexico in the interest of science; he is\nnot, however, a mere dry-as-dust collector of knowledge, and is very\nmuch inclined to unbend himself to the lighter moods and pursuits of his\nless scholarly fellow-men.\n\nThis well-groomed, handsome man of forty is James Morley of Bangor.\n\nHe has come to try this healing air for a slight, but persistent, lung\naffection.\n\nMr. Morley is known to be a man of means, with all the advantages thus\nimplied; but all the same, he is given to railing at most things under\nthe sun; hence by the boarders he is surreptitiously dubbed \"the\nGrumbler.\" Mr. Morley's growl is a foregone conclusion, and one may\nsafely reckon on his bark; but as for his bite, it is simply nowhere.\n\nAlready he has manifested a most considerate kindness for this gray-eyed\nlittle lady from Marblehead, Miss Mattie Norcross,--a sweet-mannered,\nquiet gentlewoman, who is currently reported as scant of filthy lucre,\nand hence compelled to content herself with a cramped, inexpensive\nbedroom for herself and her invalid sister, who has one hopelessly\ndiseased lung. This cheery-faced Irishman, who with his shy little wife\nis, for a stubborn bronchial trouble, making the grand tour of the\nworld's health resorts, and is now trying New Mexico, is, strange as it\nmay seem, a Methodist minister. His name is Patrick Haley. It may be\nsaid of Mr. Haley that he has the genial temperament indigenous to Green\nErin, and he has already won golden opinions at Alamo Ranch by the\nconsiderate brevity of his grace before meat.\n\nAmong the invalids attended by their wives are Mr. Bixbee, from Ohio,\nand Mr. Fairlee, from New York City.\n\nMr. Bixbee has been bidden by his medical dictator to repair his damaged\nvitality by rest and nourishing food. It is predicted that this\nsurfeited \"lunger,\" in escaping his Scylla of consumption, bids fair to\nstrand upon the Charybdis of liver complaint, since Mrs. Bixbee, in her\nwifely zeal, not only plies him all day long with lunches, but makes\nnight hideous by the administration of raw eggs throughout its drowsy\nhours.\n\nMr. Roger Smith, an over-worked Harvard athlete, is taking as a\nrestorative a lazy winter in this restful land. He has also other irons\nin the fire, of which, later, we shall hear more. Roger Smith is known\nin Boston society as one having heaps of money, but badly off for\npedigree. All the same, he is, in manner and appearance, a gentleman,\nand has distinctly the hall-mark of Beacon Hill. He is here known as the\n\"Harvard man.\"\n\nAlso, among the sound-lunged invalids, is Mr. Harry Warren, a brilliant\nChicago journalist. Mr. Warren is taking a vacation in Mesilla Valley,\nwhere he is said to be collecting material for future articles, and\npossibly for a book.\n\nThe Browns have also two table-boarders from Boston,--Miss Paulina\nHemmenshaw and her beautiful niece, Louise, a superbly healthy brunette.\nTheir friend, Mr. Henry Hilton, during an absence abroad, has lent for\nthe winter to these ladies his toy ranch, with its aesthetically\nfashioned dwelling-house.\n\nThe Hemmenshaws dine and sup at Alamo Ranch, and the aunt, a\ncooking-school graduate, is known to make at Hilton Ranch for herself\nand niece wonderful blazer breakfasts, consisting mainly of dishes\nnew-fangled of name, and eminently trying to mortal digestion. There\nare, besides, some half-dozen male lungers unaccompanied by friends; and\ntwo impecunious invalids to whom the kind-hearted landlord, George\nBrown, allows bed and board in return for light-choring about the ranch.\nThese latter are democratically counted in with the dining-room\nboarders.\n\nLeon Starr, by common consent the \"star boarder\" of Alamo Ranch, has\nalready been presented to the reader. He has taken the large\ntwo-windowed room on the ground-floor commanding a glorious view of the\ndistant Organ Mountains. After getting his breath in this unaccustomed\naltitude, Leon's next care has been for the depressed lungers who daily\ngather on the boarding-house piazza and wonder if life is still worth\nliving. To get them outside themselves by cheery good-fellowship, to\nperform for them little homely services, not much in the telling, but\nmaking their lives a world easier, has been a part of his method for\nuplifting their general tone.\n\nOf an inventive turn of mind, and an amateur mechanic, he has brought\nwith him a tiny tool chest; and it soon becomes the family habit to look\nto Leon Starr for general miscellaneous tinkering, as the mending of\ndoor and trunk locks, the regulating watches and clocks, the adjustment\nof the bedevilled sewing-machine of their good landlady, and the\nrestoration of harmonious working to all disgruntled mechanical gear,\nfrom garret to cellar. He it is who, on rainy days, manufactures denim\nclothes-bags for clumsy-fingered fellows; who fashions from common canes\ngathered on banks of irrigating ditches, photo-frames for everybody, and\nshows them how to arrange the long cane tassels with decorative effect\nabove door and window, and how to soften the glare of kerosene lamps by\nmaking for them relieving shades of rose- paper.\n\nPessimistic indeed is that lunger who, succumbing to the charm of this\ngracious nature, does not feel the cheery lift in his heavy atmosphere.\n\nFrom the landlord and his wife, both worn by the strain of doing their\nbest for chronically discontented people, down to Fang Lee, the Chinese\nchef, Dennis Kearney, the table-waiter, the over-worked Mexican\nhouse-maids, and the two native chore-boys--one and all rise up to call\nthe star boarder blessed.\n\nOut on the mesa the air is finer and brighter than on the lower plane of\nthe ranch, and full of the life and stir of moving things,--quail,\nrabbits, and doves.\n\nLeon had at first found the thin air of this altitude somewhat\ndifficult; but since time and use have accustomed his lungs to these\nnovel atmospheric conditions, shooting on the mesa has become a part of\nhis daily programme, and his quail, rabbits, and pigeons prove a\ntoothsome contribution to the already excellent ranch table.\n\nA small, shy Mexican herd-boy, pasturing his lean goats on the mesa,\ngradually makes friends with the tall, kindly sportsman. As they have\nbetween them but these two mutually intelligible words, _bueno_ (good)\nand _mucho calor_ (very warm), their conversation is circumscribed. Kind\ndeeds are, however, more to the point than words, and go without the\nsaying; and when Leon instructed the ragged herd-boy in the use of his\nbow, and made and weighted his arrows for him, he _understood_, and\nbecame his devoted henchman, following in his path all through the\nweek-day tramps, and on Sundays coming to the ranch with clean face and\nhands to adore his fetich, and watch, with admiring eyes, his novel\nworks and ways.\n\n\n\n\nCHAPTER III\n\n\nAfter a protracted interval of tranquil sunshine, a stormy wind came\nblustering from the west, bringing to Mesilla Valley, in its wintry\ntrain, sunless days, light flurries of snow, and general dreariness.\n\nThe boarders, weather-bound and dull, grew sullenly mutinous; and on the\nthird of these stormy days, gathering in the ranch parlor after the\nmid-day meal, their discontent found vent in banning right and left this\n\"land of sun, silence, and adobe.\"\n\n\"Beastly weather!\" muttered the Grumbler, drawing into the stove with a\ndiscontented shiver.\n\n\"A precious sample, this, of your fine climate, Brown,\" jeered Bixbee,\nturning mockingly to the disheartened landlord, who, reckless of\nexpense, commanded of the chore-boy fresh relays of fuel, and\nincontinently crammed the parlor air-tight, already red-hot.\n\n\"I say, fellows,\" drolled the Harvard man, \"let's make tracks for\nBoston, and round up the winter with furnace heat and unlimited water\nprivileges, as the house-broker has it.\"\n\n\"And with cut-throat plumbers thrown in,\" suggested the Grumbler with a\nmalicious grin.\n\n\"See here, you folks, draw it mild,\" laughed the star boarder, crossing\nthe room with a finger between the leaves of a volume which he had been\nreading by the dim afternoon light of this lowering day. \"Here, now, is\nsomething that fits your case to a T. Let me read you how they doctored\nyour complaint in these parts, aeons before you were born.\"\n\n\"Anything for a change,\" muttered Bixbee, and, with the general consent,\nLeon read the following:\n\n\"'When the people came out of the cold, dark womb of the underworld,\nthen the great sun rose in the heavens. In it dwelt Payatuma, making his\ncircuit of the world in a day and a night. He saw that the day was light\nand warm, the night dark and cold. Hence there needed to be both summer\nand winter people.\n\n\"'He accordingly apportioned some of each to every tribe and clan, and\nthus it is down to the present day. Then those above (that is, the\nSun-father and the Moon-mother), mindful lest the people on their long\njourney to the appointed abiding-place succumb to weariness and fall by\nthe way, made for them a koshare, a delight-maker. His body was painted\nin diagonal sections of black and white, and his head, in lieu of the\nregulation feather-decorations, was fantastically arrayed in withered\ncorn-leaves.\n\n\"'This koshare began at once to dance and tumble. Then the people\nlaughed, and were glad. And ever from that day, in their wanderings in\nsearch of a satisfactory settling-place in the solid centre of the big\nweary world, the koshare led them bravely and well.\n\n\"'He it was who danced and jested to make happiness among the people.\nHis it was to smile on the planted maize till it sprouted and flowered\nin the fertile bottoms, to beam joyously on the growing fruit, that it\nmight ripen in its season.\n\n\"'From that day there have been delight-makers in all the Pueblo tribes.\nThe koshare became in time with them an organization, as the\nFree-masons, or the Knights of Pythias, with us. This necessity, we are\ntold, arose from the fact that among the Pueblos there were summer\npeople who enjoy the sunshine, and winter people,--people who\ndeterminedly prefer to live in the dark and cold.'\n\n\"Is it not so,\" said Leon, turning down a leaf and closing his book,\n\"with every people on the face of the earth?\n\n\"Is not the 'delight-maker,'--the koshare,--under various names and\nguises, still in demand? It has struck me,\" continued he, looking\nquizzically at this disgruntled assemblage, \"that the koshare might be\nan acceptable addition to our despondent circle.\"\n\n\"Amen!\" fervently responded the Methodist minister.\n\n\"Right you are,\" said the Harvard man. \"Write me as one who approves the\nkoshare!\"\n\n\"Yes! yes!\" eagerly exclaimed approving voices. \"Let us have the koshare\nhere and at once!\"\n\n\"A capital move,\" said Miss Paulina Hemmenshaw (born and reared in the\nclimatic belt of clubdom, and regent of a Chapter of Daughters of the\nRevolution). \"Let us have a Koshare Club.\"\n\n\"Good!\" echoed Mrs. Fairlee, among her intimates surnamed \"the Pourer,\"\nbecause of her amiable readiness to undertake for her friends the\nhelpful office that among afternoon tea-circles has been distinguished\nby that name. \"We might give afternoon teas to the members.\"\n\n\"And why not have recitations, with humorous selections?\" bashfully\nsuggested the gray-eyed school-mistress, who rejoiced in a fine-toned\nvoice and in a diploma from the School of Oratory.\n\n\"Yes, indeed; and music, acting, and dancing, and all manner of high\njinks,\" exclaimed Miss Louise, who, an accomplished musician, and\ndistinguished for her amateur acting, with her superb health and\nunfailing flow of spirits, might be counted in as a born koshare.\n\n\"And we might unite improvement with diversion, and have, now and then,\na lecture, to give interest to our club,\" suggested Mrs. Bixbee; and\nhere she looked significantly at Mr. Morehouse, \"the Antiquary,\" who as\na lecturer was not unknown to fame.\n\n\"Lectures,\" observed the Minister, \"though not strictly kosharean,\nwould be highly entertaining, and we can, no doubt, count upon our\nfriend, Mr. Morehouse, to give us the result of some of his research in\nMexican Antiquities.\"\n\nThe Antiquary, with a smile, accepted the part assigned him by his\nfellow-boarder. Here the boarders went to supper, after which the more\nsleepy sought their beds. The evening blew stormily in; but, gathered\nabout the centre table in the warm parlor, the leading spirits of Alamo\nRanch bade the storm go by, while they inaugurated the Club of The New\nKoshare.\n\nThe star boarder was chosen president. The Minister was elected\nvice-president, Miss Paulina secretary, and the Harvard man treasurer.\nThese preliminaries well arranged, a programme was voted on, and by\ngeneral approval carried.\n\nMrs. Fairlee--the Pourer--was to give to the club-members a weekly\nafternoon tea. An entertainment open to the entire household was, on\nevery Thursday evening, to be given in the ranch dining-room by the\nKoshare, consisting of music, tableaux, and recitations. A\nshooting-match, under the direction of Leon, was to come off weekly on\nthe grounds of the establishment. There should be among the clubbists a\nfund collected for magazines; and on fortnightly Saturday evenings Mr.\nMorehouse promised to give them lectures, the result of his antiquarian\nresearches in Mexico, New and Old; and during this course papers and\ntalks relating to this subject should supplement his own.\n\n\"The Pueblo,\" commented the Grumbler, \"would not have found magazines\nstrikingly kosharean; let us by all means have them,\" and suiting deed\nto word, he subscribed to the book-fund on the spot, and paid\nsurreptitiously the subscription of the little school-ma'am, who had\npreviously withdrawn in the interest of her invalid sister.\n\nIn this fashion was inaugurated \"The New Koshare\" of Mesilla Valley;\nthereafter the Hemmenshaws bundled themselves in winter wraps and,\nhanded into their vehicle by the Harvard man, set out in the storm for\ntheir ride to Hilton Ranch, and the Koshare betook themselves to rest.\n\n\n\n\nCHAPTER IV\n\n\nOn the morrow the sun shone warm and bright, and on the mesa, and on all\nthe desert-stretches of mesquite and sage-brush, on the broad alfalfa\nfields and outlying acres of Alamo Ranch, there was no longer a flake of\nsnow.\n\nEarly in this sunny day the star boarder and the Pourer, driven by a\nleisurely chore-boy, might have been seen taking their way to Las\nCruces, the nearest village and postal centre, intent on the procurement\nof sundry wafers, biscuit, and other edibles pertaining to an afternoon\ntea.\n\nEl Paso, the Texan border-town, some forty miles distant, is properly\nthe emporium of that region. Between it and Las Cruces lies a stretch of\ndesert more barrenly forlorn than the Long Island pine-lands, since it\nis totally void of forest growth, and has but here and there a sprinkle\nof mesquite-bushes about three feet in height, the rest being bare\nsand-ridges.\n\nAt El Paso one may ride in street cars, luxuriate in rain-proof\ndwellings, lighted by electricity, and pretty with lawns and\nflower-pots. But even at its best, modern civilization, with its push\nand bustle, ill becomes the happy-go-lucky native Mexican sunning\nhimself in lazy content against the adobe of his shiftily built\ndwelling.\n\nIn a land of well-nigh perpetual blue sky, why need mortal man scramble\nto make hay while the sun shines? Yesterday has already taken care of\nitself. To-day is still here, and always there is _manana_--to-morrow.\n\nAs for our own upstart civilization, in this clime of ancient Pueblo\nrefinements one must own that it takes on the color of an impertinence,\nand as incongruously exhibits itself as a brand-new patch on a long-worn\ngarment.\n\nBut to return to Las Cruces, which is \"fearfully and wonderfully made.\"\nTo look at the houses one might well fancy that the pioneer settlers had\nfolded their hands and prayed for dwellings, and when the answering\nshower of mud and adobe fell, had contentedly left it where it stuck.\nAll these structures are one-storied, and square-built; each has its one\ndoor, a window or two, and a dumpy roof, fashioned for the most part of\nwattles, for, as it seldom rains here, the Las Crucean has no\ntroublesome prejudice in favor of water-tight roofs. When the sun shines\nhe is all right; and when it rains, he simply moves from under the drip.\nHere, among confectionery that had long since outlived its desirability,\namong stale baker's cookies and flinty ginger snaps, the Koshare\ncommissariat foraged discouragedly for the afternoon tea.\n\nDuly supplied with these time-honored sweets, Leon and the Pourer, thus\nindifferently provisioned, turned their faces homeward, at such moderate\npace as seemed good in the eyes of an easy-going Mexican pony and his\nlazy Indian driver.\n\nOn the afternoon of that day Mrs. Bixbee, in her airy bed-chamber,\nwhere the folding-bed in the day-time masqueraded as a black walnut\nbookcase, gave the first Koshare afternoon tea.\n\nMrs. Fairlee poured from a real Russian Samovar brought over from the\nHilton Ranch for this grand occasion. Somewhat to the general surprise,\nthe Grumbler made his bow to the hostess in evening clothes, and though\nnot exuberantly Koshare, he was in an unwontedly gracious mood;\npartaking with polite zest of the stale chocolates, tough cookies, and\nflinty ginger snaps; munching long-baked Albert biscuit; serenely\nbolting puckery Oolong tea; and even handing the cups,--large and\nsubstantial ones, kindly furnished from their landlady's pantry,--and\ncommending their solidity and size as far preferable to the Dresden and\nJapanese \"thimbles\" commonly appearing on afternoon tea-tables. As for\nthe Pourer, it must be recorded that her grace, facility, and charm of\nmanner gave even stone china tea-cups an air of distinction, and lent to\nOolong tea and stale cakes a flavor of refinement. It was on Monday that\nthis function came off successfully.\n\nThe next Koshare festivity in regular order was the shooting-match.\n\nLeon, who had inherited from some Nimrod of his race, long since turned\nto dust, that _true eye_ and steady hand which make gunning a success,\nwas here master of ceremonies as well as contributor of prizes.\n\nThe first of these, a pair of gold sleeve-links, he, himself, easily\nwon, and subsequently donated to Dennis the dudish table-waiter. Of the\nfive prizes, two others were won by the two impecunious lungers, one by\nthe Harvard man, and another by the Antiquary. The shooting-match,\nenjoyed as it was by the near population of Mesilla Valley, proved a big\nsuccess, and weekly grew in grace with the aborigines as having a fine\nflavor of circus shows and Mexican bull-fights, and was considered by\nthe Koshare as one of their happiest hits.\n\nEqually successful was the Thursday entertainment, held in the big\ndining-room, under the auspices of the landlord and his wife, with the\ncook, waiter, maids, and chore-boys gathered about the open door.\n\nIt consisted of vocal and instrumental music, and recitations in prose\nand rhyme; and, at a late hour, wound up with a bountiful supper\ncontributed to the occasion by the generous landlord.\n\nMiss Hemmenshaw, the star performer, gave, with admirable Rachelesque\ngesture and true dramatic fire, \"The Widow of the Grand Army,\" recited\nwith exquisite delicacy Shelley's \"Cloud,\" and sent shivers down the\nbacks of the entire assemblage, by a realistic presentation of\nRossetti's \"Sister Helen.\" The grey-eyed school-marm recited with\ngenuine \"School of Oratory\" precision and finish \"Barbara Frietchie,\"\nHolmes' \"Chambered Nautilus,\" Longfellow's \"Sandalphon,\" and \"Tom\nO'Connor's Cat.\" Leon read, with admirable humor, some of Mr. Dooley's\nbest; and the Harvard man brought down the house with Kipling's \"Truce\nof the Bear.\"\n\nThere was some fine piano and banjo playing, and the singing of duets;\nand the Journalist rendered, in his exquisite tenor, Ben Jonson's rare\nold love-song, \"Drink to me only with thine eyes.\"\n\n\"Strange,\" commented the Antiquary (who in his miscellaneous mental\nstorage had found room for some fine old Elizabethan plays), turning to\nMiss Hemmenshaw in the pause of the song, \"Ben Jonson is dust these\nthree hundred years, and still his verses come singing down the ages,\nkeeping intact their own immortal flavor. The song-maker's is, indeed,\nan art that 'smells sweet, and blossoms in the dust.' Well might they\nwrite him, 'O rare Ben Jonson.'\"\n\n\"And how exquisitely,\" responded the lady, \"is the air married to the\nwords!\" And now the Minister brought forward his Cremona. He was a\nfinished violinist, with a touch that well-nigh amounted to genius. All\npraised his performance. At its close the Grumbler, in an aside to the\nAntiquary, thus delivered himself:--\n\n\"To _some_, God giveth common-sense; to _others_, to play the fiddle!\"\n\nFrom the entry audience the fiddler won rousing rounds of applause, and\nDennis, the waiter, ventured on the subdued shuffle of an Irish jig.\n\nThis it was that suggested to the Koshare an impromptu dance, and\nthereupon the young people straightway took the floor. The Minister,\nkindly oblivious of his cloth, fiddled on; Miss Paulina called off the\nfigures, and so, merrily, ended the first Koshare evening\nentertainment.\n\n\n\n\nCHAPTER V\n\n\nAs it is not proposed to give this record of the doings of the \"New\nKoshare\" the circumstantiality of a diary, the chronicler may be allowed\nto include the ensuing teas, shooting-matches, and all the lighter\nkosharean festivities in the one general and final statement, that they\neach came off duly and successfully; and leaving their details\n\"unhonored and unsung,\" proceed to a more extended account of the\nSaturday evening entertainments,--as all members of the club were\ninvited to contribute to these evenings, and it was expected that the\nMinister would, from the storehouse of his travelling experience,\ncontribute liberally to their delectability; and that the Journalist\n(who naturally thought in paragraphs, and, like the fairy who \"spoke\npearls,\" conversed in exquisitely fashioned sentences) would supplement\nthe papers of the Antiquary by his own brilliant talks.\n\nAnd so it was that on the initial Saturday evening, with a full\nattendance and great expectations, the Koshare found themselves\nconvened, the president in the chair, the secretary with notebook in\nhand, and all in dignified attention.\n\nThe Antiquary--with this apt quotation from Cumming's \"Land of Poco\nTiempo\"--began his first lecture before the club.\n\n\"'New Mexico,'\" quoted he, \"'is the anomaly of the Republic. It is a\ncentury older in European civilization than the rest, and several\ncenturies older still in a happier semi-civilization of its own.\nIt had its little walled cities of stone before Columbus had\ngrandparents-to-be; and it has them yet.'\n\n\"There are,\" stated Mr. Morehouse, \"three typical races in New Mexico.\nThe American interpolation does not count as a type.\n\n\"Of Pueblo Indians there are nine thousand, 'peaceful, home-loving, and\nhome-dwelling tillers of the soil.' Then, here, and in Arizona, there\nare about twenty thousand Navajo Indians,--nomad, horse-loving,\nhorse-stealing vagrants of the saddle, modern Centaurs. Then come the\nApaches, an uncounted savage horde, whose partial civilization has been\neffected by sheer force of arms, and inch by inch: who accept the\nreservation with but half a heart, and break bounds at every\nopportunity. Last of all come the Mexicans, shrunken descendants of the\nCastilian world-finders; living almost as much against the house as in\nit; ignorant as slaves, and more courteous than kings; poor as Lazarus,\nand more hospitable than Croesus; and Catholics from A to izzard.\n\n\"The Navajos and Apaches,\" said Mr. Morehouse, \"have neither houses nor\ntowns; the Pueblos have nineteen compact little cities, and the Mexicans\nseveral hundred villages, a part of which are shared by the invader.\n\n\"'The numerous sacred dances of the Pueblos,' says Cummings, 'are by far\nthe most picturesque sights in America, and the least viewed by\nAmericans, who never found anything more striking abroad. The mythology\nof Greece and Rome is less than theirs in complicated comprehensiveness;\nand they are a far more interesting ethnological study than the tribes\nof inner Africa, and less known of by their white countrymen.'\n\n\"The Pueblos of New Mexico,\" explained the Antiquary, \"are by no means\nto be confounded with the Toltecs or Aztecs. It is, however, barely\npossible that in prehistoric ages the race in possession of Mexico may\nhave had some tribal characteristics of the latter-day Pueblo. As of\nthat remote time, there is not even a traditionary record; this\nsupposition is absolutely conjectural.\n\n\"By investigation and comparison it has, however, been proved that the\nPueblos have racial characteristics connecting them with some mysterious\nstage of human life even older than that of the more barbarous Toltecs\nor Aztecs.\n\n\"This race has from time immemorial had its book of Genesis. It is not,\nlike that of the Hebrew, a written record, but has been orally handed\ndown, and with careful precision, beginning with their original\nemergence, as half-formed human beings, from the dark of the mystic\nunderworld of 'Shipapu' to the world of light.\n\n\"After the fashion of most barbarous races, the Pueblo appears\noriginally to have 'pitched his moving tent' in various parts of Mexico;\nand it may be inferred that he endured many casualities before settling\nhimself in life. It was to tide over this trying epoch in his existence\nthat 'Those Above,' according to tradition, made for the tribes that\nquaint 'Delight-Monger,' with whom we have already made acquaintance,\nwho led them in their wanderings from the womb of Shipapu to the solid\ncentre of their world; but, as has been already stated, this record,\ngoing back to an indefinite period of time, and having only the dubious\nauthority of folk-lore, is only of traditional value.\n\n\"The Pueblo, no less than the Aztec, is the most religious of human\nbeings. His ceremonial, like that of the age of Montezuma, is\nwonderfully and minutely elaborated; and though originating in a\ncivilization less splendid and refined, it is really less barbarous,\nsince its rites have never, like those of the Aztec, included the\nhorrors of human sacrifice and cannibalism.\n\n\"The Pueblo, since his exit from the womb of mother Earth, seems to have\ngiven his principal attention to the cultivation of its soil. All the\nsame, he appears never to have shirked the less peaceful\nresponsibilities of his tribe,--putting on his war-paint at the shortest\nnotice, to settle the quarrels of his clan.\n\n\"Although like most men of savage birth and breeding, cruel in warfare,\nhe seems never to have been abstractedly blood-thirsty, never to have\nkilled, like his ever-belligerent neighbor, the Apache, purely for\nkilling's sake; but, his quarrel once ended, and the present security of\nhis clan well achieved, he has contentedly returned to the peaceful ways\nof life; diligently sowing, weeding, and harvesting his crops of maize,\nmelons, squashes, and beans, and--ever mindful of the propitiative\nrequirements of 'Those Above'--taking careful heed of his religious\nduties.\n\n\"For a succinct account of the Pueblo cave (or cliff) dwellers,\" said\nthe Antiquary, \"I am largely indebted to Bandelier, from whose valuable\nPueblo researches I shall often take the liberty to quote.\n\n\"The imperfectly explored mountain range skirting the Rio Grande del\nNorte is picturesquely grand.\n\n\"Facing the river, the foundation of the chain is entirely volcanic.\n\n\"Colossal rocks form the abrupt walls of the gorges between these\nmountains, and are often so soft and friable that, in many places they\nwere easily scooped out with the most primitive tools, or even detached\nwith the fingers alone.\n\n\"In these gorges, through many of which run unfailing streams of water,\noften expanding to the proportions of regular valleys, the Pueblo Indian\nraised the modest crop that satisfied his vegetable craving.\n\n\"As it is easier to excavate dwellings than to pile up walls in the open\nair, the aboriginal Mexican's house-building effort was mostly confined\nto underground construction. He was, in fact, a 'cave-dweller,' yet\ninfinitely of more advanced architectural ideas than our own remote\nforbears of Anglo Saxon cave-dwelling times.\n\n\"Most of these residences might boast of from three to four rooms. They\nwere arranged in groups, or clusters, and some of them were several\nstories high.\n\n\"Rude ladders were used for mounting to the terrace or roof of each\nsuccessive story. The Pueblo had, literally, a hearthstone in his\nprimitive home. His fireplace was supplied with a hearth of\npumice-stone. A rudely built flue, made of cemented rubble, led to a\ncircular opening in the front wall of his cave-dwelling. Air-holes\nadmitted their scanty light to these dusky apartments, in which there\nwere not only conveniences for bestowing wearing-apparel, but niches for\nornamental pottery, precious stones, and the like Indian bric-a-brac.\nThe ground-floor entrance was a rude doorway closed by a hide, or mat.\nPlaited mats of Yucca leaves, and deer-hide, by day rolled up in corners\nof the sleeping-apartments, served for mattresses at night. A thick\ncoating of mud, washed with blood, and carefully smoothed, gave to the\nfloor a glossy effect. Some of the rooms are known to have been in\ndimension ten feet by fourteen. Their walls were whitewashed with burnt\ngypsum.\n\n\"Though the time when these traditional cliff-dwellers wooed and wed,\nlived and died in the Rialto vale is long, long gone by, the ruins of\ntheir homes may still be seen. Some of them are tolerably intact; others\nare crumbled away to mere shapeless ruins.\n\n\"And now, having described their dwellings, let us note some of the most\nmarked and interesting characteristics of the men and women who made in\nthem their homes.\n\n\"We are apt,\" said the Antiquary, \"to accord to our more enlightened\ncivilization the origin of communism; yet, antedating by ages our\nlatter-day socialistic fads, the communal idea enthused this unlettered\npeople, and to a certain extent seems to have been successfully carried\nout.\n\n\"Let not the strong-minded Anglo-Saxon woman plume herself upon the\ndiscovery of the equality of the sexes. While our own female suffragists\nwere yet unborn, the Pueblo wife had been accorded the inalienable right\nto lord it over her mankind.\n\n\"Among the Mexican cliff-dwellers, 'woman's rights' seem to have been as\nindigenous to the soil as the pinon and the prickly pear.\n\n\"In the primitive Pueblo domicile, the wife appears, by tribal consent,\nto have been absolutely 'cock of the walk.' The husband had no rights as\nowner or proprietor of the family mansion, and, as an inmate, was\nscarcely more than tolerated.\n\n\"The wife, in those ever-to-be-regretted days, not only built and\nfurnished the house,--contributed to the kitchen the soup pot, water\njars, and other primitive domestic appliances,--but figured as sole\nproprietor of the entire establishment.\n\n\"The Pueblo woman, though married, still had, with her children, her\nholding in her own clan. In case of her death, the man's home being\nproperly with _his_ clan, he must return to it.\n\n\"The wife was not allowed to work in the fields. Each man tilled the\nplot allotted him by his clan. The crops, once housed, were controlled\nby the woman, as were the proceeds of communal hunts and fisheries.\n\n\"The Pueblos had their system of divorce. It goes without saying that it\nwas not attended by the red-tape complications of our time. As the\nhusband's continuance under the family roof-tree depended absolutely on\nhis acceptability to the wife, at any flagrant marital breach of good\nbehavior she simply refused to recognize him as her lord. In vain he\nprotested, stormed, and menaced; the outraged better half bade him _go_,\nand he _went_! Thus easily and informally were Pueblo marriages\ndissolved; and, this summary transaction once well concluded, each party\nhad the right to contract a second marriage.\n\n\"The Pueblo Indian is historically known as a Catholic; that is to say,\nhe told his beads, crossed his brow with holy water, and duly and\ndevoutly knelt at the confessional. This done, he tacitly reserved to\nhimself the privilege of surreptitiously clinging to the Paganism of his\nforbears, and zealously paid his tithe of observances at the ancient\nshrine of 'the Sun Father' and 'the Moon Mother.'\n\n\"Some of the Pueblo tribes are said still to retain the use of that\nancient supplicating convenience, 'the prayer-stick.'\n\n\"'Prayer-sticks, or plumes,'\" explained the Antiquary, \"are but painted\nsticks tufted with down, or feathers, and, by the simple-minded Indian,\nsupposed especially to commend him to the good graces and kindly offices\nof 'Those Above.' In a certain way, the aboriginal prayer-stick seems to\nhave been a substitute for an oral supplication.\n\n\"The Pueblo, pressed for time, might even forego the hindering\nceremonial of verbal request, adoration, or thanksgiving, and hurriedly\ndeposit, as a votive offering to his easily placated gods, this tufted\nbit of painted wood; and, furthermore, since prayer-sticks were not\nalways within reach, it was permitted him in such emergencies to gather\ntwo twigs, and, placing these crosswise, hold them in position by a rock\nor stone. And this childish make-shift passed with his indulgent gods\nfor a prayer!\n\n\"The most trivial commonplace of existence had, with the superstitious\nPueblo, its religious significance; and it would seem to have been\nincumbent on him literally to 'pray without ceasing.' Hence the\nprayer-plume, or its substitute, was, with him, one of the necessities\nof life. Time would fail me to tell of the ancient elaborate religious\nrites and superstitions of the Mexican Indian; to recount his latter-day\nceremonials, wherein Pagan dances, races, and sports are like the jumble\nof a crazy quilt, promiscuously mixed in with Christian festas and holy\nsaint-days; and indeed the subject is too large for my sketchy handling.\nIt may not, however, be amiss to notice the yearly celebration of the\nfestival of San Estevan. It may be still witnessed, and seems to have\nbeen the original Harvest-home of the Mexican Indian, the observance of\nwhich has been handed down in various ways from all times, and among all\npeoples, and is probably the parent of our Thanksgiving holiday.\n\n\"The monks of the early Catholic church, in their missionary endeavor to\ncommend the Christian religion to the pagan mind, took care to graft\nupon each of the various festas of the Pueblo one of their own saint-day\nnames. Thus it was that the Acoma harvest-home masquerades under the\nguise of a saint-name, though an absolutely pagan ceremonial.\n\n\"It is still observed by them with genuine Koshare delight. There are\ndances, races, and tumbling, and the carnival-like showering of Mexican\nconfetti from the roofs of adobe houses. In summing up this brief\naccount of the sedentary New Mexican, I quote literally the forceful\nassertion of Cummings. 'The Pueblos,' says this writer, 'are Indians who\nare neither poor nor naked; who feed themselves, and ask no favors of\nWashington; Indians who have been at peace for two centuries, and fixed\nresidents for perhaps a millennium; Indians who were farmers and\nirrigators, and six-story housebuilders before a New World had been\nbeaten through the thick skull of the Old. They had,' he continues, 'a\nhundred republics in America centuries before the American Republic was\nconceived.'\n\n\"This peaceably minded people, as has already been stated, are by no\nmeans to be confounded with the roving New Mexican aborigines, with the\nuntamed Navajo scouring the plains on the bare back of his steed, or the\nfierce Apache, murderous and cruel.\n\n\"We must not,\" said Mr. Morehouse, \"take leave of the Pueblo, without\nsome reference to the great flat-topped, slop-sided chain of rock-tables\nthat throughout the length and breadth of his territory rises from the\nsandy plains, the most famous and best explored of which is known as 'La\nMesa Encantada,'--'the Enchanted Mesa.'\n\n\"According to tradition the Mesa Encantada gains its romantic name from\nan event which centuries ago--declares the legend--destroyed the town,\nthen a well-populated stronghold of the Acomas. As a prelude to this\nlegend, let me state that the Pueblo cliff-dwellers often perched their\nhabitations on lofty, sheer-walled, and not easily accessible mesas, a\nnatural vantage-ground from which they might successfully resist their\nenemies, the nomadic and predatory tribes formerly over-running the\ncountry.\n\n\"The steep wall of the Acoma Mesa, with its solitary trail, surmounted\nby means of hand and foot holes pecked in the solid rock, was so well\ndefended that a single man might keep an army at bay. What fear, then,\nshould these Acomas have of their enemies?\n\n\"The Acomas, like other Pueblo Indians, have from time immemorial been\ntillers of the soil.\n\n\"From the fertile sands of their valley and its tributaries they won by\npatient toil such harvests of corn, beans, squashes, and cotton as\nsecured them a simple livelihood; and 'their granaries,' it is asserted,\n'were always full enough to enable them, if need be, to withstand a\ntwelvemonth's siege.' How long the top of Katzimo, the site of the\nEnchanted Mesa, had been inhabited when the catastrophe recorded in the\nlegend befell, no man may say, not even the elders of the tribe; this\nmuch is, however, known,--the spring-time had come. The sun-priest had\nalready proclaimed from the housetops that the season of planting was at\nhand. The seeds from last year's harvest had been gathered from the\nbins; planting-sticks had been sharpened, and all made ready for the\nauspicious day when the seer should further announce the time of\nrepairing to the fields. On that day (so runs the tale), down the ragged\ntrail, at early sunrise, clambered the busy natives; every one who was\nable to force a planting-stick into the compact soil, or lithe enough to\ndrive away a robber crow, hurried to the planting. Only a few of the\naged and ailing remained on the mesa.\n\n\"While the planters worked in the hot glare of the valley below, the sun\nsuddenly hid his face in angry clouds. The busy planters hastened their\nwork, while the distant thunder muttered and rolled about them. Suddenly\nthe black dome above them was rent as by a glittering sword, and down\nswept the torrent, until the entire valley became a sheet of flood. The\nplanters sought shelter in the slight huts of boughs and sticks from\nwhich the crops are watched.\n\n\"The elders bodingly shook their heads. Never before had the heavens\ngiven vent to such a cataract.\n\n\"When the sudden clouds as suddenly dispersed, and the sun-lit crest of\nKatzimo emerged from the mist, the toilers trudged toward their mountain\nhome. Reaching the base of the trail, they found their pathway of the\nmorning blocked by huge, sharp-edged pieces of stone, giving mute\ntestimony of the disaster to the ladder-trail above.\n\n\"The huge rock mass, which had given access to the cleft by means of the\nholes pecked in the trail-path, had in the great cloud-burst become\nfreed from the friable wall, and thundered down in a thousand\nfragments, cutting off communication with the mesa village. The Acomas,\nwhen asked why their ancestors made no desperate effort to reach the\nsufferers whose feeble voices were calling to them from the summit for\nsuccor, but left their own flesh and blood to perish by slow starvation,\ngravely shook their heads.\n\n\"The ban of enchantment had already, for these superstitious pagans,\nfallen upon the devoted table-land; it had become 'La Mesa Encantada.'\n\n\"The publication by Mr. Charles F. Lummis, who resided for several years\nat the pueblo of Iselta, of the story of Katzimo, the tradition of which\nwas repeated to him by its gray-haired priests some twelve years ago,\naroused the interest of students of southwestern ethnology in the\nhistory of 'La Mesa Encantada,' and, subsequently, Mr. F. W. Hodge was\ndirected by the Bureau of American Ethnology, of the Smithsonian\nInstitute, to scale the difficult height of this giant mountain, for the\npurpose of supplementing the evidence already gained, of its sometime\noccupancy as a Pueblo town. His party found decided evidence of a former\noccupancy of the mesa, such as fragments of extremely ancient\nearthenware, a portion of a shell bracelet, parts of two grooved stone\naxes, lichen-flecked with age. Here, too, was an unfeathered\nprayer-stick, a melancholy reminder of a votive offering made, at the\nnearest point of accessibility, to 'Those Above.'\n\n\"'When I consider,' says Mr. Hodge, in his charming paper, 'The\nEnchanted Mesa,' published in the 'Century Magazine,' some three or\nfour years ago, 'that the summit of Katzimo, where the town was, has\nlong been inaccessible to the Indians, that it has been swept by winds,\nand washed by rains for centuries, until scarcely any soil is left on\nits crest, that well-defined traces of an ancient ladder trail may still\nbe seen pecked on the rocky wall of the very cleft through which the\ntraditionary pathway wound its course; and, above all, the large number\nof very ancient potsherds in the earthy talus about the base of the\nmesa, which must have been washed from above, the conclusion is\ninevitable that the summit of 'La Mesa Encantada' was inhabited prior to\n1540, when the present Acoma was discovered by Coronado, and that the\nlast vestige of the village itself has long been washed or blown over\nthe cliff.'\"\n\nWith this account of the Enchanted Mesa, Mr. Morehouse, amid general\napplause, ended his interesting paper on the Pueblo Indians; and after a\nshort discussion by the Club of the ancient and modern characteristics\nof these remarkable aborigines, the Koshare, well pleased with the\nsuccess of its endeavor to combine improvement with delight, adjourned\nto the next Monday in January.\n\nLittle dreamed Roger Smith as, that night, after the Club entertainment,\nhe handed the Hemmenshaw ladies to their wagon, for the return ride to\nHilton Ranch, that the very next week he was to undertake, on their\nbehalf, a hand-to-hand encounter with a blood-thirsty Apache. Yet so was\nit ordained of Fate.\n\nIt has already been stated that these ladies were but day-boarders at\nAlamo Ranch, occupying, together with Sholto, a Mexican\nman-of-all-work, the Hilton Ranch, a good mile distant from the\nboarding-house.\n\nLouise Hemmenshaw, usually in exuberant health, was ill with a severe\ninfluenza. It was the third and cumulative day of this disease. Sholto\nhad already been despatched to Brown's for the dinner; Miss Paulina had,\nin this emergency, undertaken to turn off the breakfasts and suppers\nfrom her chafing-dish.\n\nAfter replenishing, from the wood basket, the invalid's chamber fire,\nMiss Paulina administered her teaspoonful of bryonia, gave a settling\nshake to her pillow, and hurried down to fasten the back door behind\nSholto.\n\nLingering a moment at the kitchen window, the good lady put on her\nfar-off glasses for a good look across the mesa, stretching--an unbroken\nwaste of sage-brush and mesquite-bush--from the Hilton kitchen garden to\nthe distant line of the horizon.\n\nAs she quietly scanned the nearer prospect, Miss Paulina's heart made a\nsudden thump beneath her bodice, and quickened its pulses to fever-time;\nfor there, just within range of her vision, was the undoubted form of an\nApache savage, clad airily in breech-clout, and Navajo blanket. Skulking\nwarily along the mesa, he gained the garden fence and sprang, at a\nbound, over the low paling. For a moment the watcher stood paralyzed\nwith wonder and dismay.\n\nMeantime, under cover of a rose-trellis, the Apache, looking bad enough\nand cunning enough for any outrage, coolly made a reconnoisance of the\npremises. This done, still on all-fours, he gained the bulkhead of the\nsmall dark vegetable cellar beneath the kitchen. It chanced to have been\ninadvertently left open.\n\nWith a satisfied grunt (and eschewing the paltry convenience of steps)\nhe bounded at once into its dusky depths.\n\nSummoning her failing courage, this \"Daughter of the Revolution\"\nresolutely tiptoed out the front door, and, with her heart in her mouth,\nwhisking round the corner of the devoted house, shot into place the\nstout outside bolt of the bulkhead door.\n\nThis feat accomplished, she made haste to gain the safe shelter of the\nadobe dwelling. She next looked well to the bolt fastening the trap-door\nat the head of the ladder-like stairway leading perilously from the\nkitchen to the dim region below, where the Apache might now be heard\nbumping his head against the floor-planks, in a fruitless endeavor to\ndiscover some outlet, from this underground apartment, to the family\ncircle above. With the frightful possibility of a not distant escape of\nher prisoner, the good lady lifted her heart in silent prayer, and\nhurrying promptly to the chamber of her niece, gave a saving punch to\nthe fire, a glass of port wine to the invalid, and, feigning an\nappearance of unconcern, left the room, and slipped cautiously down to\nthe kitchen. Here she dragged an ironing-table, a clothes-horse, and a\nwood-box on to the trap-door, and breathlessly waited for the Apache's\nnext move.\n\nAnd now, a step might be heard on the driveway, followed by a rap at the\nfront door.\n\nPrudently scanning her visitor through the sidelight, and assuring\nherself that he was no breech-clouted savage, but a fellow white man,\nMiss Paulina let in through the narrowest of openings,--who but their\nfriend the Harvard man! \"Dear soul!\" tearfully exclaimed the good lady,\nwhile Roger Smith stood in mute wonder at the warmth of her greeting.\n\nIt was but the work of a moment to explain the situation and acquaint\nhim with the peril of the moment.\n\nSholto, at his leisurely Mexican pace, now opportunely appeared at the\nback door with the hot dinner.\n\n\"There is a time for all things,\" said the \"president of Chapter 18th,\"\nas (having pulled the bewildered Mexican inside) she vigorously shot the\ndoor-bolt in place, deposited the smoking viands on the sideboard, and\nthus addressed him. \"Sholto,\" said Miss Paulina, \"I have an Apache here\nin the cellar. For the time being his ability to work us harm is\nlimited; but an Apache is never nice to have round; and, besides, he\nmust have terribly bumped himself poking round there all this time in\nthe dark. One would not unnecessarily hurt even a savage. We must\ntherefore let him up, bind him fast, and take measures for delivering\nhim to the police at Las Cruces. Here is a clothes-line: it is good and\nstrong; make up a lasso, and when I open the trap-door, as his head bobs\nin sight, throw it, and then help Mr. Smith haul him out, and tie him.\"\n\nSholto's lasso was soon in working order. The trap-door once raised, the\nhead of the unsuspecting savage flew up like a Jack in a box, and with\nsuch a rubber-like bound that Sholto's lasso went wide of the mark. In\nthis dilemma, a scientific blow from the fist of a Harvard athlete\ndeftly floored him, and, in the consequent lapse of consciousness, he\nwas easily bound, and safely deposited in the bottom of the Hilton\nexpress wagon. This accomplished, Sholto and the Harvard man summarily\ntook the road for Las Cruces, some four miles distant. The horse and his\ndriver being in absolute accord as to the ratio of miles proper to the\nhour, the captors drove leisurely along; the Harvard man meantime\nrelieving the slow monotony of the way, with incident and anecdote, and\nSholto, in turn, imparting much interesting New-Mexican information.\n\nPresently a faint stir, as of the quiet, persistent nibbling of a mouse\nin the wall, might (but for the talking) have been heard from the bottom\nof the wagon. \"Poor beggar!\" said the Harvard man, at last recalling to\nmind the captive Apache; \"he must, by this time, be about ready to come\nto.\" And taking from his over-coat pocket a tiny flask of brandy, he\nturned on his seat with the humane intention of aiding nature in\nbringing about that restoration. \"Gone! clean gone! by George!\"\nexclaimed the astonished athlete. The cunning savage had, with his\nsharp, strong teeth, actually gnawed through his wrist cords, and, with\ntooth and nail extricating himself from the knotted clothes-line, was\nalready on his return from the unsatisfactory husks of Mesilla Valley,\nto the fatted veal of the U. S. government, in his father's house,--\"The\nReservation.\" \"_They are fleet steeds that follow!_\" quoted the Harvard\nman as the jubilant Apache, with flying heels, loomed tantalizingly on\nthe distant plain. The startled cotton-tail, swept by \"the wind of his\ngoing,\" scurried breathlessly to his desert fastnesses among the\nsage-brush and mesquite.\n\nWith a humorous glance at his fast-vanishing form, the Harvard man\nmeasured with his eye the intervening distance, the speed of the escaped\ncaptive, and the pace of the propeller of the Hilton express, and\ngracefully accepted the situation. Sholto lazily turned the horse's\nhead, and in process of time the discomfited captors of Miss Paulina's\nApache--like John Gilpin--\n\n \"Where they did get up\n Did get down again.\"\n\nMeantime, Miss Hemmenshaw brought up the mid-day meal.\n\n\"Auntie,\" said the invalid, \"this feverish cold puts queer fancies in my\nhead. While you were away, I must have taken a little nap, and when I\nawoke there seemed to be some sort of a rumpus going on below; after\nwhich I fancied that a team started away from the back door. It could\nnot have been Sholto's; for he would be coming from Brown's about that\nhour with our dinner.\"\n\n\"It may have been just a part of your dream, dear,\" pacified the aunt;\n\"but come, now, here is our dinner. Let us have it together. A\nwonderfully nice dinner Mrs. Brown has sent us, too, and you can\nventure to-day on a quail, and a bit of orange pudding. For myself, I am\nas hungry as a bear;\" and, removing the books from the oval bedroom\ntable, Miss Paulina laid the cloth, set out the dishes and glasses, and\ndaintily arranged the viands, which the two ladies discussed with\nevident relish.\n\n\"And now,\" said the aunt, \"since you have dined, and have something to\nbrace you up, I will 'tell my experience;'\" and forthwith she related to\nthe astonished Louise the adventure of the morning. The good lady had\nbut accomplished her exciting account, when the valiant captors of the\nApache drove up.\n\nMiss Paulina, with the concentrated importance of her entire \"Chapter,\"\nmet and opened the door to her hero.\n\n\"Well?\" asked she of the crestfallen athlete.\n\n\"No: ill!\" replied he; \"the Apache never reached Las Cruces. He managed\nto unbind himself, and slipped from our hands by the way. The\nclothes-line has come back safe; but the savage is, long ere this, well\non his road to the Mescalero Reservation.\"\n\n\"Well,\" said Miss Paulina, judicially, \"I can't say that I'm sorry. The\ncreature had a rough time bumping about that low, dark cellar; and your\nblow on his head was a tough one. And when one considers the\nslip-shodness of things at Las Cruces, and the possible insecurity of\ntheir jail, _we_, on the whole, are the safer for his escape; and _he_\nwill, of course, feel more at home now in the Reservation, and will\nprobably remain there for a while, after the fright we gave him.\"\n\nThus reassured, the Harvard man accepted Miss Hemmenshaw's invitation to\nstay to supper. And presently the convalescing invalid came down to\nexpress her thanks for his devoir of the morning. Reclining on the\nparlor lounge, in a cream-white tea gown, she looked so lovely that a\nman might well have dared a whole tribe of savages in her defence. By\nand by they had a quiet game of chess. It goes without saying that the\nlady won. There _might_ be men hard-hearted enough to beat Louise\nHemmenshaw at chess. The Harvard man was not _of_ them.\n\nSo slipped away this happy afternoon; and, at sunset Sholto appeared\nwith the tea equipage, and the young people covertly made merry over a\nchafing-dish mess achieved by the Cooking School pupil; and under cover\nof rarebit, water-biscuit, and cups of Russian tea, the Harvard man made\nhay for himself in this bit of sunshine, and grew in favor with both\naunt and niece.\n\nWith Miss Paulina Hemmenshaw, true to her aristocratic birth and\nbreeding, pedigree far out-weighed filthy lucre. To be well born was, in\nher estimation, to be truly acceptable to gods and men.\n\nRoger Smith, with his plebeian surname and unillustrious \"tanner\"\ngrandfather, was by no means a suitable husband for her motherless\nniece, to whom, as the head of her brother's household, she had for\nyears filled a parent's place. Louise Hemmenshaw, as the good lady\nshrewdly guessed, was the magnet that drew this undeclared lover to\nMesilla Valley. During the preceding winter they had met at many social\nfunctions in Boston and Cambridge, and he had become the willing captive\nof her bow and spear. He had never told his love.\n\nThe social discrepancy between the lovely aristocrat and Roger--the\ngrandson of Roger the Tanner--was too wide to be easily overstepped.\n\nOstensibly the Harvard man had come to New Mexico to recruit his spent\nenergies; but in his heart of hearts he knew that dearer than health was\nthe hope of winning the heart of Louise Hemmenshaw. Already his native\nrefinement and charm of manner had commended him to Miss Paulina; and\nnow, his prowess in the day's adventure had made her, for good and all,\nhis warm friend. As to her niece, he told himself, as, that night, by\nthe light of a low moon, he took his way to Alamo Ranch, recalling the\ntender pressure of the invalid's white hand, when, with a rosy blush,\nshe bade him good-night, that in his wooing he had to-day \"scored one;\"\nand with the confident egotism of presumptuous mortals, when events play\nunexpectedly into their hands, he decided that Fate had prearranged this\ntimely call of his on the Hemmenshaws, and had timed the arrival of the\nApache at that opportune hour, with an especial view to the fulfilment\nof his own cherished wishes.\n\n\n\n\nCHAPTER VI\n\n\nAnother two weeks of lighter Koshare festivities had again brought round\nthe more solid fortnightly entertainment of the Club.\n\nIts members duly assembled, the president in his chair, and the\nsecretary at attention, Mr. Morehouse thus began his second paper.\n\n\"Before Texas,\" said he, \"became a part of an independent republic, and\nuntil after the Mexican war (when we forced Mexico to sell us all\nCalifornia, New Mexico, and Arizona, nearly all of Utah and Nevada,\nbesides Texas, and the greater part of Colorado), Mexico proper reached\nway up here; and it is thought by some archaeologists that the mesas or\ntable-mountain land especially characterizing the New Mexican landscape\nmay have afforded the suggestion for the Teocallis of the great\npyramid-like mounds, with terraced sides, built by the Aztecs. Some\nscholars have even convinced themselves that the Aztec culture must have\noriginated here in the North. Others wholly discard the conclusion.\n\n\"Mr. Baxter, in his valuable and interesting book of Mexican travel,\nsays, decidedly, 'The New Mexican Indians were not Aztecs, and Montezuma\nhad no more to do with New Mexico than he did with New England.' And\nwith this assertion I think we must all, perforce, agree.\n\n\"Of the Toltecs, the probable predecessors in Mexico of the Aztecs, all\nwritten records,\" said the Antiquary, \"have long since perished. They\nare known to us only through traditionary legends orally handed down by\nthe races that succeeded them.\n\n\"They are said to have entered the Valley of Anahnac from a northerly\ndirection, coming from a mysterious unknown region, and probably before\nthe close of the seventh century. They appear to have been a far more\ngentle and refined nation than their immediate successors, the\nhalf-savage Aztecs, who, at last, with their semi-civilization,\ndominated Mexico. By general archaeological agreement, the Toltecs were\nwell instructed in agriculture, and many of the most useful mechanic\narts.\n\n\"'They were,' declares Prescott, 'nice workers in metals.' They invented\nthe complex arrangement of time adopted by the Aztecs, who are said to\nhave been largely indebted to them for the beginnings of that\nincongruous civilization which reached its high-water mark in the reign\nof the Montezumas. So late as the time of the Spanish Conquest the\nremains of extensive Toltec buildings were to be found in Mexico.\n\n\"'The noble ruins of religious and other edifices,' says the same\nwriter, 'still to be seen in Mexico, are referred to this people, whose\nname, _Toltec_, has passed into a synonym for _Architect_.'\n\n\"After a period of four centuries--having succumbed to famine,\npestilence, and unsuccessful wars--this remarkable people disappeared\nfrom the land as silently and mysteriously as they had entered it. It\nis conjectured that some of them may have spread over the region of\nCentral America and the neighboring isles; and that the majestic ruins\nof Mitla and Paleque are the work of this vanished race. Tradition\naffirms that a remnant of Toltecs still lingering in Anahnac 'gave\npoints' to the next inhabitants; and the Tezcucans are thought to have\nderived their gentle manners and comparatively mild religion from the\nhandful of Toltecs who still remained in the country. A Spanish priest,\nwith that keen relish for the marvellous common to his kind, accounts\nfor this mysterious disappearance by supernatural stories of giants and\ndemons.\n\n\"According to good authorities, more than a hundred years elapsed\nbetween the strange disappearance of the Toltecs from the land of\nAnahnac and the arrival on its borders of the Aztecs.\n\n\"After the nomadic fashion of barbarous races, this people did not at\nonce make a permanent settlement, but pitched their tents in various\nparts of the Mexican valley, enduring many casualties and hardships, and\nbeing at one time enslaved by a more powerful tribe, whom their prowess\nsubsequently dominated.\n\n\"Some of these wanderings and adventures are perpetuated in their oral\ntraditional lore.\n\n\"One of these legends is well substantiated, and current at this day,\nhaving been the origin of the device of the eagle and cactus, which form\nthe arms of the present Mexican republic, and may be found on the face\nof the Mexican silver dollar. Thus it runs: 'Having in 1325 halted on\nthe southwestern borders of the larger Mexican lakes, the Aztecs there\nbeheld, perched on the stem of a prickly pear, which shot out from a\ncrevice of a rock that was washed by the waves, a royal eagle of\nextraordinary size and beauty, with a serpent in his talons, and his\nbroad wings open to the rising sun.\n\n\"'They hailed the auspicious omen, which the oracle announced as an\nindication of the site of their future city.'\n\n\"The low marshes were then half buried in water; yet, nothing daunted,\nthey at once proceeded to lay the sloppy foundation of their capital, by\nsinking piles into the shallows. On these they erected the light\ndwelling-fabrics of reeds and rushes,--the frail beginnings of that\nsolid Aztec architecture carried to such elegant elaboration in the time\nof the Montezumas. In token of its miraculous origin they called their\ncity Tenochtitlan. Later it was known as Mexico, a name derived from the\nAztec war-god, Mexitil.\n\n\"It has been shown that the Aztec race, once permanently established in\nMexico, finally attained to a civilization far in advance of the other\nwandering tribes of North America.\n\n\"'The degree of civilization which they had reached,' says Prescott, 'as\ninferred by their political institutions, may be considered not far\nshort of that enjoyed by our Saxon ancestors under Alfred. In respect to\nthe nature of it, they may better be compared to the Egyptians; and the\nexamination of their social relations and culture may suggest still\nstronger points of resemblance to that ancient people.\n\n\"'Their civilization,' he goes on to say, 'was, at the first, of the\nhardy character which belongs to the wilderness. The fierce virtues of\nthe Aztec were all his own. They refused to submit to European\nculture--to be engrafted on a foreign stock. They gradually increased in\nnumbers, made marked improvements both in polity and military\ndiscipline, and ultimately established a reputation for courage as well\nas cruelty in war which made their name terrible throughout the valley.'\nIn the early part of the fifteenth century--nearly a hundred years after\nthe foundation of the city--that remarkable league--of which it has been\naffirmed that 'it has no parallel in history'--was formed between the\nstates of Mexico and Tezcuco, and the neighboring little kingdom of\nTlacopan, by which they agreed mutually to support each other in their\nwars, offensive and defensive, and that in the distribution of the spoil\none-fifth should be assigned to Tlacopan and the remainder be\ndivided--in what proportions is uncertain--between the two other powers.\n\n\"What is considered more remarkable than the treaty itself, however, is\nthe fidelity with which it was kept.\n\n\"During a century of uninterrupted warfare that ensued no instance, it\nis declared, occurred in which the parties quarrelled over the\ndistribution of the spoil. By the middle of the fifteenth century the\nallies, overleaping the rocky ramparts of their own valley, found wider\noccupation for their army, and under the first Montezuma, year after\nyear saw their return to the Mexican capital, loaded with the spoils of\nconquered cities, and with throngs of devoted captives.\n\n\"No State was able long to resist the accumulated strength of the\nconfederates; and at the beginning of the sixteenth century, on the\narrival of the Spaniards, the Aztec dominion reached across the\ncontinent, from the Atlantic to the Pacific.\"\n\nHere Mr. Morehouse ended his paper on the Toltecs, and the Koshare, with\nmany thanks for his interesting account of these ancient races,\nsupplemented his information by a general discussion of the genuineness\nof the accepted authorities for the early history of the Aztecs and of\nthe time of Montezuma.\n\n\"Prescott,\" said the Minister, \"traces some points of resemblance\nbetween the history of the Aztecs and that of the ancient Romans;\nespecially in polity and military success does he compare them.\"\n\n\"Unfortunately,\" observed the Antiquary, \"the earlier records of the\nMexican people can only be scantily gleaned from oral tradition and\nhiero-graphical paintings.\"\n\n\"Later, however,\" remarked the Journalist, \"we have the seemingly more\ndefinite and reliable accounts of the Spanish chronicles.\"\n\n\"These,\" returned the Minister, \"being usually ecclesiastic, have warped\ntheir record to suit their own bigoted views; consequently, much of the\nnarrative popularly known as Mexican history is to be taken with more\nthan the proverbial pinch of salt.\"\n\n\"It has,\" said the Journalist, \"been urged by realistic critics of our\nown fascinating historian--Prescott--that since he drew his historic\ndata, with the exception of the military record of the Spaniards, from\nthese unreliable sources, his history is little other than the merest\nromance. Plainly, the assertions of some of the chroniclers are scarce\nmore worthy of credence than the equally fascinating adventures of\nSinbad the Sailor, and the impossible stories of Baron Munchausen.\n'Bernard Diaz'--that enigmatical personage from whom many of Prescott's\ndata are drawn--tells us that the Aztecs actually fattened men and women\nin cages, like spring chickens, for their sacrifice, and asserts that at\nthe dedication of one of their temples a procession of captives two\nmiles long, and numbering seventy-two thousand persons, were led to\nsacrifice! By the way, it has, however, been latterly proved that the\nso-called sacrificial stone, now exhibited in the National Museum of\nMexico, is not a relic of the Aztecs, but of the earlier Toltecs (who\nwere not addicted to human sacrifice), and is as innocent of human blood\nas the Calendar Stone, referred to the same period. The critics of Diaz\nhave detected in his account constant blunders in many important\nmatters, and his glaring geographical errors would seem to prove that,\nthough he claims to have been, all through the Conquest, the very shadow\nof Hernando Cortez, he has never even been in the country he describes!\"\n\n\"From what I have read of Bernald,\" said Leon, \"I think we may finish\nhim off with 'Betsy Prig's' very conclusive objection to Sairey Gamp's\n'Mrs. Harris'--there ain't no sich person!\"\n\n\"Even so,\" exclaimed the Minister, \"I, for one, agree with certain\ndownright critics who contend that Diaz was a pure fabrication, a\npriestly scheme of the Roman Church to screen the cruel enormities of\ntheir agent, Cortez. Father Torquemada, another of Prescott's\nauthorities, is thought to be scarcely more reliable. Las Casas, another\nof our historian authorities, whose history was, at the time, promptly\nsuppressed by the all-powerful Inquisition, declares these Spanish\nhistories of the Conquest to be 'wicked and false.'\"\n\n\"And yet, in spite of these strictures,\" contended Leon, \"I, for one,\nstill pin my faith to Prescott and his implicit honesty of purpose. He\ngave us, in his own learned and fascinating way, the narrative of these\npriestly chroniclers as he found it. If the chroniclers lied, why, so\nmuch the worse for the chroniclers.\"\n\n\"Lying,\" complained the Grumbler, \"is a malady most incident to\nhistorians;\" and thereupon rose to open the parlor door for the\ngray-eyed school teacher, who just then bade the Koshare good-night,\nadding that she had already been too long away from her sister.\n\nAnd now the chairman announced the next paper in the Koshare course for\nthe second Saturday in February, and the members, one and all,\ndispersed.\n\nSholto, roused from a most enjoyable series of naps, brought his wagon\nto the side door, and with a friendly grasp from the hand of Miss\nPaulina, and a shy, tremulous clasp from that of her niece, the Harvard\nman saw the ladies off.\n\n\n\n\nCHAPTER VII\n\n\nFebruary had come, bringing in its train such weather as verified the\nwarmest praise of New Mexico's perfect climate.\n\nIt was on one of its most spring-like afternoons that a walking party of\neight set out to pay a long-proposed visit to the ladies at Hilton\nRanch.\n\nAs the little party went gayly along the mesa, Leon, carrying his gun,\nshot doves for the evening meal, while the rest walked on, chatting\nmerrily.\n\nThe ladies talking over, by the way, the late attempt of the Apache on\nHilton Ranch, Mrs. Bixbee declared herself curious to see the cellar in\nwhich Miss Paulina had caught that prowling savage. On their arrival\nthat good lady, informed of this desire, kindly proceeded to gratify her\nguest, and the entire party was presently led by her to the kitchen, the\nhero of this adventure modestly walking beside the fair lady of his\nlove. Sholto, busied about the place, was just then out of call, and\nMiss Hemmenshaw, intent to afford them a peep into the cellar, begged\nthe Harvard man to raise for her the heavy trap-door.\n\nThe dear lady never quite knew how it was that, leaning forward, she\nlost her balance, and, but for the prompt help of Roger Smith, might\nhave landed, pell-mell, on the cellar bottom; or how, in rescuing her,\nhe himself made the misstep that, ere he could recover his poise, threw\nhim to the end of the ladder-like cellar stairs.\n\nRecovering breath, Roger Smith cheerily called up to the affrighted\ngroup at the top, \"All right!\" but, on pulling himself together to make\nthe ascent, he suddenly found all wrong. He had sprained his ankle; and\nit was with painful effort that he won to the top. At this juncture\nSholto, aroused by the unwonted rumpus, made his appearance,\nanticipating no less a disaster than the reappearance of the slippery\nsavage, for whom he still held the lasso \"in pickle.\" Disabled by the\nsprain, the Harvard man submitted himself to the stout arms of the\nMexican, and, by Miss Paulina's direction, was carried into the bedroom\nadjoining the ranch parlor.\n\nThere, laid upon a movable couch which served the double purpose of sofa\nand bed, Sholto having, not without difficulty, removed his boot and\nstocking, he submitted the swollen foot to the careful inspection of\nMiss Hemmenshaw, who, with a steadiness of nerve not unworthy of her\n\"Chapter,\" put the dislocated joint in place, bandaged the injured\nmember with arnica, administered an internal dose of the same\nrestorative, and duly followed it with a glass of old Port. This done,\nSholto wheeled the sufferer's couch into the adjoining parlor. Half an\nhour later Leon came in with a well-filled game-bag; and after an hour\nof mild Koshare merriment, in which the athlete but feebly joined (the\npain of his ankle was still terrible), the little party took its way, in\nthe fading sunlight, to Alamo Ranch. Miss Paulina, having promptly\ndecided that her patient was unequal to the return by way of the jolting\nHilton express team, sent to Mrs. Brown an order for supper for her\nguest, Louise, and herself. It was duly conveyed to Hilton's by an Alamo\nchore-boy. Sholto, as the sole male dependence of Hilton's, must stick\nto his post; for, sagely observed the \"Daughter of the Revolution,\" two\nwomen, heroic though they might be, were no match for an Apache\nmarauder; and as for poor Roger Smith, he could now neither \"fight\" nor\n\"run away.\"\n\nSholto lighted the lamps, laid the supper on the low Queen Anne table,\nadded fresh water from the spring, and when a pot of tea had been made\nby the hostess' own careful hand, and Sholto had wheeled up the couch of\nthe invalid, that he might take his supper _a la Roman_, the three made\na cheery meal.\n\nWhen the man had removed the supper things, and piled fresh wood on the\nandirons, the ladies brought their work-baskets; and while they busied\nthemselves with doily and centre-piece, the Harvard man, lying in the\ncomfort of partial relief from pain, watched the dainty fingers of\nLouise Hemmenshaw as she bent industriously over her embroidery, and\nfell fathoms deeper in love with the dear and beautiful girl.\n\nRoger Smith stayed on at Hilton Ranch, where, thrown day after day in\nsemi-helplessness on the kind attendance of Miss Paulina and the sweet\nsociety of her niece, he (I grieve to say) fell a ready prey to the\nsuggestions of a certain wily personage who (according to Dr. Watts)\nfinds employment for idle hands, and thus conceived the wickedness of\ncunningly using this accident to further his own personal ends. Thus\ndevil-tempted, this hitherto upright young person resolved that it\nshould be a long day before his sprained ankle should permit him to\nreturn to Brown's, and lose this precious opportunity of establishing\nhimself in the good graces of the aunt, and winning the love of the\nniece.\n\nFar from approving the crooked policy which led Roger Smith to feign\nlameness long after the injured ankle had become as sound as ever, the\npresent historian can only, in view of this lapse from integrity, affirm\nwith Widow Bedott that \"we're poor creeturs!\" and, with that\ndepreciative view of humanity, go on with this truthful narrative.\n\nA whole delicious month had been passed by the Harvard man in this\nparadise,--Elysian days, while, waited on by Sholto, petted by Miss\nPaulina, and companioned by the loveliest of houris, he dreamed out his\ndream.\n\nAt last, on a certain decisive evening, Roger Smith found himself alone\nin the gloaming with Louise Hemmenshaw. The aunt, who through all these\nweeks had zealously chaperoned her niece, had passed into the\ndining-room to evolve some chafing-dish delicacy for the evening meal.\nWithout, the setting sun flooded all the west with gold, touched the\ndistant mountain peaks with splendor, and threw a parting veil of glory\nover the wide mesa. Within, the firelight made dancing shadows on the\nparlor wall, where the pair sat together in that eloquent silence so\ndear to love. \"Well,\" said the athlete to himself (compunctiously\nglancing at his superfluous crutches, left within easy reach of his\nhand), \"this performance can't go on forever. I have made believe about\nlong enough; what better may I do than own up this very night, and\nsomehow bring this base deceit to an end.\"\n\nMentally rehearsing the formula, in which, over and over, he had asked\nthe hand of this beautiful aristocrat, his mind still sorely misgave\nhim. \"Why,\" thought this depressed lover, \"was not my name Winthrop,\nEndicott, or Sturgis, instead of Smith; and my grandfather a senator, a\njudge, or even a stockbroker, rather than a tanner?\"\n\nNeither Miss Paulina nor her brother, he discouragedly mused, would ever\ncountenance this unequal match. His millions would with them weigh\nnothing against \"the claims of long descent.\"\n\nThe sun had gone down, the after-glow had faded to gray. They were still\nalone. The firelight half revealed the lovely figure beside the hearth.\nIn that gown of golden-brown velvet, with the creamy old lace at wrists\nand throat, the brown hair combed smoothly from the white forehead,\nknotted behind and fastened with a quaint arrow of Etruscan gold, Louise\nHemmenshaw was simply adorable! It was indeed good to be here; and why\nshould not a life so sweet and satisfying go on indefinitely?\n\n\"It is four weeks to-day since I fell down cellar,\"--such was the\ncommonplace beginning to this much considered tale of love.\n\n\"Really?\" said the lady, looking innocently up from an absorbed\ncontemplation of the fender. \"It has not seemed so long. I never before\nrealized what a serious thing it is to sprain one's ankle. You have been\na most patient sufferer, Mr. Smith; and, indeed, for the past two weeks,\na most jolly one. Aunt Paulina was saying to-day that it was high time\nwe all went back to Alamo for our meals, and helped out the Koshare\ndoings of the Club.\"\n\n\"Dear Miss Hemmenshaw,\" here blurted out the culprit, \"do not despise me\nfor my meanness, since it is all for love of you that I have been\nshamming lameness. For these last two weeks I could at any time have\nwalked as well as ever.\" And, hereupon, without the slightest reference\nto his crutches, he rose from his chair and skipped over to her side. \"A\nsprain,\" explained this audacious lover, \"may be cured in a fortnight,\nbut it takes a good month to woo and win a fair lady. Having soon after\nmy accident decided that point, I have done my best. Tell me, dear\nLouise,\" pleaded he, \"that my time has been well spent. Say that,\ndeceitful ingrate though I am, you will take me, for good and all.\"\n\n\"Roger Smith,\" replied the lady, with much severity, \"you have repaid\nthe devoted care of two unsuspecting females by a whole fortnight of\nwilful duplicity. For my aunt I cannot answer; for myself, I can only\nreply,--since to err is human; to forgive, womanlike,--dear Roger, on\nthe whole, I will.\"\n\nMiss Paulina, a moment later entering the parlor, surprised her invalid\nguest, standing crutchless on his firm feet, with his arm thrown about\nthe waist of her niece. \"Well, well!\" exclaimed the astonished lady,\n\"and without his crutches!\"\n\n\"Dear Miss Paulina,\" said Roger Smith with a happy laugh, \"my ankle is\nas well as ever; and your niece has promised to marry me. Say that you\nwill have me for your nephew.\"\n\n\"I seem already to have gotten you, my good sir, whether I will or no,\"\nlaughed Miss Hemmenshaw. \"But, my stars and garters\" (mentally added\nshe), \"what ever will my brother say? A tanner's grandson coming into\nthe family! and he a Hemmenshaw, and as proud as Lucifer!\" \"Never mind,\nAuntie dear,\" said the smiling fiancee, guessing her thoughts. It will\nbe all right with father when he comes to know Roger; and besides, let\nus remember that under the 'Star Spangled Banner' we have our\n'Vanderbilts,' our 'Goulds,' and our 'Rockefellers;' but _no_ Vere de\nVeres. And if we _had_, why, Love laughs at heraldry, and is\n\n \"'Its own great loveliness alway.'\"\n\n\"To-morrow,\" said Miss Paulina decisively, \"we will all dine at Alamo\nRanch.\"\n\n\n\n\nCHAPTER VIII\n\n\nThrough this month of wooing and betrothing at Hilton Ranch, the\nKoshare, at Alamo, never once remitted its endeavor to hearten the\ndespondent.\n\nThe weekly entertainments took their regular course, and were\nsuccessfully carried on, and, in due time, the fortnightly club convened\nto listen to the Antiquary's account of \"Montezuma and his Time.\"\n\nAnd here the Koshare chronicle returns on its track to record that able\npaper.\n\n\"As a consistent Koshare,\" said Mr. Morehouse, to his eager listeners,\n\"it behooves me to give--without that dry adherence to facts observed by\nthe 'Gradgrind' historian--the charming melodramatic details of that\nromantic monarch's life and times afforded by the popular\nMunchausen-like data of the Spanish chroniclers, albeit they have in\ntheir entirety, all the fascination, and, sometimes, all the\nunbelievableness of a fairy tale.\n\n\"The Aztec government,\" prefaced the Antiquary, \"was an elective\nmonarchy, the choice always restricted to the royal family.\n\n\"The candidate usually preferred must have distinguished himself in war;\nthough, if (as in the case of the last Montezuma) he was a member of the\npriesthood, the royal-born priest, no less than the warrior was, with\nthe Aztec, available as an emperor.\n\n\"When the nobles by whom Montezuma the Second was made monarch went to\ninform the candidate of the result of the election, they are said to\nhave found him sweeping the court of the temple to which he had\ndedicated himself. It is further asserted that when they led him to the\npalace to proclaim him king, he demurred, declaring himself unworthy the\nhonor conferred on him. It is a humiliating proof of the weakness of\nhuman nature in face of temptation, to find that, later, this pious king\nso far forswore his humility as to pose before his subjects as a god;\nthat five or six hundred nobles in waiting were ordered to attend daily\nat his morning toilet, only daring to appear before him with bared feet.\n\n\"It was not until, by a victorious campaign, he had obtained a\nsufficient number of captives to furnish victims for the bloody rites\nwhich Aztec superstition demanded to grace his inauguration,\nthat--amidst that horrible pomp of human sacrifice which stained the\ncivilization of his people--Montezuma was crowned.\n\n\"The Mexican crown of that day is described as resembling a mitre in\nform, and curiously ornamented with gold, gems, and feathers.\n\n\"The Aztec princes, especially towards the close of the dynasty, lived\nin a barbaric Oriental pomp, of which Montezuma was the most conspicuous\nexample in the history of the nation.\n\n\"Elevation, like wine, seems to have gone to the head of the second\nMontezuma.\n\n\"An account of his domestic establishment reads like the veriest record\nof midsummer madness. Four hundred young nobles, we are told, waited on\nthe royal table, setting the covers, in their turn, before the monarch,\nand immediately retiring, as even his courtiers might not see Montezuma\neat. Having drunk from cups of gold and pearl, these costly goblets,\ntogether with the table utensils of the king, were distributed among his\ncourtiers. Cortez tells us that so many dishes were prepared for each\nmeal of this lordly epicure, that they filled a large hall; and that he\nhad a harem of a thousand women. His clothes, which were changed four\ntimes a day (like his table service), were never used a second time, but\nwere given as rewards of merit to nobles and soldiers who had\ndistinguished themselves in war. If it happened that he had to walk, a\ncarpet was spread along his way, lest his sacred feet should touch the\nground. His subjects were required, on his approach, to stop and close\ntheir eyes, that they might not be dazzled by his effulgent majesty. His\nostentatious humility gave place to an intolerable arrogance. He\ndisgusted his subjects by his haughty deportment, exacting from them the\nmost slavish homage, and alienating their affection by the imposition of\nthe grievous taxes demanded by the lavish expenditure of his court.\n\n\"In his first years Montezuma's record was, in many respects,\npraiseworthy. He led his armies in person. The Aztec banners were\ncarried far and wide, in the furthest province on the Gulf of Mexico,\nand the distant region of Nicaragua and Honduras. His expeditions were\ngenerally successful, and during his reign the limits of the empire\nwere more widely extended than at any preceding period.\n\n\"To the interior concerns of his kingdom he gave much attention,\nreforming the courts of justice, and carefully watching over the\nexecution of the laws, which he enforced with stern severity.\n\n\"Like the Arabian ruler,--Haroun Alraschid, of benign memory,--he\npatrolled the streets of his capital in disguise, to make personal\nacquaintance with the abuses in it. He liberally compensated all who\nserved him. He displayed great munificence in public enterprise,\nconstructing and embellishing the temples, bringing water into the\ncapital by a new channel, and establishing a retreat for invalid\nsoldiers in the city of Colhuacan.\n\n\"According to some writers of authority there were, in Montezuma's day,\nthirty great caciques, or nobles, who had their residence, at least a\npart of the year, in the capital.\n\n\"Each of these, it is asserted, could muster a hundred thousand vassals\non his estate. It would seem that such wild statements should be 'taken\nwith a pinch of salt.' All the same, it is clear, from the testimony of\nthe conquerors, that the country was occupied by numerous powerful\nchieftains, who lived like independent princes on their domains. It is\ncertain that there was a distinct class of nobles who held the most\nimportant offices near the person of their emperor.\n\n\"In Montezuma's time the Aztec religion reached its zenith. It is said\nto have had as exact and burdensome a ceremonial as ever existed in any\nnation. 'One,' observes Prescott, 'is struck with its apparent\nincongruity, as if some portion had emanated from a comparatively\nrefined people, open to gentle influences, while the rest breathes a\nspirit of unmitigated ferocity; which naturally suggests the idea of two\ndistinct sources, and authorizes the belief that the Aztecs had\ninherited from their predecessors a milder faith, on which was\nafterwards engrafted their own mythology.' The Aztecs, like the\nidolaters to whom Paul preached, declaring the 'Unknown God' of their\n'ignorant worship,' recognized a Supreme Creator and Lord of the\nUniverse.\n\n\"In their prayers they thus addressed him: 'The God by whom we live,\nthat knoweth all thoughts, and giveth all gifts;' but, as has been\nobserved, 'from the vastness of this conception their untutored minds\nsought relief in a plurality of inferior deities,--ministers who\nexecuted the creator's purposes, each, in his turn, presiding over the\nelements, the changes of the seasons, and the various affairs of man.'\nOf these there were thirteen principal deities, and more than two\nhundred inferior; to each of whom some special day or appropriate\nfestival was consecrated.\n\n\"Huitzilopotchli, a terrible and sanguinary monster, was the primal of\nthese; the patron deity of the nation. The forms of the Mexican idols\nwere quaint and eccentric, and were in the highest degree symbolical.\n\n\"The fantastic image of this god of the unpronounceable name was loaded\nwith costly ornaments; his temples were the most stately and august of\ntheir public edifices, and in every city of the empire his altars reeked\nwith the blood of human hecatombs.\n\n\"His name is compounded of two words, signifying 'humming-bird' and\n'left;' from his image having the feathers of this bird on his left\nfoot.\n\n\"Thus runs the tradition respecting this god's first appearance on\nearth: 'His mother, a devout person, one day, in her attendance on the\ntemple, saw a ball of bright- feathers floating in the air. She\ntook it and deposited it in her bosom, and, consequently, from her, the\ndread deity was in due time born.' He is fabled to have come into the\nworld (like the Greek goddess, Minerva) armed _cap-a-pie_ with spear and\nshield, and his head surmounted by a crest of green plumes.\n\n\"A far more admirable personage in their mythology was Quetzalcoatl, god\nof the air; his name signifies 'feathered serpent' and 'twin.' During\nhis beneficent residence on earth he is said to have instructed the\npeople in civil government, in the arts, and in agriculture. Under him\nit was that the earth brought forth flower and fruit without the fatigue\nof cultivation.\n\n\"Then it was that an ear of corn in two days became as much as a man\ncould carry; and the cotton, as it grew beneath his fostering smile,\ntook, of its own accord, the rich dyes of human art.\n\n\"In those halcyon days of Quetzalcoatl all the air was sweet with\nperfumes and musical with the singing of birds.\n\n\"Pursued by the wrath of a brother-god, from some mysterious cause\nunexplained by the fabler, this gracious deity was finally obliged to\nflee the country. On his way he is said to have stopped at Cholula,\nwhere the remains of a temple dedicated to his worship are still shown.\n\n\"On the shores of the Mexican Gulf Quetzalcoatl took leave of his\nfollowers, and promising that he and his descendants would revisit them\nhereafter, entered his 'Wizard Skiff,' and embarked on the great ocean\nfor the fabled land of Tlapallan.\n\n\"The Mexicans looked confidently for the second coming of this\nbenevolent deity, who is said to have been tall in stature, with a white\nskin, long, dark hair, and a flowing beard. Undoubtedly, this cherished\ntradition, as the chroniclers affirm, prepared the way for the reception\nof the Spanish conquerors.\n\n\"Long before the landing of the Spaniards in Mexico, rumors of the\nappearance of these men with fair complexions and flowing beards--so\nunlike their own physiognomy--had startled the superstitious Aztecs. The\nperiod for the return of Quetzalcoatl was now near at hand. The priestly\noracles were consulted; they are said to have declared, after much\ndeliberation, that the Spaniards, though not gods, were children of the\nSun; that they derived their strength from that luminary, and were only\nvulnerable when his beams were withdrawn; and they recommended attacking\nthem while buried in slumber. This childish advice, so contrary to Aztec\nmilitary usage, was reluctantly followed by these credulous warriors,\nand resulted in the defeat and bloody slaughter of nearly the whole\ndetachment.\n\n\"The conviction of the supernaturalism of the Spaniard is said to have\ngained ground by some uncommon natural occurrences, such as the\naccidental swell and overflow of a lake, the appearance of a comet, and\nconflagration of the great temple.\n\n\"We are told that Montezuma read in these prodigies special\nannunciations of Heaven that argued the speedy downfall of his empire.\n\n\"From this somewhat digressive account of the Aztec superstition, in\nregard to the 'second coming' of their beneficent tutelar divinity,\nwhich, as may be seen, played into the hands of Cortez, and furthered\nhis hostile designs upon Mexico, let us return to the time in Aztec\nhistory when no usurping white man had set foot upon Montezuma's\nterritory.\n\n\"We are told that this people, in their comparative ignorance of the\nmaterial universe, sought relief from the oppressive idea of the endless\nduration of time by breaking it up into distinct cycles, each of several\nthousand years' duration. At the end of each of these periods, by the\nagency of one of the elements, the human family, as they held, was to be\nswept from the earth, and the sun blotted out from the heavens, to be\nagain freshly rekindled. With later theologians, who have less excuse\nfor the unlovely superstition, they held that the wicked were to expiate\ntheir sins everlastingly in a place of horrible darkness. It was the\nwork of a (so-called) Christianity to add to the Aztec place of torment\nthe torture of perpetual fire and brimstone. The Aztec heaven, like the\nScandinavian Valhalla, was especially reserved for their heroes who fell\nin battle. To these privileged souls were added those slain in\nsacrifice. These fortunate elect of the Aztecs seem to have been\ndestined for a time to a somewhat lively immortality, as they at once\npassed into the presence of the Sun, whom they accompanied with songs\nand choral dances in his bright progress through the heavens. After\nyears of this stirring existence, these long-revolving spirits were\nkindly permitted to take breath; and thereafter it was theirs to animate\nthe clouds, to reincarnate in singing birds of beautiful plumage, and to\nrevel amidst the bloom and odors of the gardens of Paradise.\n\n\"Apart from this refined Elysium and a moderately comfortable hell, void\nof appliances for the torture of burning, the Aztecs had a third place\nof abode for immortals. Thither passed those 'o'er bad for blessing and\no'er good for banning,' who had but the merit of dying of certain\n(capriciously selected) diseases. These commonplace spirits were fabled\nto enjoy a negative existence of indolent contentment. 'The Aztec\npriests,' says Prescott, 'in this imperfect stage of civilization,\nendeavored to dazzle the imagination of this ignorant people with\nsuperstitious awe, and thus obtained an influence over the popular mind\nbeyond that which has probably existed in any other country, even in\nancient Egypt.'\n\n\"Time will not permit here a detailed account of this insidious\npriesthood; its labored and pompous ceremonial; its midnight prayers;\nits cruel penance (as the drawing of blood from the body by\nflagellation, or piercing of the flesh with the thorns of the aloe),\nakin to the absurd austerities of Roman Catholic fanaticism. The Aztec\npriest, unlike the Roman, was allowed to marry, and have a family of his\nown; and not _all_ the religious ceremonies imposed by him were austere.\nMany of them were of a light and cheerful complexion, such as national\nsongs and dances, in which women were allowed to join. There were, too,\ninnocent processions of children crowned with garlands, bearing to the\naltars of their gods offerings of fruit, ripened maize, and odoriferous\ngums. It was on these peaceful rites, derived from his milder and more\nrefined Toltec predecessors, that the fierce Aztec grafted the loathsome\nrite of human sacrifice.\n\n\"To what extent this abomination was carried cannot now be accurately\ndetermined. The priestly chroniclers, as has been shown, were not above\nthe meanness of making capital for the church, by exaggerating the\nenormities of the pagan dispensation. Scarcely any of these reporters\npretend to estimate the yearly human sacrifice throughout the empire at\nless than twenty thousand; and some carry the number as high as fifty\nthousand. A good Catholic bishop, writing a few years after the\nconquest, states in his letter that twenty thousand victims were yearly\nslaughtered in the capital. A lie is brought to absolute perfection when\nits author is able to believe it himself.\n\n\"Torquemada, another chronicler, often quoted by Prescott, turns this\ninto twenty thousand _infants_!\n\n\"These innocent creatures, he tells us, were generally bought by the\npriests from parents poor enough and superstitious enough to stifle the\npromptings of nature, and were, at seasons of drought, at the festival\nof Haloc, the insatiable god of the rain, offered up, borne to their\ndoom in open litters, dressed in festal robes, and decked with freshly\nblown flowers, their pathetic cries drowned in the wild chant of the\npriests. It is needless to add that this assumption has but the\nslightest groundwork of likelihood.\n\n\"Las Casas, before referred to, thus boldly declares: 'This is the\nestimate of brigands who wish to find an apology for their own\natrocities;' and loosely puts the victims at so low a rate as to make it\nclear that any specific number is the merest conjecture.\n\n\"Prescott, commenting on these fabulous statements, instances the\ndedication of the great temple of the 'Mexican War God' in 1486, when\nthe prisoners, for years reserved for the purpose, were said to have\nbeen ranged in files forming a procession nearly two miles long; when\nthe ceremony consumed, as averred, several days, and seventy thousand\ncaptives are declared to have perished at the shrine of this terrible\ndeity. In view of this statement, Prescott logically observes: 'Who can\nbelieve that so numerous a body would have suffered themselves to be led\nunresistingly, like sheep, to the slaughter? Or how could their remains,\ntoo great for consumption in the ordinary way, be disposed of without\nbreeding a pestilence in the capital? One fact,' he adds, 'may be\nconsidered certain. It was customary to preserve the skulls of the\nsacrificed in buildings appropriate to the purpose; and the companions\nof Cortez say they counted one hundred and thirty-six thousand skulls in\none of the edifices.'\n\n\"Religious ceremonials were arranged for the Aztec people by their\ncrafty and well-informed priesthood, and were generally typical of some\ncircumstances in the character or history of the deity who was the\nobject of them. That in honor of the god called by the Aztecs 'the soul\nof the world,' and depicted as a handsome man endowed with perpetual\nyouth, was one of their most important sacrifices. An account of this\nsanguinary performance is gravely given by Prescott and other writers.\nThough highly sensational and melodramatic, since our betters have found\nit believable, we transcribe it for the New Koshare; thus runs the\ntale:--\n\n\"'A year before the intended sacrifice, a captive, distinguished for his\npersonal beauty, and without a single blemish on his body, was selected\nto represent this deity. Certain tutors took charge of him, and\ninstructed him how to perform his new part with becoming grace and\ndignity. He was arrayed in a splendid dress, regaled with incense and\nwith a profusion of sweet-scented flowers, of which the ancient Mexicans\nwere as fond as are their descendants at the present day. When he went\nabroad he was attended by a train of the royal pages; and as he halted\nin the streets to play some favorite melody the crowd prostrated\nthemselves before him, and did him homage as the representative of their\ngood deity. In this way he led an easy, luxurious life until within a\nmonth of his sacrifice. Four beautiful girls were then given him as\nconcubines; and with these he continued to live in idle dalliance,\nfeasted at the banquets of the principal nobles, who paid him all the\nhonors of a divinity. At length the fatal day of sacrifice arrived. The\nterm of his short-lived glories was at an end.\n\n\"'He was stripped of his gaudy apparel, and bade adieu to the fair\npartners of his revelry. One of the royal barges transported him across\nthe lake to a temple which rose on its margin, about a league from the\ncity. Hither the inhabitants flocked to witness the consummation of the\nceremony. As the sad procession wound up the sides of the pyramid, the\nunhappy victim threw away his gay chaplets of flowers, and broke in\npieces the musical instruments with which he had solaced the hours of\nhis captivity.\n\n\"'On the summit he was received by six priests, whose long and matted\nlocks flowed disorderedly over their sable robes, covered with\nhieroglyphic scrolls of mystic import. They led him to the sacrificial\nstone, a huge block of jasper with its upper surface somewhat convex. On\nthis the prisoner was stretched. Five priests secured his head and\nlimbs, while the sixth, clad in a scarlet mantle, emblematic of his\nbloody office, dexterously opened the breast of the wretched victim with\na sharp razor of _itzli_ (a volcanic substance hard as flint), and,\ninserting his hand in the wound, tore out the palpitating heart. The\nminister of death, first holding the heart up towards the sun (also an\nobject of their worship) cast it at the feet of the god, while the\nmultitudes below prostrated themselves in humble adoration.'\n\n\"The tragic circumstances depicted in this sanguinary tale were used by\nthe priests to 'point a moral.' The immolation of this unhappy youth was\nexpounded to the people as a type of human destiny, which, brilliant in\nits beginning, often closes in sorrow and disaster.\n\n\"In this loathsome manner, if we may believe the account given, was the\nmangled body disposed of. It was delivered by the priests to the warrior\nwho had taken the captive in battle, and served up by him at an\nentertainment given to his friends.\n\n\"This, we are told, was no rude cannibal orgy, but a refined banquet,\nteeming with delicious beverages, and delicate viands prepared with\ndainty art, and was attended by guests of both sexes, and conducted with\nall the decorum of civilized life. Thus, in the Aztec religious\nceremonial, refinement and the extreme of barbarism met together.\n\n\"The Aztec nation had, at the time of the Conquest, many claims to the\ncharacter of a civilized community. The debasing influence of their\nreligious rites it was, however, that furnished the fanatical conquerors\nwith their best apology for the subjugation of this people. One-half\ncondones the excuses of the invaders, who with the cross in one hand and\nthe bloody sword in the other, justified their questionable deeds by the\nabolishment of human sacrifice.\n\n\"The oppressions of Montezuma, with the frequent insurrections of his\npeople,\" concluded the Antiquary, \"when in the latter part of his reign\none-half the forces of his empire are said to have been employed in\nsuppressing the commotions of the other, disgust at his arrogance, and\nhis outrageous fiscal exactions, reduced his subjects to that condition\nwhich made them an easy prey to Cortez, whose army at last overpowered\nthe emperor and swept the Aztec civilization from the face of the\nearth.\"\n\n\"I find it strange,\" said the Journalist (in the little talk that\nfollowed Mr. Morehouse's able paper), \"that civilized nations have held\nan idea so monstrous as the necessity of vicarious physical suffering of\na victim to appease the wrath of a divine being with the erring\ncreatures who, such as they are, are the work of his hands.\n\n\"That unenlightened races, from time immemorial, should have supposed\nthat the shedding of blood propitiated their angry god, or gods, is but\nthe natural outcome of ignorance and superstition; but, that in this\ntwentieth century, civilized worshippers should sing--\n\n 'There is a fountain filled with blood\n Drawn from Immanuel's veins;\n And sinners plunged beneath that flood\n Lose all their guilty stains'--\n\npasses my understanding.\"\n\n\"In the ruins of Palenque there is,\" said the Antiquary, \"a scene\nportrayed on its crumbling walls, in which priests are immolating in a\nfurnace placed at the feet of an image of Saturn the choicest infants of\nthe nation, while a trumpeter enlivens the occasion with music, and in\nthe background a female spectator, supposed to be the mother of the\nvictim, looks on.\"\n\n\"The sacrifices to Moloch (or Saturn),\" interpolated the Minister, \"were\nmarked features of the Phoenician idolatry. In the Bible account we read\nthat even their kings 'made their children to pass through the fire to\nMoloch.'\"\n\n\"Well,\" commented the Grumbler, \"it may be said of a portion of this\nevening's entertainment that it is distinguished by the charm found by\n'Helen's' sanguinary-minded 'baby,' in the story of 'Goliath's\nhead,'--it is 'all bluggy.'\"\n\n\"Right you are,\" responded the star boarder with a shudder. \"Cold\nshivers have meandered along my poor back until it has become one\ndreadful block of ice; and, judging by the horror depicted on these\nladies' faces as they listened to the details of the Aztec sacrifice, I\nfancy that they too have supped o'er-full of horrors.\"\n\nThe Minister's eye rested for a moment affectionately on his stanch\nlittle wife. He sighed, and looked with mild rebuke on these godless\ntriflers.\n\nAnd now the Koshare (some of them stoutly orthodox) wisely put by the\nquestion of vicarious atonement, and summarily adjourned.\n\n\n\n\nCHAPTER IX\n\n\nIt was but the next week when, unexpectedly as thunderbolts now and then\nsurprise us on days of serene, unclouded sky, an unlooked-for domestic\ncalamity startled Alamo Ranch.\n\nDennis, the good-natured Irish waiter, and Fang Lee, the Chinese cook,\nhad come to blows. The battle had been (so to put it) a religious\ncontroversy, and such, as we know, have a bitterness all their own. It\nwas inaugurated by Dennis, who, as a good Catholic, had, on a Friday,\nrefused to sample one of Fang's _chef-d'oeuvres_,--a dish of veal\ncutlets with mushroom sauce. A mutual interchange of offensive words,\ntaunts highly derogatory to his holiness Pope Leo XIII. and equally\ninsulting to the memory of that ancient Chinese sage, Confucius, had\nfinally led to a bout of fisticuffs. In this encounter, Fang Lee, a\nslightly built, undersized celestial, had naturally been worsted at the\nhand of the robust Hibernian, a good six feet five in his stockings.\nDennis, the \"chip well off his shoulder,\" had peacefully returned to the\nduties of his vocation, nonchalantly carrying in the dinner, removing\nthe plates and dishes, and subsequently whistling \"St. Patrick's Day in\nthe Morning\" under the very nose of the Confucian, as he unconcernedly\nwashed his plates and glasses, and scoured his knives. Fang, having\nmeantime sent in his dinner, cleaned his pots and pans, brushed his\nbaggy trousers, adjusted his disordered pigtail, and straightway gave in\nhis notice; and with sullen dignity retired to the privacy of his\nbedroom, for the avowed purpose of packing his box. On the ensuing\nmorning he would shake from his feet the dust of Alamo Ranch.\n\nVain were the endeavors of his discomfited employers to gain the ear of\nthe implacable Fang Lee. He stood out resolutely for the privacy of his\nsmall sleeping apartment, obstinately refusing admission to outsiders.\n\nIn a house replete with boarders, and forty miles from available cooks,\nFang's pending loss was indeed a calamity.\n\nIn this dilemma, the disheartened landlord and his wife begged the\nintercession of the star boarder,--always in high favor with the\ndomestics, and known to be especially in the good graces of the\nChinaman. Long did this envoy of peace unsuccessfully besiege the\nbedroom door of the offended Fang Lee. In the end, however, he gained\nadmittance; and with adroit appeals to the better nature of the irate\ncook, and a tactful representation of the folly of giving up a good\nsituation for the sake of a paltry quarrel, he finally brought Fang Lee\ndown from his \"high horse,\" and persuading good-natured Dennis to make\nsuitable friendly advances, effectually healed the breach.\n\nEre nightfall amity reigned in the ranch kitchen, and the respective\npockets of the belligerents were the heavier for a silver dollar,--a\nprivate peace-offering contributed by the arbitrator. An Irishman is\nnothing if not magnanimous; Dennis readily \"buried the hatchet,\" handle\nand all.\n\nNot so Fang Lee, who, smugly pocketing his dollar, covertly observed to\nthe giver, by way of the last word, \"All samee, Pope bigee dam foolee.\"\n\nWith genial satisfaction the star boarder received the thanks of the\nBrowns for having saved to them their cook, and, with simple pleasure in\nthe result of his diplomacy, met the encomiums of his fellow-boarders.\n\nTo this gracious and beautiful nature, replete with \"peace and good-will\nto man,\" to help and serve was but \"the natural way of living.\"\n\n\n\n\nCHAPTER X\n\n\nAt mid-March, in this sun-loved land, the genial season far outdoes our\nown belated Northern May. Already, in Mesilla Valley, the peach, pear,\nand apricot buds of the orchard are showing white and pink. In the\ngarden, rose-bushes are leaving out, and mocking-birds make the air\nsweet with song.\n\n\"In the spring,\" said Leon Starr, parodying Tennyson one morning at the\nbreakfast-table, \"the Koshare fancy lightly turns to thoughts of Shalam.\nWhy not make to-day our long-planned excursion to that famous colony?\"\n\n\"All right,\" responded the entire Koshare; and that afternoon a party of\ntwelve set out from Alamo Ranch to explore that remarkable colony, some\nseven miles up the valley.\n\nA description of the place and an account of this excursion is copied\nverbatim by the present writer from the journal of one of the party.\n\n\"To begin at the beginning,\" says the narrator, \"the colony was started\nby one Dr. ----, a dentist from Philadelphia. He enlisted as a partner\nin his enterprise a man from that region of fads--Boston, Mass. To this\nchimera of the doctor's brain, the latter, a man of means, lent his\napproval, and, still more to the point, the money to carry out the\ndoctor's plans.\n\n\"Some few years ago the original founder of Shalam died, leaving to his\npartner the work of carrying out his half-tried experiment.\n\n\"Mr. ---- lived on in the place, assuming its entire charge, and finally\nmarrying the doctor's widow,--a lady of unusual culture and refinement,\nbut having a bent towards occult fads, as Spiritualism, Mental Science,\nand their like.\n\n\"Well, we arrived safely at Shalam, and were met by Mrs. ---- and a\ndozen or more tow-headed kids. It is noticeable that the whole\ntwenty-seven children selected for this experiment have light hair and\nblue eyes. Mrs. ---- kindly presented us to her husband,--apparently a\nman of refined natural tendencies and fair intellectual culture, but\nevidently, like 'Miss Flite,' 'a little _m-m_, you know.'\n\n\"Conventionally clothed, Mr. ---- would undoubtedly have been more than\npresentable; in his Shalam undress suit he was, to say the least,\nunique.\n\n\"His long, heavy beard was somewhat unkempt. His feet were in sandals,\nwithout stockings. His dress consisted of a pair of white cotton pants,\nand a blouse of the same material, frogged together with blue tape, the\nends hanging down over his left leg. Hitched somehow to his girdle was a\nplain watch-chain, which led to a pocket for his watch, on the front of\nhis left thigh, placed just above the knee. When he wants time he raises\nthe knee and takes out the watch, standing on one leg the while.\n\n\"The place is beautifully situated on the banks of the Rio Grande, with\na range of high mountains across the river.\n\n\"It consists of two parts: 'Leontica,' a village for the workers, where\nthey have many nice cottages, an artesian well for irrigation, and a big\nsteam pump to force the water through all the ditches; Shalam, the home\nof the children, has a big tank, with six windmills pumping water into\nit all the time. Near the tank is the dormitory,--a building about one\nhundred and fifty feet in dimension. Through its middle runs a large\nhall for the kids to gambol in. On each side are rooms for the\nattendants and the larger children.\n\n\"Chiefly noticeable was the cleanliness of the hall, and the signs over\nthe doors of the chambers, each with its motto, a text from\n'_Oahspe_,'--the Shalam bible.\n\n\"At each end of the hall was a big sign, reading thus: '_Do not kiss the\nchildren._' As none of them were especially attractive, this command\nseemed quite superfluous. After looking over the dormitory, we were led\nto the main building, projected by the late Dr. ----. This encloses a\ncourt about one hundred and fifty feet by sixty in size, and planted\nwith fig trees.\n\n\"The front of the building is taken up by the library of the doctor; on\nthe opposite side is his picture gallery.\n\n\"Rooms or cells for the accommodation of guests occupy the long sides of\nthis structure.\n\n\"I was cordially invited to occupy one of these; but the place is too\ncreepy for me! The pictures in the gallery were all done by the deceased\ndoctor, under the immediate direction of his 'spirit friends.' To look\nat them (believing this) is to be assured that artists do not go to\nheaven, since not even the poorest defunct painter would have\nperpetrated such monstrosities.\n\n\"They all represent characters and scenes from the doctor's\nbible,--known as Oahspe, and written by him at the dictation of spirits.\nThe drawing is horrible, the coloring worse; and no drunkard with\ndelirium tremens could have conceived more frightful subjects!\n\n\"Mr. ----, the doctor's successor, is a curious compound of crank and\ncommon-sense; the latter evinced by his corral and cattle, which we next\nvisited. I have never seen so fine a corral nor such handsome horses and\ncattle. They are all blooded stock; many of the cows and calves having\ncome from the farm of Governor Morton, in New York State. The cows were\nbeautiful, gentle creatures; one of them is the largest 'critter' I ever\nsaw, weighing no less than fifteen hundred pounds!\n\n\"The county authorities--scandalized by the meagreness of the Shalam\nbill of fare--compelled Mr. ---- to enrich the children's diet with\nmilk, and, thus officially prodded, he is trying to give them the best\nin the land.\n\n\"The stock department of Shalam seems to be his undivided charge; while\nMrs. ---- manages the garden. She kindly showed us all over it; and it\nis a beauty! With water flowing all through it, celery, salisfy, and\nlettuce all ready to eat, and other vegetables growing finely. She gave\nus a half bushel of excellent lettuce, which we all enjoyed.\n\n\"The Shalam idea is to take these children from all parts of the\ncountry, to bring them up in accordance with its own dietetic fad (which\nin many respects corresponds with that of our own dream-led Alcott),\nfeeding them exclusively on a vegetable diet so that they won't develop\ncarnal and combative tendencies, and thus start from them a new and\nimproved race. Will they succeed? God knows; but they seem to have\nstarted wrong; for the children are largely the offspring of outcasts,\nand you can't expect grapes from thistle seed. However, Mr. ---- and\nMrs. ---- are both sincere, kind-hearted reformers, trying to do what\nthey think right in their own peculiar way. They are doing no harm by\ntheir experiment--hurting no one; and if the children turn out badly, it\nis no worse than they would if left alone; and if well, it is a distinct\ntriumph of brain over beastliness. It may be well to state that no\n_materia medica_ is tolerated at Shalam. The health of the colony is\nentrusted absolutely to the 'tender mercies' of mental healing. Mr. ----\nis himself the picture of health, and says he does not know what it is\nto feel tired. ('They that be whole need no physician!') As for the Lady\nof Shalam, there is a look in her face that led me to think she was\ndeadly tired of the whole business, but was too loyal either to her dead\nor living husband to 'cry quits.'\n\n\"These children know not the taste of physic. All their ailments are\ntreated in strict accordance with Mental Science. They eat no eggs,\nfish, or other animal matter, save the county-prescribed milk, living\nsolely on grains, vegetables, and fruits; and it must be said that they\nall look extremely healthy. Mr. ---- informs us that he rises daily at\nthree A.M., goes directly to his corral and milks, comes in a little\nafter four and prepares the children's breakfast. They are called at\nfour forty-five, and breakfast at five. At five thirty devotional\nexercises begin, and last until six thirty, when the father of Shalam\ngoes out and starts the hands on the farm. At eight the children begin\nlessons or some kind of mental training, which lasts till dinner time.\n\n\"After dinner they run wild for the rest of the day.\n\n\"We left Shalam at about five P.M. On the homeward drive we discussed\nthis odd colony, and compared notes on what we had observed. An\nirreverent member of the party thus summed up the whole business in his\nown slangy fashion,--'a man who all winter long prances round in\npajamas, making folks shiver to look at him, ought to be put in an\ninsane asylum.' So there you have his side of the question.\n\n\"The original founder of Shalam, Dr. ----, not only aspired to be a\npainter, but, as an author, flew the highest kind of a kite, giving to\nthe world no less than a new bible.\n\n\"A glimpse at its high-sounding prospectus will scarce incite in the\nsane and sober mind a desire to peruse a revelation whose absurdity and\nfantastic assumption leaves the Mormon bible far behind, and before\nwhose 'hand and glove' acquaintance with the 'undiscovered country'\nSwedenborg himself must needs hide his diminished head.\n\n\"Thus it runs: '_Oahspe_; a new Bible in the words of Jehovih and his\nAngel Embassadors. A synopsis of the Cosmogony of the Universe; the\ncreation of planets; the creation of man; the unseen worlds; the labor\nand glory of gods and goddesses in the etherean heavens with the new\ncommandments of Jehovih to man of the present day. With revelations from\nthe second resurrection, found in words in the thirty-third year of the\nKosmon Era.'\n\n\"Oahspe's claims are thus _moderate_: 'As in all other bibles it is\nrevealed that this world was created, so in _this_ bible it is revealed\n_how_ the Creator _created_ it. As other bibles have proclaimed heavens\nfor the spirits of the dead, behold _this_ bible revealeth _where_ these\nheavens _are_.'\n\n\"Oahspe also kindly informs us 'how hells are made, and of what\nmaterial,' and how the sinner is in them mainly punished by the forced\ninhalement of 'foul smells,'--so diabolically foul are these that one is\nfain to hold the nose in the bare reading of them!\n\n\"'There is,' declares Oahspe, 'no such law as Evolution. There is no law\nof Selection.' A vegetarian diet is inculcated; and we are gravely\ninformed that 'the spirit man takes his place in the first heaven\naccording to his _diet_ while on earth!'\n\n\"A plan for the founding of 'Jehovih's Kingdom on earth through little\nchildren' is given. This 'sacred history' claims to cover in its\nentirety no less a period of time than eighty-one thousand years. At\nquarter-past six,\" concludes our informant, \"we arrived, tired and\nhungry, but glad to have gone, and glad to get back, leaving behind us\nShalam, with its spirit picture-gallery and its fantastic Oahspe, for\nthe more stable verities of commonplace existence.\"\n\n\n\n\nCHAPTER XI\n\n\nIt was on Friday that the Koshare made their little excursion to the\nShalam settlement, and the next evening they gathered in full\nforce,--with the exception of the Hemmenshaws and the Harvard man, who\nstill remained at Hilton Ranch, losing thereby two of the most\ninteresting of the Antiquary's papers; but \"time and tide\" and Saturday\nclubs \"stay for no man,\" and now came the second Aztec paper.\n\n\"The Aztec government,\" began Mr. Morehouse, \"in a few minor points is\nsaid to have borne some resemblance to the aristocratic system evolved\nby the higher civilization of the Middle Ages.\n\n\"Beyond a few accidental forms and ceremonies, the correspondence was,\nhowever, of the slightest. The legislative power both in Mexico and\nTezcuco had this feature of despotism; it rested wholly with the\nmonarch. The constitution of the judicial tribunals in some degree\ncounteracted the evil tendency of this despotism. Supreme judges\nappointed over each of the principal cities by the crown had original\nand final jurisdiction over both civil and criminal cases. From the\nsentence of such a judge there was no appeal to any other tribunal, not\neven to that of the King.\n\n\"It is worthy of notice as showing that some sense of justice is inborn;\nas even among this comparatively rude people we read that under a\nTezcucan prince a judge was put to death for taking a bribe, and another\nfor determining suits in his own house (a capital offence also, by law.)\nAccording to a national chronicler, the statement of the case, the\ntestimony, and proceedings of the trial were all set forth by a clerk,\nin hieroglyphical paintings, and handed to the court.\n\n\"In Montezuma's day the tardiness of legal processes must have gone\nmiles beyond the red tape of a nineteenth-century court of justice.\n\n\"This vivid picture of the pomp and circumstance attendant upon the\nconfirmation of a capital sentence by the king is presented by one of\nthe Mexican native chroniclers:\n\n\"'The King, attended by fourteen great lords of the realm, passed into\none of the halls of justice opening from the courtyard of the palace,\nwhich was called \"the tribunal of God,\" and was furnished with a throne\nof pure gold, inlaid with turquoises and other precious stones.\n\n\"'The walls were hung with tapestry, made of the hair of different wild\nanimals, of rich and various colors, festooned by gold rings, and\nembroidered with figures of birds and flowers. Putting on his mitred\ncrown, incrusted with precious stones, and holding, by way of sceptre, a\ngolden arrow in his left hand, the King laid his right upon a human\nskull, placed for the occasion on a stool before the throne, and\npronounced judgment. No counsel was employed and no jury. The case had\nbeen stated by plaintiff and defendant, and, as with us, supported on\neither side by witnesses. The oath of the accused was, with the Aztecs,\nalso admitted in evidence.\n\n\"'The great crimes against society were all made capital.\n\n\"'Among them murder (even of a slave) was punishable with death.\nAdulterers, as among the Jews, were stoned to death. Thieving, according\nto the degree of the offence, was punished with slavery or death. It was\na capital offence to remove the boundaries of an estate, and for a\nguardian not to be able to give a good account of his ward's property.\n\n\"'Prodigals, who squandered their patrimony, were punished. Intemperance\nin the young was punished with death; in older persons, with loss of\nrank, and confiscation of property.\n\n\"'The marriage institution was held in reverence among the Aztecs, and\nits rites celebrated with formality. Polygamy was permitted; but\ndivorces were not easily obtainable. Slavery was sanctioned among the\nancient Mexicans, but with this distinction unknown to any civilized\nslave-holding community: no one could be _born_ to slavery. The\n_children_ of the slave were _free_. Criminals, public debtors, persons\nwho from extreme poverty voluntarily resigned their freedom, and\nchildren who were sold by their parents through poverty, constituted one\nclass of slaves. These were allowed to have their own families, to hold\nproperty, and even other slaves. Prisoners taken in war were held as\nslaves, and were almost invariably devoted to the dreadful doom of\nsacrifice. A refractory or vicious slave might be led into the market\nwith a collar round his neck, as an indication of his badness, and\nthere publicly sold. If incorrigible, a second sale devoted him to\nsacrifice.\n\n\"'Thus severe, almost ferocious, was the Aztec code, framed by a\ncomparatively rude people, who relied rather on physical than moral\nmeans for the correction of evil. In its profound respect for the\ncardinal principles of morality, and a clear perception of human\njustice, it may favorably compare with that of most civilized nations.'\n\n\"'In Mexico,' says Prescott, 'as in Egypt, the soldier shared with the\npriest the highest consideration. The King must be an experienced\nwarrior. The tutelary deity of the Aztecs was the God of war. The great\nobject of their military expeditions was to gather hecatombs of captives\nfor his altars.' The Aztec, like the (so-called) _Christian crusader_,\ninvoked the holy name of religion as a motive for the perpetration of\nhuman butchery. He, too, after his own crude fashion, had his order of\nknighthood as the reward of military prowess. Whoever had not reached it\nwas debarred from using ornaments on his arms or on his person, and was\nobliged to wear a coarse white stuff, made from the threads of the aloe,\ncalled _nequen_. Even the members of the royal family were not excepted\nfrom this law. As in Christian knighthood, plain armor and a shield\nwithout device were worn till the soldier had achieved some doughty feat\nof chivalry. After twenty brilliant actions officers might shave their\nheads, and had, moreover, won the fantastic privilege of painting half\nof the face red and the other half yellow. The panoply of the higher\nwarriors is thus described. Their bodies were clothed with a close vest\nof quilted cotton, so thick as to be impenetrable to the light missiles\nof Indian warfare. This garment was found so light and serviceable that\nit was adopted by the Spaniards.\n\n\"The wealthier chiefs sometimes wore, instead of this cotton mail, a\ncuirass made of thin plates of gold or silver. Over it was thrown a\nsurcoat of the gorgeous feather work in which they excelled. Their\nhelmets were sometimes of wood, fashioned like the heads of wild\nanimals, and sometimes of silver, on the top of which waved a panache of\nvariegated plumes, sprinkled with precious stones. They also wore\ncollars, bracelets, and earrings of the same rich materials.\n\n\"'A beautiful sight it was,' says one of the Spanish conquerors, 'to see\nthem set out on their march, all moving forward so gayly, and in so\nadmirable order!'\n\n\"Their military code had the cruel sternness of their other laws.\nDisobedience of orders was punished with death.\n\n\"It was death to plunder another's booty or prisoners. It is related of\na Tezcucan prince that, in the spirit of ancient Roman, he put two of\nhis sons to death--after having cured their wounds--for violating this\nlast-mentioned law. A beneficent institution, which might seem to belong\nto a higher civilization, is said to have flourished in this semi-pagan\nland.\n\n\"Hospitals, we are told, were established in their principal cities for\nthe cure of the sick, and as permanent homes for the disabled soldier;\nand surgeons were placed over them who 'were,' says a shrewd old\nchronicler, 'so far better than those in Europe that they did not\n_protract the cure in order to increase the pay_.'\n\n\"The horse, mule, ox, ass, or any other beast of burden, was unknown to\nthe Aztecs. Communication with remotest parts of the country was\nmaintained by means of couriers, trained from childhood to travel with\nincredible swiftness.\n\n\"Post-houses were established on all the great roads, at about ten\nleagues distance apart. The courier, bearing his despatches in the form\nof hieroglyphical painting, ran with them to the first station, where\nthey were taken by another messenger, and so on, till they reached the\ncapital. Despatches were thus carried at the rate of from one to two\nhundred miles a day.\n\n\"A traveller tells us of an Indian who, singly, made a record of a\nhundred miles in twenty-four hours. A still greater feat in walking is\nrecorded by Plutarch. _His_ Greek runner brought the news of a victory\nof a hundred and twenty-five miles in a single day!\n\n\"In the funeral rites of this ruder people one traces a slight\nresemblance to those of the more cultivated Greek. They burned the body\nafter death, and the ashes of their dead, collected in vases, were\npreserved in one of the apartments of the home. After death they dressed\nthe person's body in the peculiar habiliments of his tutelar deity. It\nwas then strewed with pieces of paper, which operated as a charm against\nthe dangers of the dark road he was to travel. If a chief died he was\nstill spoken of as living. One of his slaves, dressed in his master's\nclothes, was placed before his corpse. The face of this ill-starred\nwretch was covered with a mask, and during a whole day such homage as\nhad been due to the chief was paid to him. At midnight the body of the\nmaster was burnt, or interred, and the slave who had personated him was\nsacrificed. Thereafter, every anniversary of the chief's birthday was\ncelebrated with a feast, but his death was never mentioned.\n\n\"The Spanish chroniclers have told us (and in reading these statements\ndue allowance must be made for their habit of 'stretching the truth')\nthat to the principal temple--or Teocallis--in the capital five thousand\npriests were in some way attached. These, in their several departments,\nnot only arranged the religious festivals in conformity to the Aztec\ncalendar, and had charge of the hieroglyphical paintings and oral\ntraditions of the nation, but undertook the responsibility of\ninstructing its youth. While the cruel and bloody rites of sacrifice\nwere reserved for the chief dignitaries of the order, each priest was\nallotted to the service of some particular diety, and had quarters\nprovided for him while in attendance upon the service of the temple.\n\n\"Though in many respects subject to strict sacerdotal discipline, Aztec\npriests were allowed to marry and have families of their own. Thrice\nduring the day, and once at night, they were called to prayers. They\nwere frequent in ablutions and vigils, and were required to mortify the\nflesh by fasting and penance, in good Roman Catholic fashion, drawing\ntheir own blood by flagellation, or by piercing with thorns of aloes.\nThey also, like Catholic priests, administered the rites of confession\nand absolution; but with this time-saving improvement: confession was\nmade but _once_ in a man's life,--the long arrears of iniquity, past and\npresent, thus settled, after offences were held inexpiable.\n\n\"Priestly absolution was received in place of legal punishment for\noffences. It is recorded that, long after the Conquest, the simple\nnatives, when under arrest, sought escape by producing the certificate\nof their confession.\n\n\"The address of the Aztec confessor to his penitent, with his prayer on\nthis occasion, has come down to us. As an evidence of the odd medley of\nChristianity and paganism that marked this queer civilization, it is\nquaintly interesting. 'O merciful Lord,' prayed he, 'thou who knowest\nthe secrets of all hearts, let thy forgiveness and favor descend, like\nthe pure waters of heaven, to wash away the stains from the soul. Thou\nknowest that this poor man has sinned, not from his own will, but from\nthe influences of the sign under which he was born.'\n\n\"In his address to the penitent he urges the necessity of instantly\nprocuring a slave for sacrifice to the Deity. After this sanguinary\nexhortation he enjoins upon his disciple this beautiful precept of\nChristian benevolence: 'Clothe the naked, feed the hungry, whatever\nprivations it may cost thee, for, remember, their flesh is like thine,\nand they are men like thee.'\n\n\"Sacerdotal functions (excepting those of sacrifice) were allowed to\nwomen.\n\n\"At a very tender age these priestess girls were committed for\ninstruction to seminaries of learning, in which, it is recorded, a\nstrict moral discipline for both sexes was maintained, and that, in some\ninstances, offences were punished by death itself.\n\n\"Thus were these crafty Mexican priests (the Jesuits of their age)\nenabled to mould young and plastic minds, and to gain a firm hold upon\nthe moral nature of their pupils. The priests had (as we are told) their\nown especial calendar, by which they kept their records, and regulated,\nto their liking, their religious festivals and seasons of sacrifice, and\nmade all their astrological calculations; for, like many imperfectly\ncivilized peoples, the Aztecs had their astrology. This priestly\ncalendar is said to have roused the holy indignation of the Spanish\nmissionaries.\n\n\"They condemned it as 'unhallowed, founded neither on natural reason,\nnor on the influence of the planets, nor on the course of the year; but\nplainly the work of necromancy, and the fruit of a contract with the\ndevil.'\n\n\"We are told that not even in ancient Egypt were the dreams of the\nastrologer more implicitly referred to than in Aztec Mexico.\n\n\"On the birth of a child he (the astrologer) was instantly summoned, and\nthe horoscope--supposed to unroll the occult volume of destiny--was hung\nupon by the parent in trembling suspense and implicit faith. No\nMillerite in his ascension robe, awaiting the general break-up of\nmundane affairs, ever looked forward with more confidence to the final\ncatastrophe than did the ancient Mexican to the predicted destruction of\nthe world at the termination of one of their four successive cycles of\nfifty-two years.\n\n\"Prescott gives us this romantic account of the festival marking that\ntraditional epoch:\n\n\"'The cycle would end in the latter part of December; as the diminished\nlight gave melancholy presage of that time when the sun was to be\neffaced from the heavens, and the darkness of chaos settle over the\nhabitable globe, these apprehensions increased, and on the arrival of\nthe five \"unlucky days\" that closed the year they abandoned themselves\nto despair. They broke in pieces the little images of their household\ngods, in whom they no longer trusted.\n\n\"'The holy fires were suffered to go out in the temples, and none were\nlighted in their own dwellings. Their furniture and domestic utensils\nwere destroyed, and their garments torn in pieces, and everything was\nthrown into disorder. On the evening of the last day, a procession of\npriests moved from the capital towards a lofty mountain, about two\nleagues distant. They carried with them as a victim for the sacrificial\naltar the flower of their captives, and an apparatus for kindling the\nnew fire, the success of which was an augury for the renewal of the\ncycle.\n\n\"'On the funeral pile of their slaughtered victim, the _new fire_ was\nstarted by means of sticks placed on the victim's wounded breast. As the\nlight soared towards heaven on the midnight sky, a shout of joy and\ntriumph burst forth from the multitudes, who covered the hills, the\nterraces of the temples, and the housetops with eyes anxiously bent upon\nthe mountain of sacrifice. Couriers with torches lighted at the blazing\nbeacon bore the cheering element far and near; and long before the sun\nrose to pursue his accustomed track, giving assurance that a new cycle\nhad commenced its march, altar and hearthstone again brightened with\nflame for leagues around.\n\n\"'All was now festivity. Joy had replaced despair. Houses were cleansed\nand refurnished. Dressed in their gayest apparel, and crowned with\nchaplets and garlands of flowers, the people thronged in gay procession\nto the temples to offer up their oblations and thanksgivings. It was the\ngreat secular national festival, which few alive had witnessed before,\nor could expect to see again.'\n\n\"Although we find in the counsels of an Aztec father to his son the\nfollowing assertion, 'For the multiplication of the species God ordained\n_one_ man _only_ for _one_ woman,' polygamy was nevertheless permitted\namong this people, chiefly among the wealthiest classes.\n\n\"Marriage was recognized as a religious ceremony, and its obligations\nstrictly enjoined. Their women, we are told, were treated with a\nconsideration uncommon among Indian tribes. It is recorded that their\ntranquil days were diversified by the feminine occupations of spinning,\nfeather-work, and embroidery, and that they also beguiled the hours by\nthe rehearsal of traditionary tales and ballads, and partook with their\nlords in social festivities.\n\n\"Their entertainments seem to have been grand and costly affairs.\nNumerous attendants, of both sexes, waited at the banquet; the halls\nwere scented with perfumes, flowers strewed the courts, and were\nprofusely distributed among the arriving guests.\n\n\"As they took their seats at the board, cotton napkins and ewers of\nwater were placed before them; for, as in the heroic days of Greece, the\nceremony of ablution before and after eating was punctiliously observed\nby the Aztecs. The table was well provided with meats, especially game,\namong which our own Thanksgiving bird, the turkey, was conspicuous.\nThese more solid dishes were flanked by others of vegetables, and with\nfruits of every variety found on the North American Continent.\n\n\"The different viands were skilfully prepared, with delicate sauces and\npungent seasoning, of which the Mexicans were especially fond. They were\nfurther regaled with confections and pastry; and the whole was crowned\nby an 'afterclap' of tobacco mixed with aromatic substances, to be\nenjoyed in pipes, or in the form of cigars, inserted in holders of\ntortoise shell or silver. The meats were kept warm by chafing-dishes.\nThe table was ornamented with vases of silver (and sometimes of gold) of\ndelicate workmanship.\n\n\"We are told by the chroniclers that agriculture was, before the\nConquest, in an advanced state. There were peculiar deities to preside\nover it, and the names of the months and of the religious festivals had\nmore or less reference to it. The public taxes were often paid in\nagricultural produce. As among the Pueblos, Aztec women took part in\nonly the lighter labors of the field,--as the scattering of the seed,\nthe husking of the ripened corn.\n\n\"Maize, or Indian corn, the great staple of the North American\ncontinent, grew freely along the valleys, and up the steep sides of the\nCordilleras, to the high table-land. Aztecs were, we are told, well\ninstructed in its uses, and their women as skilled in its preparation as\nthe most expert New England or Southern housewife.\n\n\"In these equinoctial regions, its gigantic stalk afforded a saccharine\nmatter which supplied them with a sugar but little inferior to that of\nthe cane itself (which, after the Conquest, was introduced among them).\nPassing by all their varieties of superbly gorgeous flowers, of\nluxuriously growing plants, many of them of medicinal value, and since\nintroduced from Mexico to Europe, we come to that 'miracle of nature,'\nthe great Mexican aloe, or _maguey_, which was, in short, meat, drink,\nclothing, and writing material for the Aztec, as from its leaves was\nmade their paper, somewhat resembling Egyptian _papyrus_, but more soft\nand beautiful.\n\n\"Specimens of this paper still exist, preserving their original\nfreshness, and holding yet unimpaired the brilliancy of color in\nhieroglyphical painting. It is averred that the Aztecs were as well\nacquainted with the uses of their mineral as of their vegetable kingdom,\ndeftly working their mines of silver, lead, and tin. It has, however,\nbeen contended by Wilson, in his 'New Conquest of Mexico,' that, in\nspite of Cortez's statement to the contrary, 'it is not to be supposed\nthat the Spaniards found the Aztecs in the possession of silver, since\nits mining requires a combination of science and mechanical power\nunknown and impossible to their crude civilization.' He considerately\nallows them the capability of gathering gold from their rich soil.\n\n\"Prescott, on the contrary, tells us that 'they opened veins for the\nprocurement of silver in the solid rock, and that the traces of their\nlabors in these galleries furnished the best indications for the early\nSpanish miners.'\n\n\"Who shall decide when doctors disagree? Not, indeed, a Koshare, whose\nlaudable purpose it is to eschew the wearisome 'gradgrinds' of history,\nand accept the infinitely more charming conclusions of the romancer.\n\n\"Gold, say the chroniclers, was easily gleaned from the beds of their\nrivers, and cast into bars, or in the form of dust, made part of the\nregular tribute of the southern provinces of Montezuma's empire. They\ncast, also, delicately and curiously wrought vessels of gold. Though\ntheir soil was impregnated with iron, its use was unknown to this\npeople. As a substitute for this metal, they used, for their tools, a\nbronze made from an alloy of tin and copper, or of itzli,--a dark\ntransparent metal, found in abundance in their hills. With the former\nthey could cut the hardest substances, such as emeralds and amethysts.\n\n\"It has been contended that an ignorance of the use of iron must\nnecessarily have kept the Mexican in a low state of civilization. On the\nother hand, it is urged that iron, if even known, was but little in use\namong the ancient Egyptians, whose mighty monuments were hewn with tools\nof bronze, while their weapons and domestic utensils were of the same\nmaterial. For the ordinary purposes of domestic life, the ancient\nMexicans made earthenware, and fashioned cups, bowls, and vases of\nlacquered wood, impervious to wet, and gorgeously .\n\n\"Among their dyes, obtained from both mineral and vegetable substances,\nwas the rich crimson of the cochineal, the modern rival of the far-famed\nTyrian purple. Later, this coloring material was introduced into Europe,\nfrom Mexico, where the curious cochineal insect was nourished with great\ncare on plantations of cactus.\n\n\"The Aztecs were thus enabled to give a brilliant coloring to their webs\nof cotton, which staple, in the warmer regions of their country, they\nraised in abundance. With their cotton fabrics, manufactured of every\ndegree of fineness, they had the original art of interweaving the\ndelicate hair of rabbits and other animals, which made a cloth of great\nwarmth as well as beauty.\n\n\"On this they often laid a rich embroidery of birds, flowers, or some\nother fanciful device. It is supposed that the Aztec 'silk,' mentioned\nby Cortez, was nothing more than this fine texture of cotton, hair, and\ndown.\n\n\"But the art in which they especially excelled was their plumage or\nfeather-work. Some few existing specimens of this ancient art (one of\nthem a vestment said to have been worn by Montezuma himself) have, we\nare told, 'all the charm of Florentine mosaic.'\n\n\"The gorgeous plumage of tropical birds, especially of the parrot-tribe,\nafforded every variety of color, and the fine and abundant down of the\nhumming-bird supplied them with a finish of soft aerial tints. The\nfeathers pasted on a fine cotton web were wrought into dresses for the\nwealthy. Hangings for apartments and ornaments for the temples were thus\nfashioned. Labor was held in honorable estimation among this people. An\naged Aztec chief thus addressed his son: 'Apply thyself to agriculture,\nor to feather-work, or some other honorable calling. Thus did your\nancestors before you. Else, how could they have provided for themselves\nand their families? Never was it heard that nobility alone was able to\nmaintain its possessor.'\n\n\"The occupation of the merchant was held by them in high respect. These\nwere of prime consideration in the body politic, and enjoyed many of the\nmost essential advantages of an hereditary aristocracy. Mexico, as their\nabundant use among the Aztecs testifies, is especially rich in precious\nstones. It is the land of the emerald, the amethyst, the turquoise, and\nthe topaz; and that superbest of gems, the fire opal, is native to its\ngenerous soil.\n\n\"One of Cortez's wedding gifts to his second bride is thus described:\n'This was five emeralds of wonderful size and brilliancy. These jewels\nhad been cut by the Aztecs into the shapes of flowers, and fishes, and\ninto other fanciful forms, with an exquisite style of workmanship which\nenhanced their original value.'\n\n\"It was gossiped at court that the Queen of Charles the Fifth had an eye\nto these magnificent gems, and that the preference given by Cortez to\nhis fair bride had an unfavorable influence on the Conqueror's future\nfortunes. Among the 'royal fifth' of the Mexican spoils sent by Cortez\nto the Spanish Emperor, we are told of a still more wonderful emerald.\nIt was cut in a pyramidal shape, and of so extraordinary a size that the\nbase of it was affirmed to have been as broad as the palm of the hand.\n\n\"This rich collection of gold and jewelry, wrought into many rare and\nfanciful forms, was captured on its road to Spain by a French privateer,\nand is said to have gone into the treasury of Francis the First.\nFrancis, we are told, looking enviously on the treasures drawn by his\nrival monarch from his colonial domains, expressed a desire to 'see the\nclause in Adam's testament, which entitled his brothers of Spain and\nPortugal to divide the New World between them.'\n\n\"The Aztec picture writing, rude though it was, seems to have served the\nnation in its early and imperfect state of civilization.\n\n\"By means of it, as an auxiliary to oral tradition, their mythology,\nlaws, calendars, and rituals were carried back to an early period of\ntheir civilization.\n\n\"Their manuscripts, the material for which has already been described,\nwere most frequently made into volumes, in which the paper was shut up\nlike a folding screen. With a tablet of wood at each extremity, they\nthus, when closed, had the appearance of books. A few of these Mexican\nmanuscripts have been saved, and are carefully preserved in the public\nlibraries of European capitals. The most important of these painted\nrecords, for the light it throws on the Aztec institutions, is preserved\nin the Bodleian Library at Oxford. The greater part of these writings,\nhaving no native interpretation annexed to them, cannot now be\nunriddled.\n\n\"A savant who, in the middle of the seventeenth century travelled\nextensively through their country, asserts that, 'so completely had\nevery vestige of their ancient language been swept away from the land,\nnot an individual could be found who could afford him the least clue to\nthe Aztec hieroglyphics.'\n\n\"Some few Aztec compositions, which may possibly owe their survival to\noral tradition, still survive. These are poetical remains, in the form\nof odes, or relics of their more elaborate prose, and consist largely of\nprayers and public discourses, that show that, in common with other\nnative orators, the Aztecs paid much attention to rhetorical effect. The\nAztec hieroglyphics included both the representative and symbolical\nforms of picture-writing.\n\n\"They had various emblems for expressing such things as, by their\nnature, could not be directly represented by the painter; as, for\nexample, the years, months, days, the seasons, the elements, the\nheavens, and so on.\n\n\"A serpent typified time, a tongue denoted speaking, a footprint\ntravelling, a man sitting on the ground an earthquake.\n\n\"The names of persons were often significant of their adventures and\nachievement.\n\n\"Summing up this account of Aztec civilization, we find that, although\nof the countries from which Toltec and Aztec in turn issued tradition\nhas lost the record, it is nevertheless affirmed, by so reliable an\nhistorian as Humboldt, that the former introduced into Mexico the\ncultivation of maize and cotton; that they built cities, made roads, and\nconstructed pyramids. 'They knew,' says this authoritative historian,\n'the uses of hieroglyphical paintings; they could work metals, and cut\nthe hardest stones; and they had a solar system more perfect than that\nof the Greeks and Romans.'\n\n\"After their mysterious disappearance from the table-lands of Mexico,\nthe Aztecs, who succeeded them, gradually amalgamated all that was best\nin their civilization, and, engrafting upon it their own, became as a\nnation what they were in the time of the second Montezuma, when Cortez\nand his conquering army treacherously swept their civilization from the\nface of the earth.\n\n\"A thoughtful traveller still finds in Mexico traces of this people, its\nearly possessors.\n\n\"The Mexicans, in their whole aspect,\" he observes, \"give a traveller\nthe idea of persons of decayed fortune, who have once been more\nprosperous and formidable than now, or who had been the offshoot of a\nmore refined and forcible people.\"\n\n\n\n\nCHAPTER XII\n\n\nIt was but the day after the delivery of this most interesting paper by\nMr. Morehouse, that the laggards from Hilton Ranch, who had missed it,\nand the preceding one, returned to their places at the dinner-table; and\non that very afternoon Miss Paulina, with all due formality, announced\nthe engagement of her niece to Mr. Roger Smith. Recovered from the first\nshock of surprise, the Koshare celebrated the betrothal by a pink\nafternoon tea, and made such slight engagement offerings as were found\navailable, remote from silversmith, florist, and bric-a-brac dealer.\n\nThe ladies gave bureau scarfs, table doilies, and centre-pieces _ad\ninfinitum_; the Antiquary bestowed a bit of Mexican pottery dating back\nto the \"cliff-dwellers.\" Leon framed the photographs of the handsome\npair in Mexican canes, as an engagement gift; and the most despondent\n\"lunger\" of them all had a kindly wish for their young and happy\nfellow-boarders, setting out on that beautiful life-journey to whose\nuntimely end he, himself, was sadly tending.\n\nAmong the more observing of the Koshare, much wonder was expressed at\nthe slow mending of Roger Smith's sprained ankle. It was at the\nengagement tea that Miss Paulina innocently said, in response to these\nstrictures, \"Yes, it _did_ take a long time to cure dear Roger's sprain.\nYears ago,\" continued the good lady, \"I had the same accident; and, if I\nremember rightly, in less than a fortnight after the sprain I was\nwalking without any crutches. One would think now,\" she went on, \"that\nin this lovely dry climate a sprain would mend rapidly; but, though I\ndid my very best, the result was far less prompt than I had hoped.\"\n\n\"Sprains differ,\" interposed the audacious subject of these remarks,\nunawed by the disapproving glances of his betrothed; \"the surgeons tell\nus that fractures are both simple and compound. Mine, dear Miss\nHemmenshaw, was undoubtedly compound.\"\n\nThis he said by way of accounting to his friends for his tardy\nconvalescence. To himself he thought, looking at this kind, unsuspicious\nnew auntie, \"Dear, delicious old goose!\"\n\nThis is what the niece said when, later, she got this incorrigible lover\nto herself: \"Roger, I am quite convinced that your conscience is seared\nwith a hot iron, whatever that process, supposed to indicate utter moral\ncallousness, may be.\"\n\n\"My dear girl,\" laughed the unabashed culprit, \"I am, as you know and\ndeplore, a good Catholic, and consequently hold with the astute Jesuit\nFathers that the end justifies the means.\"\n\n\n\n\nCHAPTER XIII\n\n\nIt was in the sunny, lengthened days of early March that the Antiquary,\nthe Journalist, the star boarder, and the Grumbler undertook their\nlong-projected trip to the Sacramento Mountains, there to visit the\nGovernment Reservation, nestled in the sheltered Mescalero Valley, which\ngives its name.\n\nWell equipped with camping conveniences, the four Koshares set forth on\ntheir journey of one hundred and twenty-five miles.\n\nIt was their intention to \"make haste slowly,\" and nothing could better\nhave suited the leisurely pair of Mexican horses, and the equally\neasy-going Mexican driver, who, with his team, had been hired for the\nexpedition. The first night of their journey was passed beneath the open\nsky, with the rounded moon riding clear and fair above them, and the\ndesert of sand and sage-brush all about them. On the second, they lodged\nat the solitary dwelling of a ranchman, whose nearest neighbor was\nthirty-five miles distant.\n\nAt the journey's end, they were cordially received by Lieutenant\nStottler, Government Agent at the Mescalero Reservation, and throughout\ntheir visit were treated by him with a kindly hospitality and a genial\ncourtesy beyond praise.\n\nOf the Apache, now transformed by the iron hand of civilization from a\nblood-thirsty savage to a passably decent and partially self-supporting\nmember of the republic, it has been aptly said that Nature has given him\n\"the ear of the cat, the cunning of the fox, and the ferocious courage\nand brutishness of the gray wolf.\"\n\nThe whole vast realm of his native ranges, desert though they seem, are\nknown to teem with ever-present supplies for his savage menu.\n\nThere are found fat prairie mice, plump angle-worms, gray meat of\nrattlesnake and lizard, and of leathery bronco,--all easy-coming \"grist\nfor that 'unpernickety' mill,\" his hungry stomach.\n\nIs he minded for a vegetable diet, for him the mescal lavishly grows;\nand the bean of mesquite, reduced to meal, makes him palatable cakes.\nFruit of Spanish bayonet dried in the sun, and said thus to resemble\ndates, is at hand for his dessert; and of mountain acorns alone he may\nmake an excellent and nutritious meal.\n\nFrom the primeval years this belligerent savage is said to have\nespecially harried that dismal waste in New Mexico known as _Jornado del\nMuerta_, \"Journey of Death.\"\n\nThis awful desert is declared to be literally \"the battle-ground of the\nelements.\" In the winter it is made fearful by raging storms of wind and\nsnow, in which frozen men and animals leave their bodies, as carrion\nprey, to the hungry mountain wolf. In later times it is \"the skulking\nplace of unscrupulous outlaws, and many a murdered traveller makes good\nthe name it bears.\"\n\nIt is thus finely depicted by a modern traveller: \"Near the southern\nboundary of New Mexico stretches a shadeless, waterless plateau, nearly\none hundred miles long, and from five to thirty miles wide, resembling\nthe steppes of northern Asia. Geologists tell us this is the oldest\ncountry on the earth, except, perhaps, the backbone of Central Africa;\nat least, the one which has longest been exposed to the influence of\nagents now in action. The grass is low and mossy, with a wasted look;\nthe shrubs are soap-weed and bony cactus; the very stones are like the\nscoria of a furnace. It is sought by no flight of bird; no bee or fly\nbuzzes on the empty air; and, save the lizard and horned frog, there is\nno breath of living thing. One might fancy that this dreary waste had\nserved its time, had been worn out, unpeopled, and forgotten.\"\n\nIn the (not long past) day of his power and might, to steal and murder,\nunder the show of friendship; to beat out the brains of unsuspecting\nmen; to carry off to captivity, worse than death, the women and larger\nchildren, was, with the Apache, merely a question of opportunity.\n\nIn the Apache war--ending in October, 1880, and lasting but a year and a\nhalf,--it is estimated that more than four hundred white persons were\nscalped and tortured to death with devilish ingenuity.\n\nThe details of Indian fighting are everywhere much the same; but in\nstrategy and cruelty that of the Apache surpasses all the sons of men.\nVictorio, the chief who led the war with his band, was surrounded at\nlast, and captured, and killed in the mountains of Mexico.\n\nWith the death of Victorio (whose only son, Washington, was shot in the\nfall of 1879, leaving no one to succeed him) the cause was lost.\n\nHis wife, we are told, after Victorio's death, cut off her hair, in the\nold Greek fashion, and buried it,--an offering to the spirit of this\nfallen chief, to whom (devil though he was) she was devoted.\n\nIt is told of Rafael, one of Victorio's band, that when maddened by\n_tiswin_ (an intoxicant made by the Indian from corn), he fatally\nstabbed his wife, and, after her death, overcome with penitence,\nsacrificed all his beads and most of his clothes to the \"dear departed,\"\ncut his and his children's hair short, and sheared the manes and tails\nof his horses. These manifestations of anguish over, he went up into a\nhigh hill, and howled with uplifted hands.\n\nWomen are regarded by the Apaches as an incumbrance. They are of so\nlittle account that they are not even given a name. Mothers _mourn_ at\ntheir birth.\n\nThe Indians occupying a reservation of seven hundred square miles in\nsouthern New Mexico, and numbering, at the present writing, about four\nhundred and fifty souls, are typical Apaches, and closely related by\nblood to the other Apaches of Arizona and New Mexico. They exhibit the\nusual race characteristics,--of ignorance, stubbornness, superstition,\ncruelty, laziness, and treachery.\n\nIn December, 1894, Lieutenant Stottler first assumed the charge of these\nIndians. In spite of the fact that for many years a generous government\nhad supplied them annually with rations, clothing, working implements,\netc., they were then living in _tepees_, or brush shelters, on the side\nhills; clad in breech-clout and blanket, wearing paint, and long hair,\nand thanklessly receiving their rations of beef, flour, coffee, sugar,\nsalt, soap, and baking-powder. A few of them condescended to raise corn\nand oats; but acres of tillable land on the reservation were still\nunused.\n\n\"They were,\" says Lieutenant Stottler, in an able and interesting\nreport, \"not only contented with this order of things, but desirous and\ndetermined to prolong it indefinitely.\"\n\nFifty per cent of their children were in school, but the parents were\nwholly opposed to their education. Among them were twenty strong,\nbroad-shouldered Indian adults, educated at the expense of thousands of\ndollars, yet still running about the reservation in breech-clout and\nblanket, wilder than any uneducated Indian on it.\n\nThe girls were held from school, and at ten and twelve years of age were\ntraded for ponies, into a bondage worse than any known slavery.\n\nFourteen Indian policemen are allowed the agent. Their especial duty is\nto see that the herd of beef cattle for their own eating is properly\ncared for. The police, each had a cabin to live in; but each, in scorn\nof this civilized innovation, had carefully planted alongside of his\ncabin a _tepee_ to sleep in. To get these policemen into civilized\nclothing, under threat of duress, and to order all _tepees_ away from\ntheir cabins, was the agent's first move. Next, it was decided that all\nchildren five years old and upwards _must_ be placed in school at the\nbeginning of the school year, whether the parents were willing or not.\nEvery Indian man was ordered to select a piece of land, and put in his\nposts. To break up the influence of chiefs or bands, who, claiming the\nwhole country, deterred the people from work, by threats, appears to\nhave been up-hill work; \"but now,\" says the agent (in 1897), \"there are\nno chiefs, and 'work or starve' is the policy.\" Formerly, government\nsupplies of clothing, wagons, harness, and utensils, as soon as issued,\nhad been packed on burros and sold for a mere song to settlers about the\nreservation. This abuse was promptly stopped, as also was the making of\n_tiswin_.\n\nThis native drink, made from Indian corn, is said to be more maddening\nin its effect than any other known intoxicant; Indians brutalized by\n_tiswin_ fought, as do our own drunkards, and often wounded or killed\neach other. For corn to make this detestable beverage, an Indian would\ntrade away the last article in his possession.\n\nIt was proclaimed by the agent that the maker of this poison would be\nimprisoned for six months, at hard labor, in the guard-house. This\nstopped its manufacture, and there are no longer drunken Indians at the\nreservation. Occasionally they still get liquor at Las Cruces, when sent\nthere for freight.\n\nAll supplies are hauled from the railroad over-land. The distance is one\nhundred and ten miles; about one hundred thousand pounds are annually\nbrought in this way to the reservation, and without harm or loss. Much\nof the Indian's savagery lies (like Samson's strength) in his hair; to\nhis long, matted tresses he clings tenaciously. As a beginning,\nLieutenant Stottler induced one old fellow--a policeman--with the\nreward of a five-dollar gold piece to cut his precious locks. Thus\nmetamorphosed, he became \"the cynosure of all eyes.\" His squaw made life\na burden to him; and thus badgered, he, in turn, pestered the agent to\nget the entire police force to cut theirs.\n\nIt was long before the general consent to part with these cherished\ntresses could be won; and it became necessary to put some of the Indians\nin the guard-house to accomplish this reform. Finally, orders were asked\nfrom Washington, and received, compelling submission to the shearing.\n\nWhen the Indians saw the Washington order, they all gave in, with the\nexception of a last man, who had to be \"thumped into it.\" Their hair\nwell cut, a raid was made on breech-clout and blanket. Now they all\nappear in civilized clothing. This seems to have been the turning-point\nin their wildness.\n\n\"Now,\" says the agent, \"they come and ask for scissors and comb to cut\ntheir hair, and volunteer the information that they were 'fools to\noppose it.'\"\n\nAbout half a dozen of these Indians were found by Lieutenant Stottler\nwith two wives; since none others were permitted, this matrimonial\nindulgence, polygamy, is, consequently, dying a natural death at\nMescalero. It is found hard to control the ancient practice of dropping\na wife and taking up another without the troublesome formality of a\ndivorce, which has practically the same result as polygamy. In spite of\nthe slip-shodness of the marriage-tie among the Indians, \"they are,\"\nsays the Lieutenant, \"about as badly henpecked as it is possible to\nimagine. Not by the wife, however; but by that ever dreaded being, her\nmother.\" He gives in his paper a most amusing account of the relation\nbetween the son-in-law and this much-maligned treasure of our higher\ncivilization. \"Just why it is,\" he says, \"no Indian has ever been able\nto explain to me, but an Indian cannot look at his mother-in-law.\n\n\"If she enters his _tepee_, he leaves; if he enters and she is within,\nhe flees at once. He cannot stay in her august presence. If his wife and\nhe quarrel, his mother-in-law puts in an appearance, and manages his\naffairs during his enforced absence so long as she pleases. Perhaps she\ntakes his wife to her own _tepee_, where he dare not follow. In this\ndilemma, he either comes to terms, or the situation constitutes a\ndivorce.\n\n\"Does the agent wish a child brought to school, or a head of a family to\ntake land, and try to farm it, the mother-in-law, if hostile (and she\nusually is), appears on the scene. Then the head of the family hunts the\nwoods for refuge.\n\n\"The sight of several stalwart bucks hiding behind doors, barrels, and\ntrees, because a dried-up, wizened squaw heaves in sight, is a spectacle\nthat would be ludicrous, were it not for its far-reaching results. As an\nIndian may take, in succession, many wives, who still stand to his\ncredit, the agent has, practically, many mothers-in-law to contend with.\nConsequently, these family magnets have been officially informed that\nthe guard-house awaits any of them who may be found maliciously\ninterfering with the families of their children.\n\n\"Hard labor added to this sentence, it is hoped, may at length have the\neffect of breaking up this absurd superstition.\"\n\nBy this account it may be seen that \"one of the most far-fetched notions\nthat ever entered into the minds of men\" is found domesticated among the\nMexican aborigines. It is asserted, as a chronological fact, that the\nMexican Pueblos \"invented the mother-in-law joke gray ages before it\ndawned upon our modern civilization.\"\n\nThe lamented Cushing, in his account of the \"restful, patriarchal,\nlong-lonely world\" of his research, tells us that he found the\nmother-in-law a too pronounced factor in the Zuni family circle; and, as\nwe know, in our own higher civilization the mother-in-law, held in\ngood-natured reprobation, serves to point many a harmless jest.\n\nWhite enthusiasts--with whom the \"wrongs of the Indian\" are a standing\ngrievance--but imperfectly realize the difficulty of taming these\nsavages, getting them well off the warpath, and making them cleanly and\nself-supporting. It may, therefore, be well to present the side shown us\nby the agent in his able paper of statistical facts.\n\n\"The Apache tribe,\" he tells us, \"has one hundred and sixteen children\nat school,--nineteen at Fort Lewis, Colorado, and ninety-seven at the\nreservation boarding-school. Each child has one-half day in class and\none-half day of industrial work. The girls take their turns in the\nlaundry, sewing-room, and kitchen, and at dormitory work. The boys do\nthe heavy work in the kitchen and laundry, chop the wood, and till the\nfarm under the charge of the industrial teacher. All the vegetables for\ntheir use are raised on the farm, and the surplus sold.\n\n\"The aim of the school is to teach the rising generation of Apaches how\nto make a living with the resources of the reservation, and, in time, to\nbecome self-supporting.\n\n\"To this end useful rather than fancy trades are taught. Boys are\ndetailed with the blacksmith and carpenter, to learn the use of common\ntools. To do away with the inborn contempt of the aboriginal male for\nthe women of his tribe, boys and girls at the reservation are not only\ntrained to study, recite, and sit at meals with girls, but a weekly\n'sociable' is held for the scholars.\n\n\"On such nights they have games and civilized dances. Every boy is\nrequired formally to approach and request, 'Will you dance this dance\nwith me?' and to offer his partner his arm when the reel, quadrille,\netc., is finished, and escorting her to her seat, leave her with a\npolite 'thank you.'\"\n\nIn the agent's report for the years 1896-97, \"this year,\" he says, \"the\nIndian boys raised twenty-five thousand pounds beets, twenty thousand\npounds cabbage, one thousand pounds cauliflower, five hundred pounds\nturnips, one thousand four hundred pounds celery, five hundred pounds\nradishes, one thousand four hundred pounds of onions, nineteen thousand\npounds of pumpkins and squash, four hundred pounds of peas, nine hundred\nand sixty pounds of corn, six thousand five hundred pounds of potatoes,\nbesides cucumbers, pie-plant, and asparagus.\n\n\"The school has a pen of swine, a flock of chickens, and a fine herd of\nmilch cows; and all the hay and fodder for them and the horses are\nraised on the farm. Oats and corn are purchased from the Indians, who,\nin 1895, raised one hundred and fifty thousand pounds.\n\n\"The adult Indians,\" he adds, \"cut this year one hundred and sixty cords\nof wood for the school, for which I paid them two dollars and fifty\ncents per cord. In the winter of 1896 the industry of blanket-making was\nintroduced into the reservation. Navajo blanket-makers were employed to\nteach to the Mescalero women their incomparable method of carding,\nspinning, and dyeing wool, and weaving blankets. Twenty of the\nMescaleros,\" boasts the agent, \"can to-day make as good blankets as the\nNavajos themselves.\n\n\"The reservation is mountainous, and one of the finest sheep ranges in\nthe country. Government has allowed five thousand sheep for general\ndistribution at the reservation, and in addition, five hundred head for\nthe school; where a room is now set aside for the looms of the older\ngirls, who will, in their turn, become instructors in this useful art.\nThis puts into their hands another opportunity to become\nself-supporting.\"\n\nThe visitors from Mesilla Valley were kindly admitted behind the scenes\nat the reservation, to make acquaintance with its people, both old and\nyoung; and were highly interested and entertained by the picturesqueness\nof the Indian character.\n\nThe Grumbler had brought his camera along. He was a skilled amateur\nphotographer, and had offered his services in that capacity to the\nlittle party.\n\nTo bring his household under the focus of that apparatus was no easy\ntask for the courteous agent. An Indian is nothing if not a believer in\nwitches. In his aboriginal mode of life witch-hunting and\nwitch-punishing are among his gravest occupations. He pursues them with\na vigorous hand, and with a superstitious zeal equal to that of the most\npersistent white man in the palmiest days of Salem witch-hunting and\nwitch-burning. The Mescaleros, to a soul, are believers in witchcraft.\nThe camera, as might be seen from its effect, was plainly bewitched.\nThey would have none of it.\n\nThe school children, having no choice, must needs range themselves in\nscared, sullen rows, and be \"took\" under compulsion.\n\nSuspiciously eying the operator, they sullenly took their prescribed\npose, and heedless of the immemorial request, \"Now look pleasant,\" went\nsourly through the terrible ordeal.\n\nSome of the older girls, pleased with the novelty, submitted more\ncheerfully; but the younger pupils, looking askance at the white men,\ncovered their faces, so far as was possible, with hair, or hands, and\nwere thus providentially carried safely through this process of\nbewitchment.\n\nSome of the schoolboys had fine, intelligent faces; of others, the\nGrumbler subsequently observed that \"they were the kind that grow up and\nscalp white settlers.\"\n\nA curious young squaw, from the opened slit of her _tepee_, watched the\napproach of the party with their bedevilled machine. Her position was\nexcellent; but no sooner had the operator arranged his camera for a snap\nshot at this picturesque subject, than, with a scared yell, the woman\nbounded out of range, closing behind her the aperture--her front door.\n\nThe result was merely an uninteresting view of an Indian _tepee_, which\nis like nothing more than a mammoth ant-hill, minus the symmetry and\nnice perpendicular of that more intelligently fashioned structure.\n\nTwo incorrigible squaws in \"durance vile\" for making _tiswin_, as they\nsullenly served their sentence of hard labor at the reservation\nwoodpile, looked defiantly up from their task of chopping fuel, and\nscowled viciously at the witch machine and its abettors.\n\nThey, however, succeeded in getting a fairly good picture of these\nhideous-faced beings, as \"withered and wild\" as the uncanny sisters who\nbrewed \"hell broth\" before the appalled Macbeth, beneath the midnight\nmoon, on Hampton Heath.\n\nA mild-eyed Indian woman, whose peaceful occupation was to scrub the\nreservation floors, kindly submitted to the bother of being put into a\npicture, along with the insignia of her office,--a scrubbing-pail.\n\nNot so \"Hot Stuff,\" a highly picturesque squaw, claiming the proud\ndistinction due to the \"oldest inhabitant.\" This \"contrairy\" female,\nimpervious to moral suasion, was finally induced to pose before the\nterrible \"witch-thing\" by the threat of having her rations withheld\nuntil her consent to be \"taken\" was obtained. Scared and reluctant, she\nwas at last photographed; but required Lieutenant Stottler to protect\nher with his arm through the perils of this unfamiliar ordeal. This he\ngood-naturedly did, and is immortalized along with this aged squaw.\n\nAfter an interesting visit of two nights and a day at the reservation,\nthe Koshare turned their faces towards Mesilla Valley, where, after two\nuneventful days, they arrived in safety, full of the novelties\nencountered, charmed with the courteous and gentlemanly agent, but\nwearied with the long ride, and heartily glad to return to white\ncivilization.\n\n\n\n\nCHAPTER XIV\n\n\nIt was at the close of the week succeeding that of the little journey\nacross the mountains that the Koshare held their last Saturday evening\nsession. To punctuate the finality of this gathering, a variation from\nthe usual programme was proposed by the Antiquary. Members of the Club\nwere requested to supplement his brief paper by giving such written or\nverbal statements, along the same line as their own research might\nenable them to make. To this proposal many of the Koshare had agreed,\nand had come well primed for lively discussion.\n\nThe attendance was unusually full, nearly all the boarders, in addition\nto the regular Club members, being in attendance.\n\nThe Antiquary led with the following interesting paper, which, as he\nexplained, was, in a way, supplementary to those on the Aztecs.\n\n\"As the Tezcucans were of the family of the Aztecs,\" began Mr.\nMorehouse, \"and are said far to have surpassed them in intellectual\nculture and the arts of social refinement, some slight notice of their\ncivilization may not prove irrelevant.\n\n\"Ixtilxochitl is the uneuphonious name of the native chronicler,\npurporting to be a lineal descendant of the royal line of Tezcuco, who\nhas given us his highly narrative of the Tezcucan civilization.\nIt may be prefaced with the information that Ixtilxochitl (who\nflourished so late as the century of the Conquest) has had his\nreputation so torn to tatters by the critics of later years that he has,\nfiguratively, 'not a leg to stand on.'\n\n\"But as Prescott commends his 'fairness and integrity,' and says 'he has\nbeen followed, without misgiving, by such Spanish chroniclers as could\nhave access to his manuscripts,' without attempting to settle the vexed\nquestion of the probability of its details (which are a combination of\n'Munchausen' and 'Arabian Nights'), we also will follow his marvellous\nstory of the Tezcucan Prince Nezahualcoyotl. Passing lightly over the\nfascinating chapter of that prince's romantic adventures,--his\nmarvellous daring, his perilous escapes from the fierce pursuit of the\nusurper Maxtla, and the dethronement and violent end of that\nbloody-minded monarch,--we come to the time when Nezahualcoyotl,\nrestored to the throne of his fathers, is firmly established in the love\nand fealty of his people, and may turn his attention to the production\nof the odes and addresses handed down in Castilian by his admiring\ndescendant Ixtilxochitl. This admirable monarch was, we are informed,\n'the Solon of Anahauc.' His literary productions turn, for the most\npart, on the vanity and mutability of human life, and strikingly embody\nthat Epicurean poetic sentiment, expressed, at a later time, by our own\nEnglish poet, Herrick, in such verses as 'Gather ye rose-buds while ye\nmay.'\n\n\"'Banish care,' sings the royal Tezcucan bard; 'if there be bounds to\npleasure, the saddest life must also have an end. Then wear the chaplet\nof flowers, and sing thy songs in praise of the all-powerful God; for\nthe glory of the world soon fadeth away.\n\n\"'Rejoice in the green freshness of thy spring; for the day will come\nwhen thou wilt sigh for these joys in vain. Yet the remembrance of the\njust' (piously adds the poet) 'shall not pass away from the nations; and\nthe good thou hast done shall ever be held in honor.' And\nanon,--returning to his _Epicurean_ 'muttons,'--he sings: 'Then gather\nthe fairest flowers in the gardens to bind round thy brow, and seize the\njoys of the present ere they perish.'\n\n\"An English translation of one of Nezahualcoyotl's odes has been made\nfrom the Castilian. It harps upon the same old string, as also do his\nprose essays, which have less literary merit than his verse. We are told\nby his panegyrist that not all the time of this incomparable monarch was\npassed in dalliance with the muse, but that he won renown as a warrior,\nand in the interests of peace also fostered the productive arts that\nmade his realm prosperous, as agriculture, and the like practical\npursuits. Between times he appears to have looked well after the\nwell-being of his children, who, in numbers, rivalled the progeny of our\nmodern patriarch, Brigham Young. It is recorded that by his various\nwives this monarch had no less than sixty sons and fifty daughters. (One\ncondones his disgust with life!) The Tezcucan crown, however, descended\nto the children of his one legal wife, whom he married late in life. The\nstory of his wooing and winning this fair lady is almost an exact\ncounterpart of the Bible account of King David's treacherous winning of\nUriah's beautiful consort.\n\n\"It is related of Nezahualcoyotl, that having been married for some\nyears to this unrighteously obtained wife, and not having been blest\nwith issue by his beautiful queen, the priests persuaded him to\npropitiate the gods of his country--whom he had pointedly neglected--by\nhuman sacrifice. He reluctantly consented; but all in vain was this\nmistaken concession. Then it was that he indignantly repudiated these\ninefficient Pagan deities.\n\n\"'These idols of wood and stone,' said he, 'can neither hear nor feel;\nmuch less could they make the heavens, and the earth, and man, the lord\nof it. These must be the work of the all-powerful unknown God, creator\nof the universe, on whom alone I must rely for consolation and support.'\nHe thereupon withdrew to his rural palace, where he remained forty days,\nfasting and praying at stated hours, and offering up no other sacrifice\nthan the sweet incense of copal, and aromatic herbs and gums.\n\n\"In answer to his prayer, a son was given him,--the only one ever borne\nby his queen. After this, he made earnest effort to wean his subjects\nfrom their degrading religious superstition, building a temple, which he\nthus dedicated: 'To the Unknown God, the _Cause_ of _Causes_.' No image\nwas allowed in this edifice (as unsuited to the 'invisible God'), and\nthe people were expressly prohibited from profaning its altars with\nblood, or any other sacrifice than that of flowers and sweet-scented\ngums. In his old age the king voiced his religious speculations in hymns\nof pensive tenderness.\n\n\"In one of these, he thus piously philosophizes: 'Rivers, torrents, and\nstreams move onward to their destination. Not one flows back to its\npleasant source. They must onward, hastening to bury themselves in the\nbosom of the ocean. The things of yesterday are no more to-day, and the\nthings of to-day shall cease to-morrow. The great, the wise, the\nvaliant, the beautiful,--alas, where are they?'\"\n\n\"The compositions of Nezahualcoyotl,\" observed the Grumbler, as the\nAntiquary folded away his finished paper, \"though strictly founded on\nfact, are not exhilarating. His family was too large; and the wonder is,\nnot that his odes and hymns are depressing, but that he should have the\nheart to 'drop into poetry' at all!\"\n\n\"We are told,\" rejoined the Journalist, \"by his descendant with the\nunpronounceable name, that once in every four months his entire family,\nnot even excepting the youngest child, was called together, and orated\nby the priesthood on the obligations of morality, of which, by their\nexalted rank, they were expected to be shining examples. To these\nadmonitions was added the compulsory chanting of their father's hymns.\"\n\n\"Poor beggars!\" pitied the Grumbler; \"how they must have squirmed under\nthis ever-recurring royal 'wet blanket!'\"\n\n\"You forget,\" said Leon Starr, coming to the rescue of the poet-father,\n\"that in view of their inevitable mortality the bard had already advised\nthem to 'banish care, to rejoice in the green freshness of their spring;\nto bind their brows with the fairest flowers of the garden, seize the\njoys of the present, and'--in short, had given them leave to have no end\nof larks, which, of course, they naturally and obediently did.\"\n\n\"It is a noteworthy fact,\" observed Mr. Morehouse, \"that many\naborigines--though but scantily supplied with clothing, as the natives\nof Samoa and the Sandwich Islanders--take great delight in adorning the\nbody with flowers. To this liking the Tezcucan king especially appeals\nin his odes and hymns. The Mexicans have from time immemorial doted on\nflowers. This taste three hundred years or more of oppression has not\nextinguished.\"\n\n\"Do you remember, dear,\" asked Mr. Bixbee, turning to his wife, \"the\nflower market in the Plaza at Mexico?\" (The pair had, a year or two\nearlier, explored that city)--\"that iron pavilion partly covered in with\nglass, and tended by nut-brown women and smiling Indian girls?\"\n\n\"Shall I ever forget it?\" was her enthusiastic response. \"The whole\nneighborhood was fragrant with perfume of vases of heliotrope, pinks,\nand mignonette; and such poppies, and s, and forget-me-nots I\nnever elsewhere beheld!\"\n\n\"One can believe in absolute floral perfection,\" said the Journalist,\n\"in a country which embraces all climates. 'So accurately,' observes\nWilson, 'has nature adjusted in Mexico the stratas of vegetation to the\nstate of the atmosphere, that the skilful hand of a gardener might have\nlaid out the different fields, which, with their charming vegetation,\nrise, one above another, upon the fertile mountain sides of the\ntable-land.'\n\n\"Along with many other important vegetable growths, the cotton-plant is\nsupposed to be indigenous to Mexico, as Cortez, on his first landing,\nfound the natives clothed in cotton fabrics of their own manufacture.\nIts culture continues to the present day, but with very little\nimprovement in method since the earlier time of the Spanish Conquest.\"\n\n\"And now,\" asked the Harvard man, \"since we are on the subject of\nMexican natural floral products, may I speak my little piece, which I\nmay call, 'What I have learned about the Cactus'?\"\n\nThe Koshare graciously assenting, Roger Smith thus began:\n\n\"In Mexico the cactus is an aboriginal and indigenous production.\nSeveral hundred varieties are identified by botanists. A beautiful sort\nis Cereus grandiflora. As with us, this variety blooms only at night;\nits frail, sweet flower dying at the coming of day. The cactus seems to\ngrow best in the poorest soil. No matter how dry the season, it is\nalways juicy. Protected by its thick epidermis, it retains within its\ncirculation that store of moisture absorbed during the wet season, and\nwhen neighboring vegetation dies of drought is still unharmed. Several\nvarieties of cactus have within their flowers an edible substance, which\nis, in Monterey, brought daily to market by the natives. That species\nof cactus which combines within itself more numerous uses than any known\nvegetable product is known as the maguey, or century plant.\n\n\"Upon the Mexican mountains it grows wild as a weed; but as a domestic\nplant it is cultivated in little patches, or planted in fields of\nleagues in extent. Its huge leaf pounded into a pulp makes a substitute\nboth for cloth and paper. The fibre of the leaf, when beaten and spun,\nforms a silk-like thread, which, woven into a fabric, resembles linen\nrather than silk. This thread is now, and ever has been, the sewing\nthread of the country. From the leaf of the maguey is crudely\nmanufactured sailcloth and sacking; and from it is made the bagging now\nin common use.\n\n\"The ropes made from it are of that kind called manila. It is the best\nmaterial in use for wrapping-paper. When cut into coarse straws, it\nforms the brooms and whitewash brushes of the country, and as a\nsubstitute for bristles it is made into scrub-brushes, and, finally, it\nsupplies the place of hair-combs among the common people. So much for\nthe cactus leaf; but from its sap arises the prime value of the plant.\n\n\"From this is made the favorite intoxicating drink of the common people\nof Mexico. This juice in its unfermented state is called honey water.\nWhen fermented it is known as pulque. The flowering maguey, the 'Agava\nAmerican,' is the century plant of the United States.\n\n\"In its native habitat the plant flowers in its fifteenth year, or\nthereabout; and we are assured that nowhere, as is fabled, does its\nbloom require a long century for its production. The juice of the maguey\nis gathered by cutting out the heart of the flower of the central stem,\nfor whose sustenance this juice is destined. A single plant, thus\ngingerly treated, yields daily, for a period of two or three months,\naccording to the thriftiness of the plant, from four to seven quarts of\nthe honey water, which, before fermentation, is said to resemble in\ntaste new sweet cider.\n\n\"Large private profit accrues to the owner of maguey estates, and the\ngovernment excise derived from the sale of the liquor is large. Pulque\nis the lager of the peon. It was the product of the country long before\nthe time of the Montezumas; and Ballou tells us that 'so late as 1890\nover eighty thousand gallons of pulque were daily consumed in the city\nof Mexico.'\n\n\"It is said to be the peculiar effect of pulque to create, in its\nimmoderate drinkers, an aversion to other stimulants; the person thus\nusing it preferring it to any and all other drinks, irrespective of\ncost.\"\n\nThe Minister followed Roger Smith with an account of a famous tree of\nMexico.\n\n\"It was at Papotla,\" said this much-travelled invalid, \"a village some\nthree miles from that capital, that we saw this remarkable tree, which\nis called 'The Tree of the Noche Triste' (the Dismal Night), because\nCortez in his disastrous midnight retreat from the Aztec capital is said\nto have sat down and wept under it. Be that as it may, the Noche Triste\nis undoubtedly a tree of great age. It is of the cedar family, broken\nand decayed in many parts, but still enough alive to bear foliage.\n\n\"In its dilapidated condition it measures ten feet in diameter, and\nexceeds forty feet in height. Long gray moss droops mournfully from its\ndecaying branches, and, taken altogether, it is indeed a dismal tree.\n\n\"It is much visited, and held sacred and historic by the people, who\nguard and cherish it with great care.\"\n\n\"It calls up singular reflections,\" commented the Journalist, \"to look\nupon a living thing that has existed a thousand years, though it be but\na tree. Though so many centuries have rolled over the cypresses of\nChapultepec, they are yet sound and vigorous.\n\n\"These trees are the only links that unite modern and ancient American\ncivilization; for they were in being when that mysterious race, the\nToltecs, rested under their shade; and they are said to have long been\nstanding, when a body of Aztecs, wandering away from their tribe in\nsearch of game, fixed themselves upon the marsh at Chapultepec, and,\nspreading their mats under these cypresses, enjoyed in their shadow\ntheir noontide slumber. Then came the Spaniards to people the valley\nwith the mixed races, who respected their great antiquity, so that\nduring all the battles that have been fought around them they have\npassed unharmed, and amid the strife and contentions of men have gone\nquietly on, adding many rings to their already enlarged circumference.\n'Heedless,' says Wilson, 'of the gunpowder burned over their heads and\nthe discharge of cannon that has shaken their roots, as one ephemeral\nMexican government succeeded another, these cypresses still remain\nunharmed, and may outlive many other dynasties.'\"\n\n\"Apropos of the subject,\" said the Antiquary, \"Nezahualcoyotl, according\nto his descendant, the native historian, embellished his numerous villas\nwith hanging gardens replete with gorgeous flowers and odoriferous\nshrubs. The steps to these charming terraces--many of them hewn in the\nnatural porphyry, and which a writer who lived in the sixteenth century\navers that he himself counted--were even then crumbling into ruins.\nLater travellers have reported the almost literal decay of this\nwonderful establishment. Latrobe describes this monarch's baths (fabled\nto have been twelve feet long by eight wide) as 'singular basins,\nperhaps two feet in diameter, and not capacious enough for any monarch\nlarger than Oberon to take a ducking in.'\n\n\"The observations of other travellers confirm this account. Bullock\ntells us that some of the terraces of this apparently mythical palace\nare still entire; and that the solid remains of stone and stucco\nfurnished an inexhaustible quarry for the churches and other buildings\nsince erected on the site of that ancient Aztec city.\n\n\"Latrobe, on the contrary, attributes these ruins to the Toltecs, and\nhints at the probability of their belonging to an age and a people still\nmore remote. Wilson, on the other hand, positively accords them to the\nPhoenicians.\"\n\n\"In reading up on this famous empire, Tezcuco,\" said Leon Starr, \"one is\ninclined to believe that every vestige of this proud magnificence could\nnot possibly have been obliterated in the short period of three\ncenturies, leaving on the spot only an indifferently built village,\nwhose population of three hundred Indians, and about one hundred whites,\nmaintain themselves in summer by gardening, and sending in their canoes\ndaily supplies of 'herbs and _sullers_' (whatever this last may be) to\nMexico, and, in winter, by raking the mud for the 'tegnesquita,' from\nwhich they manufacture salt.\"\n\n\"Wilson,\" said the Grumbler, \"tells us that 'the Tezcucan descendant of\nan emperor \"lied like a priest.\"' However that may be, one cannot quite\nswallow his own relation 'in its entirety.'\"\n\n\"Right you are,\" responded the Harvard man; \"and now here is Miss\nNorcross, waiting, I am sure, to cram us still further with Mexican\ninformation.\"\n\n\"It is only,\" said this modest little lady, \"some bits that I have\njotted down about Mexican gems;\" and shyly producing her paper, she thus\nread:\n\n\"In enumerating the precious stones of Mexico,--the ruby, amethyst,\ntopaz, and garnet, the pearl, agate, turquoise, and chalcedony,--one\nmust put before them all that wonder of Nature,--the Mexican fire opal,\nwhich, though not quite so hard as the Hungarian or the Australian opal,\nexcels either of them in brilliance and variety of color. Of this\nbeautiful stone Ballou has aptly said, 'It seems as if Nature by some\nsubtle alchemy of her own had condensed, to form this fiery gem, the\nhoarded sunshine of a thousand years.' He tells us that, in his Mexican\ntravels he saw an opal, weighing fourteen carats, for which five\nthousand dollars was refused. 'Really choice specimens,' he goes on to\nsay, 'are rare. The natives, notwithstanding the abundance of opals\nfound in Mexico, hold tenaciously to the price first set upon them.\nTheir value ranges from ten dollars to ten hundred.'\n\n\"In modern times, as we all know, a superstition of the unluckiness of\nthe stone long prevailed. Now, the opal has come to be considered as\ndesirable as it is beautiful, and, endorsed by fashion, takes its\nrightful place among precious gems. A London newspaper states that a\ngiant Australian opal, oval in shape, measuring two inches in length, an\ninch and a half deep, and weighing two hundred and fifty carats, is\ndestined to be given to King Edward the Seventh; and that Mr. Lyons, the\ngiver, a lawyer of Queensland, desires that it should be set in the\nKing's regalia of the Australian federation. The London lapidaries\nbelieve it to be the finest and largest opal in the world.\n\n\"Its only rival in size and beauty is the Hungarian opal, possessed by\nEmperor Francis Joseph of Austria. This gem is known as the 'Imperial\nopal,' and is said, in its rainbow beauty, to display the blended colors\nof the ruby, the emerald, and the amethyst.\n\n\"What is termed the 'fire' of the gem appears to burn in its remotest\ndepths, with a glow and fervor which at times seem to convert the stone\nfrom the opaque to the semi-transparent.\"\n\n\"We have in our own family,\" said Miss Paulina Hemmenshaw,\nsupplementing this account, \"a rare Mexican opal. Long, long ago, it was\ngiven as an engagement ring to my mother's youngest sister, by her\nlover, who, while travelling in Mexico, had secured this exquisite stone\nfor a betrothal pledge. On the very eve of her wedding-day my beautiful\nAunt Margaret died of an unsuspected heart-disease. The old superstition\nof the unluckiness of the opal being then dominant, my aunt's superb\nring was laid by as a thing malignant as beautiful.\n\n\"As a child I was sometimes allowed to take this sad memento of my dead\naunt from its nest of cotton wool and admire its harmful splendor. At my\nmother's death it descended, along with all her own jewels, to me, her\nonly daughter. Now that we have outlived the foolish superstition in\nrespect to this precious stone, I have made up my mind,\" said the good\naunt, beaming kindly on her niece, \"to take this ring from the Safety\nVault, on our return to Boston, and make it one of my wedding gifts to\nthis dear child.\"\n\n\"Many thanks, dear ladies,\" said Mrs. Bixbee, as Miss Paulina ended,\n\"for your talks about the opal. It is my favorite among precious stones.\nI even prefer it to the diamond, as something warmer and more alive. I\nam glad that its character is looking up in these days.\"\n\n\"All the same,\" said Mrs. Fairlee, complacently turning on her slim\nwhite finger a superb Hungarian sapphire, \"nothing would tempt me to\nwear a stone even suspected of uncanniness. Trials and crosses, of\ncourse, will befall one, but it seems to me foolhardy to wear jewels\nsupposed to attract misfortune, and, for my part, I am still suspicious\nof opals; and were I King Edward, I shouldn't thank my loyal Australians\nfor the gift of an ill-omened jewel, however costly and beautiful.\"\n\n\"Well,\" commented the Journalist, \"every one for his fancy; mine, I\nconfess, is to 'mouse round' among musty book-shelves. Looking over my\nportable store of odds and ends for something relevant to this evening's\ndiscussion, I came upon this extract from the 'Voyages of one \"Thomas\nPage,\"'--a black letter copy of whose long-forgotten book, printed in\nLondon, in 1677, is still extant. As a curious picture of the times, it\nis not without an especial value; and, with your approval, I will now\nread it:\n\n\"This account must be prefaced with the explanation that Thomas Page was\nan English Dominican, who, as a missionary-monk, with his brother\nDominicans travelled to his destination in Manila, by the road across\nMexico, landing, by the way, at Vera Cruz, and there depositing some\nillustrious fellow-voyagers.\n\n\"'When we came to land,' says this quaintly circumstantial writer, 'all\nthe inhabitants of the city had congregated in the Plaza to receive us.\nThe communities of monks were also there, each one preceded by a large\ncrucifix,--the Dominicans, the San Franciscans, the Mercedarios,--in\norder to conduct the Virey (the Viceroy) of Mexico as far as the\nCathedral.\n\n\"'The Jesuits and friars from the ships leaped upon the shore from the\nships. Many of them (the monks) on stepping on shore, kissed it,\nconsidering that it was a holy cause that brought them there,--the\nconversion of the Indians, who had before adored and sacrificed to\ndemons; others kneeled down and gave thanks to the Virgin Mary and other\nsaints of their devotion, and then all the monks hastened to incorporate\nthemselves with their respective orders in the place in which they\nseverally stood. The procession, as soon as formed, directed itself to\nthe Cathedral, where the consecrated wafer (called in the English\noriginal the bread God) was exposed upon the high altar, and to which\nall kneeled as they entered.... The services ended, the Virey was\nconducted to his lodgings by the first Alcalde, the magistrate of the\ntown, and judges, who had descended from the capitol to meet him,\nbesides the soldiers of the garrison and the ships. Those of the\nreligious orders that had just arrived were conducted to their\nrespective convents, crosses, as before, being carried at the head of\neach community.\n\n\"'Friar John presented us [his missionaries] to the Prior of the Convent\nof San Domingo, who received us kindly, and directed sweetmeats to be\ngiven us; and also there was given to each of us a cup of that Indian\nbeverage which the Indians call chocolate. \"This,\" the good friar tells\nus, \"was but a prelude to a sumptuous dinner, composed of flesh and fish\nof every description, in which there was no lack of turkeys and capons.\nThis feast,\" he naively apologizes, \"was not set out for the purpose of\nworldly ostentation, but to manifest to us the abundance of the\ncountry.\"\n\n\"'The Prior of Vera Cruz,' he informs us, 'was neither old nor severe,\nas the men selected to govern communities of youthful religious orders\nare accustomed to be. On the contrary, he was in the flower of his age,\nand had all the manner of a joyful and diverting youth. His fathership,\nas they told us, had acquired the Priory by means of a gift of a\nthousand ducats, which he had sent to the Father Provincial. After\ndinner he invited some of us to visit his cell, and then it was we came\nto know the levity of his life....\n\n\"'The cell of the Prior was richly tapestried, and adorned with feathers\nof birds of Michoacan; the walls were hung with various pictures of\nmerit; rich rugs of silk covered the tables; porcelain of China filled\nthe cupboards and sideboards; and there were vases and bowls containing\npreserved fruits and most delicate sweetmeats.\n\n\"'Our enthusiastic companions did not fail to be scandalized at such an\nexhibition, which they looked upon as a manifestation of worldly vanity,\nso foreign to the poverty of a begging friar....\n\n\"'The holy Prior talked to us only of his ancestry, of his good parts,\nof the influence with the Father Provincial; of the love which the\nprincipal ladies and the wives of the richest merchants manifested to\nhim, of his beautiful voice, of his consummate skill in music. In fact,\nthat we might not doubt him in this particular, he took the guitar and\nsung a sonnet which he had composed to a certain _Amaryllis_. This was a\nnew scandal to our newly arrived _religious_, which afflicted some of\nthem to see such libertinage in a prelate, who ought, on the contrary,\nto have set an example of penance and self-mortification, and should\nshine like a mirror in his conduct and words.... In the Prior's cell of\nthe Convent of Vera Cruz' (concluded this character sketch) 'we listened\nto a melodious voice, accompanied with a harmonious instrument, we saw\ntreasures and riches, we ate exquisite confectioneries, we breathed\namber and musk, with which he had perfumed his syrups and conserves. O,\nthat delicious Prior!' exclaims our English monk, the humor of the\nsituation overcoming his horror of the scandalous behavior of the\necclesiastic.\"\n\n\"And now,\" said the Minister, producing some leaves of sermon-like\nscript, \"may I call your attention, my friends, to the striking\nanalogies found in the religious usages and belief of the\nAztec,--correspondent with those of the Christian,--some of which I have\nconsidered in this little paper?\n\n\"One of the most extraordinary coincidences with Christian rites may, I\nthink, be traced in their ceremony of naming their children,--the Aztec\nbaptism. An account of this rite, preserved by Sahagan, is thus put into\nEnglish:\n\n\"'When everything,' says the chronicler, 'necessary for the baptism had\nbeen made ready, all the relations of the child were assembled, and the\nmidwife, who was the person that performed the rite of baptism. After a\nsolemn invocation, the head and lips of the infant were touched with\nwater, and a name was given it; while the goddess Cioacoatl, who\npresided over childbirth, was implored that \"the sin which was given to\nthis child before the beginning of the world might not visit the child,\nbut that, cleansed by these waters, it might live and be born anew.\"\nThis,' continues the narrator, 'is the exact formula used: \"O my child!\ntake and receive the water of the Lord of the world, which is our life,\nand is given for the increasing and renewing of our body. It is to wash\nand purify. I pray that these heavenly drops may enter into your body\nand dwell there, that they may destroy and remove from you all the sin\nwhich was given to you at the beginning of the world.\n\n\"'She then washed the body of the child with water. This done, \"He now\nliveth,\" said she, \"and is born anew; now is he purified and cleansed\nafresh, and our Mother Chalchioitlyene (the goddess of water) again\nbringeth him into the world.\" Then taking the child in both hands, she\nlifted him towards heaven, and said, \"O Lord, thou seest here thy\ncreature, whom thou hast sent into the world, this place of sorrow, and\nsuffering, and penitence. Grant him, O Lord, thy gifts and inspiration;\nfor thou art the Great God, and with thee is the great goddess.\" Torches\nof pine illuminated this performance, and the name was given by the same\nmidwife, or priestess, who baptized him.'\n\n\"The difficulty of obtaining anything like a faithful report of these\nrites from the natives,\" said the Minister, \"was complained of by the\nSpanish chroniclers, and no doubt led them to color the narrative of\nthese (to them) heathen rites and observances with interpolations from\ntheir own religious belief. 'The Devil,' said one of these bewildered\nmissionary monks, 'chose to imitate the rites of Christianity, and the\ntraditions of the chosen people, that he might allure his wretched\nvictims to their own destruction.' Leaving these monkish annalists to\ntheir own childish conclusions, and absurd interpretations of the Aztec\nreligious analogies, we pass on to the tradition of the Deluge, so\nwidely spread among the nations of the Old World, the Hebrew account of\nwhich was thus travestied by these semi-barbarians. Two persons, they\nheld, survived this historical flood,--a man named Coxcox, and his wife.\nTheir heads are represented in ancient paintings, together with a boat\nfloating on the waters.\n\n\"Another tradition (which is credited by Humboldt) affirms that the boat\nin which Typi (their Noah) weathered the flood was filled with various\nkinds of animals and birds, and that, after some time, a vulture was\nsent out by Typi, to reconnoitre,--as was done in the Hebrew flood,--but\nremained feeding on the dead bodies of the giants which had been left on\nthe earth as the waters subsided. The little humming-bird,\nHuitozitsilin, was then sent forth, and returned with a twig in his\nmouth. The coincidence of this account with the Bible narrative is\nworthy of remark.\n\n\"On the way between Vera Cruz and the capital stands the tall and\nvenerable pyramidal mound called the temple of Chulola. It rises to the\nheight of nearly one hundred and eighty feet, and is cased with unburnt\nbrick. The native tradition is that it was erected by a family of giants\nwho had escaped the great inundation, and designed to raise the building\nto the clouds; but the gods, offended by their presumption, sent on the\npyramid fires from heaven, and compelled the giants to abandon their\nattempt.\n\n\"This story was still lingering among the natives of the place at the\ntime of Humboldt's visit to it. The partial coincidence of this legend\nwith the Hebrew account of the tower of Babel cannot be denied. This\ntradition has also its partial counterpart in the Hebrew Bible.\nCioacoatl, 'our lady and mother, the first goddess who bringeth forth,'\nwho is by the Aztecs believed to have bequeathed the sufferings of\nchildbirth to women as the tribute of death, by whom sin came into the\nworld, was usually represented with a serpent near her, and her name\nsignified the 'Serpent-woman.'\n\n\"This fable, as will be seen, reminds us of the 'Eve' in the Hebrew\naccount of the Fall of Man. The later priestly narrators, minded to\nimprove upon this honest Aztec tradition, gave the Mexican Eve two sons,\nand named them Cain and Abel.\n\n\"In this Aztec rite, coming down to us through tradition, the Roman\nCatholics recognized a resemblance to their especial ceremony of\nChristian Communion. An image of the tutelary deity of the Aztecs was\nmade of the flour of maize, mixed with blood; and after consecrating by\nthe priests, was distributed among the people, who, as they ate it,\nshowed signs of humiliation and sorrow, declaring it was the flesh of\nthe deity.\n\n\"We are told by a Mexican traveller, Torquemeda, a Spanish monk, that,\nlater on, when the Church had waxed mighty in the land, the simple\nIndian converts, with unconscious irony, called the Catholic wafer 'the\nbread-God.'\"\n\nHere the discussion was, for a moment, interrupted by the withdrawal of\nMiss Mattie Norcross and her invalid sister, who, wearied with long\nsitting, had dropped her tired head upon her sister's shoulder and gone\nquietly to sleep.\n\nAs the Grumbler rose to open the door for the two, all present might see\nthe courteous air of protection and kindly sympathy which accompanied\nthis simple bit of courtesy. Evidently, the Grumbler had met his fate at\nAlamo Ranch.\n\n\"And now,\" said the star boarder, coming finally into the talk, \"since\nMr. Morehouse has kindly condensed for us the history of the aboriginal\nMexican from the far-off day of the nomadic Toltec to the splendid reign\nof the last Montezuma,--treacherously driven to the wall by the crafty\nCortez, when the Spaniard nominally converted the heathen, overthrew his\ntime-honored temples, rearing above their ruins Christian churches, and,\nintent to 'kill two birds with the same stone' filled his own pockets,\nand swelled the coffers of far-off Spain with Aztec riches,--I have\nthought it not irrelevant to take a look at the humble native Mexican as\nhe is found by the traveller of to-day.\n\n\"First, let me say that it has been asserted of Mexico that 'though\ngeographically near, and having had commercial relations with the world\nfor over three hundred years, there is probably less known of this\ncountry to-day than of almost any other claiming to be civilized.' 'To\nthe Mexicans themselves,' declares an observing traveller, 'Mexico is\nnot fully known; and there are hundreds of square miles in South Mexico\nthat have never been explored; and whole tribes of Indians that have\nnever been brought in contact with the white man.'\n\n\"Mexico may well be called the country of revolutions, having passed\nthrough thirty-six within the limit of forty years. In that\ncomparatively short period of time no less than seventy-three rulers,\n'drest in a little brief authority,' have played their parts upon the\nMexican stage until the curtain dropped (too often in blood) upon their\nacts, and they were seen no more.\n\n\"Humboldt, in the seventeenth century, pronounced the fairy-like\nenvirons of the city of Mexico 'the most beautiful panorama the eye ever\nrested upon.' On the table-land of this country the traveller is, at\nsome points, eight thousand feet above the level of the sea. At such\nheights the air is so rarefied that the least physical effort well-nigh\ndeprives the traveller of breath. 'Through this rarefied atmosphere all\nthe climates and productions of the world,' it has been affirmed, 'are\nembraced within the scope of a single bird's-eye view.' In portions of\nthe country the _vomito_ renders the climate especially unkindly to the\nalien.\n\n\"We are told that three quarters of the present Mexican population can\nneither read nor write, possess little or no property, and can form no\nintelligent ideas of political liberty, or of constitutional government.\n\n\"The degraded condition of the laboring classes is imputed in a measure\nto the constitutional inertia of a race who have no climatic conditions\nto contend with in their life-struggle; whose simple wants are easily\nsatisfied, and who (it may be inferred) never know that 'divine\ndiscontent' which is the fulcrum on which the higher civilization turns.\nThe manner of living, among this class, is thus described by Wells:\n\n\"'Their dwellings in the cities are generally wanting in all the\nrequirements of health and comfort, and consist mostly of rooms on the\nground-floor, without proper light or ventilation, often with but the\nsingle opening for entrance. In such houses there is rarely anything\nanswering to the civilized idea of a bed, the occupants sleeping on a\nmat, skin, or blanket, on the dirt floor. There are no chairs or tables.\nThere is no fireplace or chimney, and few or no changes of raiment; no\nwashing apparatus or soap, and in fact no furniture whatever, except a\nflat stone with a stone roller to grind their corn, and a variety of\nearthen vessels to hold their food and drink, and for cooking, which is\ngenerally done over a small fire within a circle of stones outside, and\nin front of the main entrance to the dwelling.\n\n\"'Their principal food is _tortillas_,--a sort of mush made of soaked\nand hand-ground Indian corn, rolled thin, and then slightly baked over a\nslow fire. Another staple of diet is boiled beans (_frijoles_). Meat is\nseldom used by laborers; but when it is attainable, every part of the\nanimal is eaten. Should one be so fortunate as to have anything else to\neat, the _tortilla_ serves as plates, after which service the plates are\neaten. When their simple needs are thus satisfied,' says this observing\ntraveller, 'the surplus earnings find their way into the pockets of the\npulque or lottery-ticket sellers, or into the greedy hands of the\nalmost omnipresent priest.'\n\n\"These lotteries are, we are told, operated by the Church, and form one\nof its never-failing sources of income, proving even more profitable\nthan the sale of indulgences.\n\n\"The idolatrous instinct, inherited from far-off Aztec ancestors,\ndecidedly inclines the native Mexican to a worship that has its pictures\nand images, and its bowings before the Virgin and countless hosts of\nsaints, and the priest finds him an easy prey.\n\n\"'While we were in the country,' says Ballou, 'a bull-fight was given in\none of the large cities on a Sunday, as a benefit towards paying for a\nnew altar-rail to be placed in one of the Romish churches.'\n\n\"Religious fanaticism takes root in all classes in Mexico, even among\nthe very highest in the land. It is recorded of the Emperor\nMaximilian--a man of elegant manners, and of much culture and\nrefinement--that he walked barefoot on a day of pilgrimage to the shrine\nof the Virgin of Guadaloupe,--distant some two or three miles from the\ncity of Mexico, over a dusty, disagreeable road.\n\n\"It is but fair to add, in conclusion,\" said Leon Starr, \"that it is\nasserted of the cultivated classes of Mexico that they are not at all in\nsympathy with the extortions and other irregularities of their\npriesthood.\"\n\nWith these interesting statistics ended the last effort of the New\nKoshare to combine improvement and entertainment.\n\nHard upon this more solid delight-making followed the last afternoon\ntea, the lighter Thursday evening entertainment, and the final\nshooting-match. All these gatherings took on a tinge of sadness from the\ncertainty that the little winter family, brought together by Fate at\nAlamo Ranch, were so soon to separate.\n\n\n\n\nCHAPTER XV\n\n\nSpring had now well come. In the shade it was already more than summer\nheat. Fortunately there is, in New Mexico, no such thing as sun-stroke;\nand one moves about with impunity, though the mercury stands at fervid\nheights.\n\nIt was on All Fools' day that the star boarder, accompanied by a little\nparty of the Koshare,--made up to escort him as far on his homeward way\nas El Paso,--turned his back upon the loveliness of Mesilla Valley.\n\nThrough all this \"winter of their discontent\" Leon had lent himself\nheartily to the work of delight-making; and the saddest of them all had\nbeen cheered by his genial atmosphere. What wonder if to these it was\nbut a dolorous leave-taking; and that amid the general hand-shaking some\neyes were wet, and some partings said with big lumps that would rise in\nswelling throats! A good face was, however, put upon it all; and even\nFang, Dennis, and the chore-boy, sent a blessing and a cheery good-bye\nin the wake of the favorite boarder.\n\nAs for the small Mexican herd-boy,--who, with his best clean face, had\ncome up to the ranch to look his last upon the adored white man under\nwhose tuition he had become \"a mighty hunter before the Lord,\"--he\nsimply \"lifted up his voice and wept.\"\n\nFollowing hard upon this departure came the general break-up of the\nKoshare circle. The Hemmenshaws, with the bridegroom elect, Roger Smith,\nwere the next to depart. Miss Paulina, as may be inferred, turned her\nface Bostonward with her heart in her mouth, in view of that account of\nher chaperonage to be rendered to the father whose daughter she had, as\nit were, handed over to the grandson of a tanner.\n\nAnd here the historian, asking leave to interrupt for a moment the\nroutine of the narrative, informs the gentle reader that that august\npersonage, Col. Algernon Hemmenshaw, was ultimately placated; and that\nif a tanner's descendant bearing the non-illustrious name of Smith was\nnot altogether a desirable graft for the Hemmenshaw ancestral tree, a\nfortune of more than a round million tipped the balance in his favor,\nand the permitted engagement came out in early May-time. Beacon Hill, at\nits announcement, threw up its hands in amazement and distaste. \"To\nthink,\" it exclaimed, \"that Louise Hemmenshaw, who might have had her\npick among our very oldest families, should take up with the grandson of\na tanner!\"\n\n * * * * *\n\nOut on the mesa it is early nightfall. The little day-time flutter and\nstir of moving things has, with the setting sun, given place to silence\nand rest.\n\nA rounded moon looks serenely down upon the grey sage-brush, the\nmesquite-bushes, on the lonely stretch of sandy desert. The last gleam\nof day has faded from the Organ Mountains, leaving them to dominate, in\nsombre grandeur, the distant landscape. In the warm, haunted silence of\nthis perfect night two lovers saunter slowly along the mesa.\n\nThese happy beings are not unknown to us. The lady is from Marblehead;\nthe other has before-time been dubbed the Grumbler.\n\nThe name no longer fits the man. His defective lung has righted itself\nin this fine New Mexican atmosphere. No more is he at odds with fate; he\nhas become sincerely in love with life, with the climate, and, most of\nall, with the sweet little teacher from Marblehead. They are to be\nmarried early in June.\n\nThe climate admirably suits the invalid sister, and it is hoped that in\nthis fine dry air her well lung may remain intact, and so serve her for\nyears to come. The Grumbler, having money enough to order his residence\nto his liking, has determined to settle permanently in New Mexico.\n\nTo that end he has, for the time, rented the Hilton place. Later, he\nintends to lay out \"as a gift for his fair\" the ranch of her dreams.\nHere, in the beautiful Mesilla Valley, we may predict that the married\npair, like the enchanting couples of fairyland, will \"live happy ever\nafter.\"\n\nAnd now it but remains for the chronicler of the New Koshare to take\nleave of \"the land of sunshine.\"\n\nA backward glance at the half-deserted Alamo shows us a dreary handful\nof incurables still tilting their piazza-chairs against its adobe front,\nwarming their depleted blood in the grateful sunshine, and each, as best\nhe may, accepting the inevitable.\n\nLong, long ago it was that the Pueblos made that traditional journey\n\"from Shipapu to the centre of their world\" with the heaven-provided\nKoshare, in particolored attire, and fantastic head-dress of withered\ncorn-husks, jesting and dancing before them to lift and lighten the\nweary road. Yet since then, through all the centuries, the\n\"Delight-Maker,\" in one shape or another, has been in requisition in\nevery land beneath the sun.\n\n\n\n\n\nEnd of the Project Gutenberg EBook of Alamo Ranch, by Sarah Warner Brooks\n\n*** ","meta":{"redpajama_set_name":"RedPajamaBook"}} +{"text":"\n\n\n\nProduced by Anne Folland, Eric Eldred, Charles Franks and\nthe Online Distributed Proofreading Team\n\n\n\n\n\n\n\n\n\n\nON NOTHING & KINDRED SUBJECTS\n\nBY\n\nHILAIRE BELLOC\n\n\n\n\nTO\n\nMAURICE BARING\n\n\n\n\nCONTENTS\n\n\nON THE PLEASURE OF TAKING UP ONE'S PEN\n\nON GETTING RESPECTED IN INNS AND HOTELS\n\nON IGNORANCE\n\nON ADVERTISEMENT\n\nON A HOUSE\n\nON THE ILLNESS OF MY MUSE\n\nON A DOG AND A MAN ALSO\n\nON TEA\n\nON THEM\n\nON RAILWAYS AND THINGS\n\nON CONVERSATIONS IN TRAINS\n\nON THE RETURN OF THE DEAD\n\nON THE APPROACH OF AN AWFUL DOOM\n\nON A RICH MAN WHO SUFFERED\n\nON A CHILD WHO DIED\n\nON A LOST MANUSCRIPT\n\nON A MAN WHO WAS PROTECTED BY ANOTHER MAN\n\nON NATIONAL DEBTS\n\nON LORDS\n\nON JINGOES: IN THE SHAPE OF A WARNING\n\nON A WINGED HORSE AND THE EXILE WHO RODE HIM\n\nON A MAN AND HIS BURDEN\n\nON A FISHERMAN AND THE QUEST OF PEACE\n\nON A HERMIT WHOM I KNEW\n\nON AN UNKNOWN COUNTRY\n\nON A FA\u00cbRY CASTLE\n\nON A SOUTHERN HARBOUR\n\nON A YOUNG MAN AND AN OLDER MAN\n\nON THE DEPARTURE OF A GUEST\n\nON DEATH\n\nON COMING TO AN END\n\n\n\n\n_King's Land,\n\nDecember the 13th, 1907\n\nMy dear Maurice,\n\nIt was in Normandy, you will remember, and in the heat of the year,\nwhen the birds were silent in the trees and the apples nearly ripe,\nwith the sun above us already of a stronger kind, and a somnolence\nwithin and without, that it was determined among us (the jolly\ncompany!) that I should write upon Nothing, and upon all that is\ncognate to Nothing, a task not yet attempted since the Beginning of\nthe World.\n\nNow when the matter was begun and the subject nearly approached, I\nsaw more clearly that this writing upon Nothing might be very grave,\nand as I looked at it in every way the difficulties of my adventure\nappalled me, nor am I certain that I have overcome them all. But I\nhad promised you that I would proceed, and so I did, in spite of my\ndoubts and terrors.\n\nFor first I perceived that in writing upon this matter I was in\nperil of offending the privilege of others, and of those especially\nwho are powerful to-day, since I would be discussing things very\ndear and domestic to my fellow-men, such as The Honour of Politicians,\nThe Tact of Great Ladies, The Wealth of Journalists, The Enthusiasm\nof Gentlemen, and the Wit of Bankers. All that is most intimate and\ndearest to the men that make our time, all that they would most defend\nfrom the vulgar gaze,--this it was proposed to make the theme of a\ncommon book.\n\nIn spite of such natural fear and of interests so powerful to detain\nme, I have completed my task, and I will confess that as it grew it\nenthralled me. There is in Nothing something so majestic and so high\nthat it is a fascination and spell to regard it. Is it not that\nwhich Mankind, after the great effort of life, at last attains, and\nthat which alone can satisfy Mankind's desire? Is it not that which\nis the end of so many generations of analysis, the final word of\nPhilosophy, and the goal of the search for reality? Is it not the\nvery matter of our modern creed in which the great spirits of our\ntime repose, and is it not, as it were, the culmination of their\nintelligence? It is indeed the sum and meaning of all around!\n\nHow well has the world perceived it and how powerfully do its\nlegends illustrate what Nothing is to men!\n\nYou know that once in Lombardy Alfred and Charlemagne and the Kaliph\nHaroun-al-Raschid met to make trial of their swords. The sword of\nAlfred was a simple sword: its name was Hewer. And the sword of\nCharlemagne was a French sword, and its name was Joyeuse. But the\nsword of Haroun was of the finest steel, forged in Toledo, tempered\nat Cordova, blessed in Mecca, damascened (as one might imagine) in\nDamascus, sharpened upon Jacob's Stone, and so wrought that when one\nstruck it it sounded like a bell. And as for its name, By Allah!\nthat was very subtle---for it had no name at all.\n\nWell then, upon that day in Lombardy Alfred and Charlemagne and the\nKaliph were met to take a trial of their blades. Alfred took a pig\nof lead which he had brought from the Mendip Hills, and swiping the\nair once or twice in the Western fashion, he cut through that lead\nand girded the edge of his sword upon the rock beneath, making a\nlittle dent.\n\nThen Charlemagne, taking in both hands his sword Joyeuse, and aiming\nat the dent, with a laugh swung down and cut the stone itself right\nthrough, so that it fell into two pieces, one on either side, and\nthere they lie today near by Piacenza in a field.\n\nNow that it had come to the Kaliph's turn, one would have said there\nwas nothing left for him to do, for Hewer had manfully hewn lead,\nand Joyeuse had joyfully cleft stone.\n\nBut the Kaliph, with an Arabian look, picked out of his pocket a\ngossamer scarf from Cashmir, so light that when it was tossed into\nthe air it would hardly fall to the ground, but floated downwards\nslowly like a mist. This, with a light pass, he severed, and\nimmediately received the prize. For it was deemed more difficult by\nfar to divide such a veil in mid-air, than to cleave lead or even\nstone.\n\nI knew a man once, Maurice, who was at Oxford for three years, and\nafter that went down with no degree. At College, while his friends\nwere seeking for Truth in funny brown German Philosophies, Sham\nReligions, stinking bottles and identical equations, he was lying on\nhis back in Eynsham meadows thinking of Nothing, and got the Truth\nby this parallel road of his much more quickly than did they by theirs;\nfor the asses are still seeking, mildly disputing, and, in a cultivated\nmanner, following the gleam, so that they have become in their Donnish\nmiddleage a nuisance and a pest; while he--that other--with the Truth\nvery fast and firm at the end of a leather thong is dragging her\nsliding, whining and crouching on her four feet, dragging her reluctant\nthrough the world, even into the broad daylight where Truth most hates\nto be.\n\nHe it was who became my master in this creed. For once as we lay\nunder a hedge at the corner of a road near Bagley Wood we heard far\noff the notes of military music and the distant marching of a\ncolumn; these notes and that tramp grew louder, till there swung\nround the turning with a blaze of sound five hundred men in order.\nThey passed, and we were full of the scene and of the memories of\nthe world, when he said to me: \"Do you know what is in your heart?\nIt is the music. And do you know the cause and Mover of that music?\nIt is the Nothingness inside the bugle; it is the hollow Nothingness\ninside the Drum.\"\n\nThen I thought of the poem where it says of the Army of the Republic:\n\n The thunder of the limber and the rumble of a hundred of the guns.\n And there hums as she comes the roll of her innumerable drums.\n\nI knew him to be right.\n\nFrom this first moment I determined to consider and to meditate upon\nNothing.\n\nMany things have I discovered about Nothing, which have proved it--to\nme at least--to be the warp or ground of all that is holiest. It is\nof such fine gossamer that loveliness was spun, the mists under the\nhills on an autumn morning are but gross reflections of it; moonshine\non lovers is earthy compared with it; song sung most charmingly and\nstirring the dearest recollections is but a failure in the human\nattempt to reach its embrace and be dissolved in it. It is out of\nNothing that are woven those fine poems of which we carry but vague\nrhythms in the head:--and that Woman who is a shade, the_ Insaisissable,\n_whom several have enshrined in melody--well, her Christian name, her\nmaiden name, and, as I personally believe, her married name as well,\nis Nothing. I never see a gallery of pictures now but I know how the\nuse of empty spaces makes a scheme, nor do I ever go to a play but I\nsee how silence is half the merit of acting and hope some day for\nabsence and darkness as well upon the stage. What do you think the\nfairy Melisende said to Fulk-Nerra when he had lost his soul for her\nand he met her in the Marshes after twenty years? Why, Nothing--what\nelse could she have said? Nothing is the reward of good men who alone\ncan pretend to taste it in long easy sleep, it is the meditation of\nthe wise and the charm of happy dreamers. So excellent and final is\nit that I would here and now declare to you that Nothing was the gate\nof eternity, that by passing through Nothing we reached our every\nobject as passionate and happy beings--were it not for the Council\nof Toledo that restrains my pen. Yet ... indeed, indeed when I think\nwhat an Elixir is this Nothing I am for putting up a statue nowhere,\non a pedestal that shall not exist, and for inscribing on it in\nletters that shall never be written:\n\nTO NOTHING\n\nTHE HUMAN RACE IN GRATITUDE.\n\nSo I began to write my book, Maurice: and as I wrote it the dignity\nof what I had to do rose continually before me, as does the dignity\nof a mountain range which first seemed a vague part of the sky, but\nat last stands out august and fixed before the traveller; or as the\nsky at night may seem to a man released from a dungeon who sees it\nbut gradually, first bewildered by the former constraint of his\nnarrow room but now gradually enlarging to drink in its immensity.\nIndeed this Nothing is too great for any man who has once embraced\nit to leave it alone thenceforward for ever; and finally, the\ndignity of Nothing is sufficiently exalted in this: that Nothing is\nthe tenuous stuff from which the world was made.\n\nFor when the Elohim set out to make the world, first they debated\namong themselves the Idea, and one suggested this and another\nsuggested that, till they had threshed out between them a very\npretty picture of it all. There were to be hills beyond hills, good\ngrass and trees, and the broadness of rivers, animals of all kinds,\nboth comic and terrible, and savours and colours, and all around the\nceaseless streaming of the sea.\n\nNow when they had got that far, and debated the Idea in detail, and\nwith amendment and resolve, it very greatly concerned them of what\nso admirable a compost should be mixed. Some said of this, and some\nsaid of that, but in the long run it was decided by the narrow\nmajority of eight in a full house that Nothing was the only proper\nmaterial out of which to make this World of theirs, and out of\nNothing they made it: as it says in the Ballade:\n\n Dear, tenuous stuff, of which the world was made.\n\nAnd again in the Envoi:\n\n Prince, draw this sovereign draught in your despair,\n That when your riot in that rest is laid,\n You shall be merged with an Essential Air:--\n Dear, tenuous stuff, of which the world was made!\n\n\nOut of Nothing then did they proceed to make the world, this sweet\nworld, always excepting Man the Marplot. Man was made in a muddier\nfashion, as you shall hear.\n\nFor when the world seemed ready finished and, as it were,\npresentable for use, and was full of ducks, tigers, mastodons,\nwaddling hippopotamuses, lilting deer, strong-smelling herbs, angry\nlions, frowsy snakes, cracked glaciers, regular waterfalls, \nsunsets, and the rest, it suddenly came into the head of the\nyoungest of these strong Makers of the World (the youngest, who had\nbeen sat upon and snubbed all the while the thing was doing, and\nhardly been allowed to look on, let alone to touch), it suddenly\ncame into his little head, I say, that he would make a Man.\n\nThen the Elder Elohim said, some of them, \"Oh, leave well alone!\nsend him to bed!\" And others said sleepily (for they were tired),\n\"No! no! let him play his little trick and have done with it, and\nthen we shall have some rest.\" Little did they know!... And others\nagain, who were still broad awake, looked on with amusement and\napplauded, saying: \"Go on, little one! Let us see what you can do.\"\nBut when these last stooped to help the child, they found that all\nthe Nothing had been used up (and that is why there is none of it\nabout to-day). So the little fellow began to cry, but they, to\ncomfort him, said: \"Tut, lad! tut! do not cry; do your best with\nthis bit of mud. It will always serve to fashion something.\"\n\nSo the jolly little fellow took the dirty lump of mud and pushed it\nthis way and that, jabbing with his thumb and scraping with his\nnail, until at last he had made Picanthropos, who lived in Java and\nwas a fool; who begat Eoanthropos, who begat Meioanthropos, who\nbegat Pleioanthropos, who begat Pleistoanthropos, who is often mixed\nup with his father, and a great warning against keeping the same\nnames in one family; who begat Paleoanthropos, who begat Neoanthropos,\nwho begat the three Anthropoids, great mumblers and murmurers with\ntheir mouths; and the eldest of these begat Him whose son was He,\nfrom whom we are all descended.\n\nHe was indeed halting and patchy, ill-lettered, passionate and rude;\nbald of one cheek and blind of one eye, and his legs were of\ndifferent sizes, nevertheless by process of ascent have we, his\ndescendants, manfully continued to develop and to progress, and to\nswell in everything, until from Homer we came to Euripides, and from\nEuripides to Seneca, and from Seneca to Boethius and his peers; and\nfrom these to Duns Scotus, and so upwards through James I of England\nand the fifth, sixth or seventh of Scotland (for it is impossible to\nremember these things) and on, on, to my Lord Macaulay, and in the\nvery last reached YOU, the great summits of the human race and last\nperfection of the ages READERS OF THIS BOOK, and you also Maurice,\nto whom it is dedicated, and myself, who have written it for gain.\n\nAmen._\n\n\n\n\nON NOTHING\n\n\n\n\nON THE PLEASURE OF TAKING UP ONE'S PEN\n\n\nAmong the sadder and smaller pleasures of this world I count this\npleasure: the pleasure of taking up one's pen.\n\nIt has been said by very many people that there is a tangible pleasure\nin the mere act of writing: in choosing and arranging words. It has\nbeen denied by many. It is affirmed and denied in the life of Doctor\nJohnson, and for my part I would say that it is very true in some rare\nmoods and wholly false in most others. However, of writing and the\npleasure in it I am not writing here (with pleasure), but of the\npleasure of taking up one's pen, which is quite another matter.\n\nNote what the action means. You are alone. Even if the room is\ncrowded (as was the smoking-room in the G.W.R. Hotel, at Paddington,\nonly the other day, when I wrote my \"Statistical Abstract of\nChristendom\"), even if the room is crowded, you must have made\nyourself alone to be able to write at all. You must have built up\nsome kind of wall and isolated your mind. You are alone, then; and\nthat is the beginning.\n\nIf you consider at what pains men are to be alone: how they climb\nmountains, enter prisons, profess monastic vows, put on eccentric\ndaily habits, and seclude themselves in the garrets of a great town,\nyou will see that this moment of taking up the pen is not least\nhappy in the fact that then, by a mere association of ideas, the\nwriter is alone.\n\nSo much for that. Now not only are you alone, but you are going to\n\"create\".\n\nWhen people say \"create\" they flatter themselves. No man can create\nanything. I knew a man once who drew a horse on a bit of paper to amuse\nthe company and covered it all over with many parallel streaks as he\ndrew. When he had done this, an aged priest (present upon that occasion)\nsaid, \"You are pleased to draw a zebra.\" When the priest said this the\nman began to curse and to swear, and to protest that he had never seen\nor heard of a zebra. He said it was all done out of his own head, and\nhe called heaven to witness, and his patron saint (for he was of the Old\nEnglish Territorial Catholic Families--his patron saint was Aethelstan),\nand the salvation of his immortal soul he also staked, that he was as\ninnocent of zebras as the babe unborn. But there! He persuaded no one,\nand the priest scored. It was most evident that the Territorial was\ncrammed full of zebraical knowledge.\n\nAll this, then, is a digression, and it must be admitted that there\nis no such thing as a man's \"creating\". But anyhow, when you take up\nyour pen you do something devilish pleasing: there is a prospect\nbefore you. You are going to develop a germ: I don't know what it\nis, and I promise you I won't call it creation--but possibly a god\nis creating through you, and at least you are making believe at\ncreation. Anyhow, it is a sense of mastery and of origin, and you\nknow that when you have done, something will be added to the world,\nand little destroyed. For what will you have destroyed or wasted? A\ncertain amount of white paper at a farthing a square yard (and I am\nnot certain it is not pleasanter all diversified and variegated with\nblack wriggles)--a certain amount of ink meant to be spread and\ndried: made for no other purpose. A certain infinitesimal amount of\nquill--torn from the silly goose for no purpose whatsoever but to\nminister to the high needs of Man.\n\nHere you cry \"Affectation! Affectation! How do I know that the\nfellow writes with a quill? A most unlikely habit!\" To that I answer\nyou are right. Less assertion, please, and more humility. I will\ntell you frankly with what I am writing. I am writing with a\nWaterman's Ideal Fountain Pen. The nib is of pure gold, as was the\nthrone of Charlemagne, in the \"Song of Roland.\" That throne (I need\nhardly tell you) was borne into Spain across the cold and awful\npasses of the Pyrenees by no less than a hundred and twenty mules,\nand all the Western world adored it, and trembled before it when it\nwas set up at every halt under pine trees, on the upland grasses.\nFor he sat upon it, dreadful and commanding: there weighed upon him\ntwo centuries of age; his brows were level with justice and\nexperience, and his beard was so tangled and full, that he was\ncalled \"bramble-bearded Charlemagne.\" You have read how, when he\nstretched out his hand at evening, the sun stood still till he had\nfound the body of Roland? No? You must read about these things.\n\nWell then, the pen is of pure gold, a pen that runs straight away\nlike a willing horse, or a jolly little ship; indeed, it is a pen so\nexcellent that it reminds me of my subject: the pleasure of taking\nup one's pen.\n\nGod bless you, pen! When I was a boy, and they told me work was\nhonourable, useful, cleanly, sanitary, wholesome, and necessary to\nthe mind of man, I paid no more attention to them than if they had\ntold me that public men were usually honest, or that pigs could fly.\nIt seemed to me that they were merely saying silly things they had\nbeen told to say. Nor do I doubt to this day that those who told me\nthese things at school were but preaching a dull and careless round.\nBut now I know that the things they told me were true. God bless\nyou, pen of work, pen of drudgery, pen of letters, pen of posings,\npen rabid, pen ridiculous, pen glorified. Pray, little pen, be\nworthy of the love I bear you, and consider how noble I shall make\nyou some day, when you shall live in a glass case with a crowd of\ntourists round you every day from 10 to 4; pen of justice, pen of\nthe _saeva indignatio_, pen of majesty and of light. I will\nwrite with you some day a considerable poem; it is a compact between\nyou and me. If I cannot make one of my own, then I will write out\nsome other man's; but you, pen, come what may, shall write out a\ngood poem before you die, if it is only the _Allegro_.\n\n * * * * *\n\nThe pleasure of taking up one's pen has also this, peculiar among\nall pleasures, that you have the freedom to lay it down when you\nwill. Not so with love. Not so with victory. Not so with glory.\n\nHad I begun the other way round, I would have called this Work, \"The\nPleasure of laying down one's Pen.\" But I began it where I began it,\nand I am going on to end it just where it is going to end.\n\nWhat other occupation, avocation, dissertation, or intellectual\nrecreation can you cease at will? Not bridge--you go on playing to\nwin. Not public speaking--they ring a bell. Not mere converse--you\nhave to answer everything the other insufficient person says. Not\nlife, for it is wrong to kill one's self; and as for the natural end\nof living, that does not come by one's choice; on the contrary, it\nis the most capricious of all accidents.\n\nBut the pen you lay down when you will. At any moment: without\nremorse, without anxiety, without dishonour, you are free to do this\ndignified and final thing (I am just going to do it).... You lay it\ndown.\n\n\n\n\nON GETTING RESPECTED IN INNS AND HOTELS\n\n\nTo begin at the beginning is, next to ending at the end, the whole\nart of writing; as for the middle you may fill it in with any rubble\nthat you choose. But the beginning and the end, like the strong\nstone outer walls of mediaeval buildings, contain and define the\nwhole.\n\nAnd there is more than this: since writing is a human and a living\nart, the beginning being the motive and the end the object of the\nwork, each inspires it; each runs through organically, and the two\nbetween them give life to what you do.\n\nSo I will begin at the beginning and I will lay down this first\nprinciple, that religion and the full meaning of things has nowhere\nmore disappeared from the modern world than in the department of\nGuide Books.\n\nFor a Guide Book will tell you always what are the principal and\nmost vulgar sights of a town; what mountains are most difficult to\nclimb, and, invariably, the exact distances between one place and\nanother. But these things do not serve the End of Man. The end of\nman is Happiness, and how much happier are you with such a\nknowledge? Now there are some Guide Books which do make little\nexcursions now and then into the important things, which tell you\n(for instance) what kind of cooking you will find in what places,\nwhat kind of wine in countries where this beverage is publicly\nknown, and even a few, more daring than the rest, will give a hint\nor two upon hiring mules, and upon the way that a bargain should be\nconducted, or how to fight.\n\nBut with all this even the best of them do not go to the moral heart\nof the matter. They do not give you a hint or an idea of that which\nis surely the basis of all happiness in travel. I mean, the art of\ngaining respect in the places where you stay. Unless that respect is\npaid you you are more miserable by far than if you had stayed at\nhome, and I would ask anyone who reads this whether he can remember\none single journey of his which was not marred by the evident\ncontempt which the servants and the owners of taverns showed for him\nwherever he went?\n\nIt is therefore of the first importance, much more important than\nany question of price or distance, to know something of this art; it\nis not difficult to learn, moreover it is so little exploited that\nif you will but learn it you will have a sense of privilege and of\nupstanding among your fellows worth all the holidays which were ever\ntaken in the world.\n\nOf this Respect which we seek, out of so many human pleasures, a\nfacile, and a very false, interpretation is that it is the privilege\nof the rich, and I even knew one poor fellow who forged a cheque and\nwent to gaol in his desire to impress the host of the \"Spotted Dog,\"\nnear Barnard Castle. It was an error in him, as it is in all who so\nimagine. The rich in their degree fall under this contempt as\nheavily as any, and there is no wealth that can purchase the true\nawe which it should be your aim to receive from waiters, serving-wenches,\nboot-blacks, and publicans.\n\nI knew a man once who set out walking from Oxford to Stow-in-the-Wold,\nfrom Stow-in-the-Wold to Cheltenham, from Cheltenham to Ledbury, from\nLedbury to Hereford, from Hereford to New Rhayader (where the Cobbler\nlives), and from New Rhayader to the end of the world which lies a\nlittle west and north of that place, and all the way he slept rough\nunder hedges and in stacks, or by day in open fields, so terrified\nwas he at the thought of the contempt that awaited him should he pay\nfor a bed. And I knew another man who walked from York to Thirsk, and\nfrom Thirsk to Darlington, and from Darlington to Durham, and so on\nup to the border and over it, and all the way he pretended to be\nextremely poor so that he might be certain the contempt he received\nwas due to nothing of his own, but to his clothes only: but this was\nan indifferent way of escaping, for it got him into many fights with\nminers, and he was arrested by the police in Lanchester; and at\nJedburgh, where his money did really fail him, he had to walk all\nthrough the night, finding that no one would take in such a\ntatterdemalion. The thing could be done much more cheaply than that,\nand much more respectably, and you can acquire with but little practice\none of many ways of achieving the full respect of the whole house, even\nof that proud woman who sits behind glass in front of an enormous\nledger; and the first way is this:--\n\nAs you come into the place go straight for the smoking-room, and\nbegin talking of the local sport: and do not talk humbly and\ntentatively as so many do, but in a loud authoritative tone. You\nshall insist and lay down the law and fly into a passion if you are\ncontradicted. There is here an objection which will arise in the\nmind of every niggler and boggler who has in the past very properly\nbeen covered with ridicule and become the butt of the waiters and\nstable-yard, which is, that if one is ignorant of the local sport,\nthere is an end to the business. The objection is ridiculous. Do you\nsuppose that the people whom you hear talking around you are more\nlearned than yourself in the matter? And if they are do you suppose\nthat they are acquainted with your ignorance? Remember that most of\nthem have read far less than you, and that you can draw upon an\nexperience of travel of which they can know nothing; do but make the\nplunge, practising first in the villages of the Midlands, I will\nwarrant you that in a very little while bold assertion of this kind\nwill carry you through any tap-room or bar-parlour in Britain.\n\nI remember once in the holy and secluded village of Washington under\nthe Downs, there came in upon us as we sat in the inn there a man whom\nI recognised though he did not know me--for a journalist--incapable of\nunderstanding the driving of a cow, let alone horses: a prophet, a\nsocialist, a man who knew the trend of things and so forth: a man who\nhad never been outside a town except upon a motor bicycle, upon which\nsnorting beast indeed had he come to this inn. But if he was less than\nus in so many things he was greater than us in this art of gaining\nrespect in Inns and Hotels. For he sat down, and when they had barely\nhad time to say good day to him he gave us in minutest detail a great\nrun after a fox, a run that never took place. We were fifteen men in\nthe room; none of us were anything like rich enough to hunt, and the\nlie went through them like an express. This fellow \"found\" (whatever\nthat may mean) at Gumber Corner, ran right through the combe (which,\nby the way, is one of those bits of land which have been stolen bodily\nfrom the English people), cut down the Sutton Road, across the railway\nat Coates (and there he showed the cloven hoof, for your liar always\ntakes his hounds across the railway), then all over Egdean, and killed\nin a field near Wisborough. All this he told, and there was not even a\nman there to ask him whether all those little dogs and horses swam\nthe Rother or jumped it. He was treated like a god; they tried to\nmake him stop but he would not. He was off to Worthing, where I have\nno doubt he told some further lies upon the growing of tomatoes\nunder glass, which is the main sport of that district. Similarly, I\nhave no doubt, such a man would talk about boats at King's Lynn,\nmurder with violence at Croydon, duck shooting at Ely, and racing\nanywhere.\n\nThen also if you are in any doubt as to what they want of you, you\ncan always change the scene. Thus fishing is dangerous for even the\npoor can fish, and the chances are you do not know the names of the\nanimals, and you may be putting salt-water fish into the stream of\nLambourne, or talking of salmon upon the Upper Thames. But what is\nto prevent you putting on a look of distance and marvel, and\nconjuring up the North Atlantic for them? Hold them with the cold\nand the fog of the Newfoundland seas, and terrify their simple minds\nwith whales.\n\nA second way to attain respect, if you are by nature a silent man,\nand one which I think is always successful, is to write before you\ngo to bed and leave upon the table a great number of envelopes which\nyou should address to members of the Cabinet, and Jewish money-lenders,\ndukes, and in general any of the great. It is but slight labour, and\nfor the contents you cannot do better than put into each envelope one\nof those advertisements which you will find lying about. Then next\nmorning you should gather them up and ask where the post is: but you\nneed not post them, and you need not fear for your bill. Your bill\nwill stand much the same, and your reputation will swell like a sponge.\n\nAnd a third way is to go to the telephone, since there are\ntelephones nowadays, and ring up whoever in the neighbourhood is of\nthe greatest importance. There is no law against it, and when you\nhave the number you have but to ask the servant at the other end\nwhether it is not somebody else's house. But in the meanwhile your\nnight in the place is secure.\n\nAnd a fourth way is to tell them to call you extremely early, and\nthen to get up extremely late. Now why this should have the effect\nit has I confess I cannot tell. I lay down the rule empirically and\nfrom long observation, but I may suggest that perhaps it is the\ncombination of the energy you show in early rising, and of the\nluxury you show in late rising: for energy and luxury are the two\nqualities which menials most admire in that governing class to which\nyou flatter yourself you belong. Moreover the strength of will with\nwhich you sweep aside their inconvenience, ordering one thing and\ndoing another, is not without its effect, and the stir you have\ncreated is of use to you.\n\nAnd the fifth way is to be Strong, to Dominate and to Lead. To be\none of the Makers of this world, one of the Builders. To have the\nmore Powerful Will. To arouse in all around you by mere Force of\nPersonality a feeling that they must Obey. But I do not know how\nthis is done.\n\n\n\n\nON IGNORANCE\n\n\nThere is not anything that can so suddenly flood the mind with shame\nas the conviction of ignorance, yet we are all ignorant of nearly\neverything there is to be known. Is it not wonderful, then, that we\nshould be so sensitive upon the discovery of a fault which must of\nnecessity be common to all, and that in its highest degree? The\nconviction of ignorance would not shame us thus if it were not for\nthe public appreciation of our failure.\n\nIf a man proves us ignorant of German or the complicated order of\nEnglish titles, or the rules of Bridge, or any other matter, we do\nnot care for his proofs, so that we are alone with him: first\nbecause we can easily deny them all, and continue to wallow in our\nignorance without fear, and secondly, because we can always counter\nwith something we know, and that he knows nothing of, such as the\nCreed, or the history of Little Bukleton, or some favourite book.\nThen, again, if one is alone with one's opponent, it is quite easy\nto pretend that the subject on which one has shown ignorance is\nunimportant, peculiar, pedantic, hole in the corner, and this can be\nbrazened out even about Greek or Latin. Or, again, one can turn the\nlaugh against him, saying that he has just been cramming up the\nmatter, and that he is airing his knowledge; or one can begin making\njokes about him till he grows angry, and so forth. There is no\nnecessity to be ashamed.\n\nBut if there be others present? Ah! _Hoc est aliud rem_, that\nis another matter, for then the biting shame of ignorance suddenly\ndisplayed conquers and bewilders us. We have no defence left. We are\nat the mercy of the discoverer, we own and confess, and become\ninsignificant: we slink away.\n\nNote that all this depends upon what the audience conceive ignorance\nto be. It is very certain that if a man should betray in some cheap\nclub that he did not know how to ride a horse, he would be broken\ndown and lost, and similarly, if you are in a country house among\nthe rich you are shipwrecked unless you can show acquaintance with\nthe Press, and among the poor you must be very careful, not only to\nwear good cloth and to talk gently as though you owned them, but\nalso to know all about the rich. Among very young men to seem\nignorant of vice is the ruin of you, and you had better not have\nbeen born than appear doubtful of the effects of strong drink when\nyou are in the company of Patriots. There was a man who died of\nshame this very year in a village of Savoy because he did not know\nthe name of the King reigning over France to-day, and it is a common\nthing to see men utterly cast down in the bar-rooms off the Strand\nbecause they cannot correctly recite the opening words of \"Boys of\nthe Empire.\" There are schoolgirls who fall ill and pine away\nbecause they are shown to have misplaced the name of Dagobert III in\nthe list of Merovingian Monarchs, and quite fearless men will blush\nif they are found ignoring the family name of some peer. Indeed,\nthere is nothing so contemptible or insignificant but that in some\nsociety or other it is required to be known, and that the ignorance\nof it may not at any moment cover one with confusion. Nevertheless\nwe should not on that account attempt to learn everything there is\nto know (for that is manifestly impossible), nor even to learn\neverything that is known, for that would soon prove a tedious and\nheart-breaking task; we should rather study the means to be employed\nfor warding off those sudden and public convictions of Ignorance\nwhich are the ruin of so many.\n\nThese methods of defence are very numerous and are for the most part\neasy of acquirement. The most powerful of them by far (but the most\ndangerous) is to fly into a passion and marvel how anyone can be\nsuch a fool as to pay attention to wretched trifles. \"Powerful,\"\nbecause it appeals to that strongest of all passions in men by which\nthey are predisposed to cringe before what they think to be a\nsuperior station in society. \"Dangerous,\" because if it fail in its\nobjects this method does not save you from pain, and secures you in\naddition a bad quarrel, and perhaps a heavy beating. Still it has\nmany votaries, and is more often carried off than any other. Thus,\nif in Bedfordshire, someone catches you erring on a matter of crops,\nyou profess that in London such things are thought mere rubbish and\ndespised; or again, in the society of professors at the\nUniversities, an ignorance of letters can easily be turned by an\nallusion to that vapid life of the rich, where letters grow\ninsignificant; so at sea, if you slip on common terms, speak a\nlittle of your luxurious occupations on land and you will usually be\nsafe.\n\nThere are other and better defences. One of these is to turn the\nattack by showing great knowledge on a cognate point, or by\nremembering that the knowledge your opponent boasts has been\nsomewhere contradicted by an authority. Thus, if some day a friend\nshould say, as continually happens in a London club:\n\n\"Come, let us hear you decline [Greek: tetummenos on],\" you can\nanswer carelessly:\n\n\"You know as well as I do that the form is purely Paradigmatic: it\nis never found.\"\n\nOr again, if you put the Wrekin by an error into Staffordshire, you\ncan say, \"I was thinking of the Jurassic formation which is the\nbasis of the formation of----\" etc. Or, \"Well, Shrewsbury ...\nStaffordshire?... Oh! I had got my mind mixed up with the graves of\nthe Staffords.\" Very few people will dispute this, none will follow\nit. There is indeed this difficulty attached to such a method, that\nit needs the knowledge of a good many things, and a ready\nimagination and a stiff face: but it is a good way.\n\nYet another way is to cover your retreat with buffoonery, pretending\nto be ignorant of the most ordinary things, so as to seem to have\nbeen playing the fool only when you made your first error. There is\na special form of this method which has always seemed to me the most\nexcellent by far of all known ways of escape. It is to show a steady\nand crass ignorance of very nearly everything that can be mentioned,\nand with all this to keep a steady mouth, a determined eye, and\n(this is essential) to show by a hundred allusions that you have on\nyour own ground an excellent store of knowledge.\n\nThis is the true offensive-defensive in this kind of assault, and\ntherefore the perfection of tactics.\n\nThus if one should say:\n\n\"Well, it was the old story. [Greek: Anankae].\"\n\nIt might happen to anyone to answer: \"I never read the play.\"\n\nThis you will think perhaps an irremediable fall, but it is not, as\nwill appear from this dialogue, in which the method is developed:\n\nSAPIENS. But, Good Heavens, it isn't a play!\n\nIGNORAMUS. Of course not. I know that as well as you, but the\ncharacter of [Greek: Anankae] dominates the play. You won't deny\nthat?\n\nSAPIENS. You don't seem to have much acquaintance with Liddell and\nScott.\n\nIGNORAMUS. I didn't know there was anyone called Liddell in it, but\nI knew Scott intimately, both before and after he succeeded to the\nestate.\n\nSAPIENS. But I mean the dictionary.\n\nIGNORAMUS. I'm quite certain that his father wouldn't let him write\na dictionary. Why, the library at Bynton hasn't been opened for\nyears.\n\nIf, after five minutes of that, Ignoramus cannot get Sapiens\nfloundering about in a world he knows nothing of, it is his own\nfault.\n\nBut if Sapiens is over-tenacious there is a final method which may\nnot be the most perfect, but which I have often tried myself, and\nusually with very considerable success:\n\nSAPIENS. Nonsense, man. The Dictionary. The _Greek_ dictionary.\n\nIGNORAMUS. What has _Ananti_ to do with Greek?\n\nSAPIENS. I said [Greek: Anankae].\n\nIGNORAMUS. Oh! h----h! you said [Greek: anankae], did you? I thought\nyou said Ananti. Of course, Scott didn't call the play Ananti, but\nAnanti was the principal character, and one always calls it that in\nthe family. It is very well written. If he hadn't that shyness about\npublishing ... and so forth.\n\nLastly, or rather Penultimately, there is the method of upsetting\nthe plates and dishes, breaking your chair, setting fire to the\nhouse, shooting yourself, or otherwise swallowing all the memory of\nyour shame in a great catastrophe.\n\nBut that is a method for cowards; the brave man goes out into the\nhall, comes back with a stick, and says firmly, \"You have just\ndeliberately and cruelly exposed my ignorance before this company; I\nshall, therefore, beat you soundly with this stick in the presence\nof them all.\"\n\nThis you then do to him or he to you, _mutatis mutandis, ceteris\nparibus_; and that is all I have to say on Ignorance.\n\n\n\n\nON ADVERTISEMENT\n\n\nHarmonides of Ephesus says in one of his treatises upon method (I\nforget which, but I think the fifth) that a matter is very often\nmore clearly presented by way of example than in the form of a\ndirect statement and analysis. I have determined to follow the\nadvice of this great though pagan authority in what you will now\nread or not read, according to your inclination.\n\nAs I was sitting one of these sunny mornings in my little Park,\nreading an article upon vivisection in the _Tablet_ newspaper,\na Domestic [Be seated, be seated, I pray you!] brought me a letter\nupon a Silver Salver [Be covered!]\n\nWhich reminds me, why do people say that silver is the only perfect\nspondee in the English language? Salver is a perfectly good spondee;\nso is North-Cape; so is great-coat; so is High-Mass; so is\nWenchthorpe; so is forewarp, which is the rope you throw out from\nthe stem to the little man in the boat who comes to moor you along\nthe west gully in the Ramsgate Harbour; so is Longnose, the name of\na buoy, and of a reef of rocks just north of the North Foreland; so\nare a great many other words. But I digress. I only put in these\nwords to show you in case you had any dissolving doubts remaining\nupon the matter, that the kind of stuff you read is very often all\nnonsense, and that you must not take things for granted merely\nbecause they are printed. I have watched you doing it from time to\ntime, and have been torn between pity and anger. But all that is\nneither here nor there. This habit of parenthesis is the ruin of\ngood prose. As I was saying, example clearly put down without\ncomment is very often more powerful than analysis for the purpose of\nconviction.\n\nThe Domestic brought me a letter upon a Silver Salver. I took it and\ncarefully examined the outside.\n\nThey err who will maintain through thick and thin upon a mere theory\nand without any true experience of the world, that it matters not\nwhat the outside of a letter may be so long as the contents provoke\nterror or amusement. The outside of a letter should appeal to one.\nWhen one gets a letter with a halfpenny stamp and with the flap of\nthe letter stuck inside, and with the address on the outside\ntypewritten, one is very apt to throw it away. I believe that there\nis no recorded case of such a letter containing a cheque, a summons,\nor an invitation to eat good food, and as for demand notes, what are\nthey? Then again those long envelopes which come with the notice,\n\"Paid in bulk,\" outside instead of a stamp--no man can be moved by\nthem. They are very nearly always advertisements of cheap wine.\n\nDo not misunderstand me: cheap wine is by no means to be despised.\nThere are some sorts of wine the less you pay for them the better\nthey are--within reason; and if a Gentleman has bought up a bankrupt\nstock of wine from a fellow to whom he has been lending money, why\non earth should he not sell it again at a reasonable profit, yet\nquite cheap? It seems to be pure benefit to the world. But I\nperceive that all this is leading me from my subject.\n\nI took up the letter, I say, and carefully examined the outside. It\nwas written in the hand of an educated man. It was almost illegible,\nand had all the appearance of what an honest citizen of some culture\nmight write to one hurriedly about some personal matter. I noticed\nthat it had come from the eastern central district, but when you\nconsider what an enormous number of people live there during the\nday, that did not prejudice me against it.\n\nNow, when I opened this letter, I found it written a little more\ncarefully, but still, written, not printed, or typewritten, or\nmanifolded, or lithographed, or anything else of that kind. It was\nwritten.\n\nThe art of writing ... but Patience! Patience!...\n\nIt was written. It was very cordial, and it appealed directly, only\nthe style was otiose, but in matters of the first importance style\nis a hindrance.\n\n_Telephone No. 666.\n\nThe Mercury,\n\n15th Nishan 5567.\n\nDear Sir,--Many people wonder, especially in your profession,_\n[what is It?] _why a certain Taedium Vitae seizes them towards\nfive o'clock in the afternoon. The stress and hurry of modern life\nhave forced so many of Us to draw upon Our nervous energy that We\nimagine that_ [Look at that 'that'! The whole Elizabethan\ntradition chucked away!] _We are exceeding our powers, and when\nthis depression comes over Us, we think it necessary to take a rest,\nand Let up from working. This is an erroneous supposition. What it\nmeans is that Our body has received insufficient nutriment during\nthe last twenty-four hours, and that Nature is craving for more\nsustenance.\n\nWe shall be very happy to offer you, through the medium of this\npaper, a special offer of our Essence of The Ox. This offer will\nonly remain open until Derby Day, during which period a box of our\nEssence of The Ox will be sent to you Free, if you will enclose the\nfollowing form, and send it to Us in the stamped envelope, which\naccompanies this letter.\n\nVery faithfully yours,_\n\nHENRY DE LA MERE ULLMO.\n\nIt seemed to me a most extraordinary thing. I had never written for\nUllmo and his _Mercury_, and I could do them no good in the world,\neither here or in Johannesburg. I was never likely to write for\nhim at all. He is not very pleasant; He is by no means rich; He is\nill-informed. He has no character at all, apart from rather unsuccessful\nmoney-grubbing, and from a habit of defending with some virulence,\nbut with no capacity, his fellow money-grubbers throughout the\nworld. However, I thought no more about it, and went on reading\nabout \"Vivisection.\"\n\nTwo days later I got a letter upon thick paper, so grained as to\nimitate oak, and having at the top a coat-of-arms of the most\ncomplicated kind. This coat-of-arms had a little lamb on it,\nsuspended by a girdle, as though it were being slung on board ship;\nthere were also three little sheaves of wheat, a sword, three\npanthers, some gules, and a mullet. Above it was a helmet, and there\nwere two supporters: one was a man with a club, and the other was\nanother man without a club, both naked. Underneath was the motto,\n\"Tout \u00e0 Toi.\" This second letter was very short.\n\n_Dear Sir,--Can you tell me why you have not answered Our letter\nre the Essence of the Ox? Derby Day is approaching, and the\nremaining time is very short. We made the offer specially to you,\nand we had at least expected the courtesy of an acknowledgment. You\nwill understand that the business of a great newspaper leaves but\nlittle time for private charity, but we are willing to let the offer\nremain open for three days longer, after which date--_\n\nHow easy it would be to criticise this English! To continue:\n\n_--after which date the price will inevitably be raised to One\nShilling.--We remain, etc._\n\nI had this letter framed with the other, and I waited to see what\nwould happen, keeping back from the bank for fear of frightening the\nfish, and hardly breathing.\n\nWhat happened was, after four or five days, a very sad letter which\nsaid that Ullmo expected better things from me, but that He knew\nwhat the stress of modern life was, and how often correspondence\nfell into arrears. He sent me a smaller specimen box of the Essence\nof The Ox. I have it still.\n\nAnd there it is. There is no moral; there is no conclusion or\napplication. The world is not quite infinite--but it is\nastonishingly full. All sorts of things happen in it. There are all\nsorts of different men and different ways of action, and different\ngoals to which life may be directed. Why, in a little wood near\nhome, not a hundred yards long, there will soon burst, in the spring\n(I wish I were there!), hundreds of thousands of leaves, and no one\nleaf exactly like another. At least, so the parish priest used to\nsay, and though I have never had the leisure to put the thing to the\nproof, I am willing to believe that he was right, for he spoke with\nauthority.\n\n\n\n\nON A HOUSE\n\n\nI appeal loudly to the Muse of History (whose name I forget and you\nnever knew) to help me in the description of this house, for--\n\nThe Muse of Tragedy would overstrain herself on it;\n\nThe Muse of Comedy would be impertinent upon it;\n\nThe Muse of Music never heard of it;\n\nThe Muse of Fine Arts disapproved of it;\n\nThe Muse of Public Instruction ... (Tut, tut! There I was nearly\nmaking a tenth Muse! I was thinking of the French Ministry.)\n\nThe Muse of Epic Poetry did not understand it;\n\nThe Muse of Lyric Poetry still less so;\n\nThe Muse of Astronomy is thinking of other things;\n\nThe Muse Polyhymnia (or Polymnia, who, according to Smith's\n_Dictionary of Antiquities_, is commonly represented in a\npensive attitude) has no attribute and does no work.\n\nAnd as for little Terpsichore whose feet are like the small waves in\nsummer time, she would laugh in a peal if I asked her to write,\nthink of, describe, or dance in this house (and that makes eleven\nMuses. No matter; better more than less).\n\nYet it was a house worthy of description and careful inventory, and\nfor that reason I have appealed to the Muse of History whose\nbusiness it is to set down everything in order as it happens,\njudging between good and evil, selecting facts, condensing\nnarratives, admitting picturesque touches, and showing her further\nknowledge by the allusive method or use of the dependent clause.\nWell then, inspired, I will tell you exactly how that house was\ndisposed. First, there ran up the middle of it a staircase which,\nhad Horace seen it (and heaven knows he was the kind of man to live\nin such a house), he would have called in his original and striking\nway \"Res Angusta Domi,\" for it was a narrow thing. Narrow do I call\nit? Yes--and yet not so narrow. It was narrow enough to avoid all\nappearance of comfort or majesty, yet not so narrow as to be quaint\nor snug. It was so designed that two people could walk exactly\nabreast, for it was necessary that upon great occasions the ladies\nshould be taken down from the drawing-room by the gentlemen to the\ndining-room, yet it would have been a sin and a shame to make it\nwider than that, and the house was not built in the days of\ncrinolines. Upon these occasions it was customary for the couples to\ngo down in order and in stately fashion, and the hostess went last;\nbut do not imagine that there was any order of precedence. Oh, no!\nFar from it, they went as they were directed.\n\nThis staircase filled up a kind of Chimney or Funnel, or rather\nParallelepiped, in the house: half-way between each floor was a\nlanding where it turned right round on itself, and on each floor a\nlarger landing flanked by two doors on either side, which made four\naltogether. This staircase was covered with Brussels carpet (and let\nme tell you in passing that no better covering for stairs was ever\nyet invented; it wears well and can be turned, and when the uppers\nare worn you can move the whole thing down one file and put the steps\nwhere the uppers were. None of your cocoanut stuff or gimcracks for\nthe honest house: when there is money you should have Brussels, when\nyou have none linoleum--but I digress). The stair-rods were of brass\nand beautifully polished, the banisters of iron painted to look like\nmahogany; and this staircase, which I may take to be the emblem of a\ngood life lived for duty, went up one pair, and two pair, and three\npair--all in the same way, and did not stop till it got to the top.\nBut just as a good life has beneath it a human basis so this (heaven\nforgive me!) somewhat commonplace staircase changed its character\nwhen it passed the hall door, and as it ran down to the basement had\nno landing, ornament, carpet or other paraphernalia, but a sound\nflight of stone steps with a cold rim of unpainted metal for the hand.\n\nThe hall that led to these steps was oblong and little furnished.\nThere was a hat-rack, a fireplace (in which a fire was not lit) and\ntwo pictures; one a photograph of the poor men to whom the owner\npaid weekly wages at his Works, all set out in a phalanx, or rather\nfan, with the Owner of the House (and them) in the middle, the other\na steel engraving entitled \"The Monarch of the Forest,\" from a\npainting by Sir Edwin Landseer. It represented a stag and was very\nugly.\n\nOn the ground floor of the House (which is a libel, for it was some\nfeet above the ground, and was led up to by several steps, as the\nporch could show) there were four rooms--the Dining-room, the\nSmoking-room, the Downstairs-room and the Back-room. The Dining-room\nwas so called because all meals were held in it; the Smoking-room\nbecause it was customary to smoke all over the house (except the\nDrawing-room); the Back-room because it was at the back, and the\nDownstairs-room because it was downstairs. Upon my soul, I would\ngive you a better reason if I had one, but I have none. Only I may\nsay that the Smoking-room was remarkable for two stuffed birds, the\nDownstairs-room from the fact that the Owner lived in it and felt at\nease there, the Back-room from the fact that no one ever went into\nit (and quite right too), while the Dining-room--but the Dining-room\nstands separate.\n\nThe Dining-room was well carpeted; it had in its midst a large\nmahogany table so made that it could get still larger by the\naddition of leaves inside; there were even flaps as well. It had\neleven chairs, and these in off-times stood ranged round the wall\nthinking of nothing, but at meal times were (according to the number\nwanted) put round the table. It is a theory among those who believe\nthat a spirit nourishes all things from within, that there was some\ncompetition amongst these chairs as to which should be used at\ntable, so dull, forlorn and purposeless was their life against the\nwall. Seven pictures hung on that wall; not because it was a mystic\nnumber, but because it filled up all the required space; two on each\nside of the looking-glass and three large ones on the opposite wall.\nThey were all of them engravings, and one of them at least was that\nof a prominent statesman (Lord Beaconsfield), while the rest had to\ndo with historical subjects, such as the visit of Prince Albert to\nthe Exhibition of 1851, and I really forget what else. There was a\nChiffonier at the end of the room in which the wines and spirits\nwere kept, and which also had a looking-glass above it; also a white\ncloth on the top for no reason on earth. An arm-chair (in which the\nOwner sat) commonly stood at the head of the table; this remained\nthere even between meals, and was a symbol that he was master of the\nhouse. Four meals were held here. Breakfast at eight, dinner at one,\ntea at six, and a kind of supper (when the children had gone to bed)\nat nine or so. But what am I saying--_quo Musa Historiae\ntendis?_--dear! dear! I thought I was back again in the old\ntimes! a thousand pardons. At the time my story opens--and closes\nalso for that matter (for I deal of the Owner and the House _in\narticulo mortis_ so to speak; on the very edge of death)--it was\nfar otherwise. Breakfast was when you like (for him, however, always\nat the same old hour, and there he would sit alone, his wife dead,\nhis son asleep--trying to read his newspaper, but staring out from\ntime to time through the window and feeling very companion-less).\nDinner was no longer dinner; there was \"luncheon\" to which nobody\ncame except on Saturdays. Then there was another thing (called by\nthe old name of dinner) at half-past seven, and what had happened to\nsupper no one ever made out. Some people said it had gone to\nPrince's, but certainly the Owner never followed it there.\n\nOn the next floor was the Drawing-room, noted for its cabinet of\ncuriosities, its small aquarium, its large sofa, its piano and its\ninlaid table. The back of the drawing-room was another room beyond\nfolding doors. This would have been convenient if a dance had ever\nbeen given in the house. On the other side were the best bedroom and\na dressing-room. Each in its way what might be expected, save that at\nthe head of the best bed were two little pockets as in the time of our\ngrandfathers; also there was a Chevalier looking-glass and on the\ndressing-table a pin-cushion with pins arranged in a pattern. The\nfire-place and the mantelpiece were of white marble and had on them\ntwo white vases picked out in bright green, a clock with a bronze\nupon it representing a waiter dressed up partly in fifteenth-century\nplate and partly in twelfth-century mail, and on the wall were two\nJewish texts, each translated into Jacobean English and illuminated\nwith a Victorian illumination. One said: \"He hath prevented all my\nways.\" The other said: \"Wisdom is better than Rubies.\" But the gothic\n\"u\" was ill made and it looked like \"Rabies.\" There was also in the\nroom a good wardrobe of a kind now difficult to get, made out of cedar\nand very reasonable in arrangement. There was, moreover (now it occurs\nto me), a little table for writing on; there was writing paper with\n\"Wood Thorpe\" on it, but there were no stamps, and the ink was dry in\nthe bottles (for there were two bottles).\n\nWell, now, shall I be at the pains of telling you what there was\nupstairs? Not I! I am tired enough as it is of detailing all these\nthings. I will speak generally. There were four bedrooms. They were\nused by the family, and above there was an attic which belonged to\nthe servants. The decoration of the wall was everywhere much the\nsame, save that it got a little meaner as one rose, till at last, in\nthe top rooms of all, there was nothing but little photographs of\nsweethearts or pictures out of illustrated papers stuck against the\nwalls. The wall-paper, that had cost 3_s_. 3_d_. a piece in the hall and\ndining-room, and 7_s_. 6_d_. in the drawing-room, suddenly began to\ncost 1_s_. 4_d_. in the upper story and the attic was merely whitewashed.\n\nOne thing more there was, a little wooden gate. It had been put\nthere when the children were little, and had remained ever since at\nthe top of the stairs. Why? It may have been mere routine. It may\nhave been romance. The Owner was a practical man, and the little\ngate was in the way; it was true he never had to shut and open it on\nhis way to bed, and but rarely even saw it. Did he leave it there\nfrom a weak sentiment or from a culpable neglect? He was not a\nsentimental man; on the other hand, he was not negligent. There is a\ngreat deal to be said on both sides, and it is too late to discuss\nthat now.\n\nHeaven send us such a house, or a house of some kind; but Heaven\nsend us also the liberty to furnish it as we choose. For this it was\nthat made the Owner's joy: he had done what he liked in his own\nsurroundings, and I very much doubt whether the people who live in\nQueen Anne houses or go in for timber fronts can say the same.\n\n\n\n\nONE THE ILLNESS OF MY MUSE\n\n\nThe other day I noticed that my Muse, who had long been ailing,\nsilent and morose, was showing signs of actual illness.\n\nNow, though it is by no means one of my habits to coddle the dogs,\ncats and other familiars of my household, yet my Muse had so pitiful\nan appearance that I determined to send for the doctor, but not\nbefore I had seen her to bed with a hot bottle, a good supper, and\nsuch other comforts as the Muses are accustomed to value. All that\ncould be done for the poor girl was done thoroughly; a fine fire was\nlit in her bedroom, and a great number of newspapers such as she is\ngiven to reading for her recreation were bought at a neighbouring\nshop. When she had drunk her wine and read in their entirety the\n_Daily Telegraph_, the _Morning Post_, the _Standard_, the _Daily\nMail_, the _Daily Express_, the _Times_, the _Daily News_, and\neven the _Advertiser_, I was glad to see her sink into a profound\nslumber.\n\nI will confess that the jealousy which is easily aroused among\nservants when one of their number is treated with any special\ncourtesy gave me some concern, and I was at the pains of explaining\nto the household not only the grave indisposition from which the\nMuse suffered, but also the obligation I was under to her on account\nof her virtues: which were, her long and faithful service, her\nwillingness, and the excess of work which she had recently been\ncompelled to perform. Her fellow-servants, to my astonishment and\npleasure, entered at once into the spirit of my apology: the still-room\nmaid offered to sit up with her all night, or at least until the\ntrained nurse should arrive, and the groom of the chambers, with\na good will that I confess was truly surprising in one of his proud\nnature, volunteered to go himself and order straw for the street\nfrom a neighbouring stable.\n\nThe cause of this affection which the Muse had aroused in the whole\nhousehold I subsequently discovered to lie in her own amiable and\nunselfish temper. She had upon two occasions inspired the knife-boy\nto verses which had subsequently appeared in the _Spectator_,\nand with weekly regularity she would lend her aid to the cook in the\ncomposition of those technical reviews by which (as it seemed) that\ndomestic increased her ample wages.\n\nThe Muse had slept for a full six hours when the doctor arrived--a\nspecialist in these matters and one who has before now been called\nin (I am proud to say) by such great persons as Mr. Hichens, Mr.\nChurchill, and Mr. Roosevelt when their Muses have been out of\nsorts. Indeed, he is that doctor who operated for aphasia upon the\nMuse of the late Mr. Rossetti just before his demise. His fees are\nhigh, but I was willing enough to pay, and certainly would never\nhave consented--as have, I regret to say, so many of my unworthy\ncontemporaries--to employ a veterinary surgeon upon such an\noccasion.\n\nThe great specialist approached with a determined air the couch\nwhere the patient lay, awoke her according to the ancient formula,\nand proceeded to question her upon her symptoms. He soon discovered\ntheir gravity, and I could see by his manner that he was anxious to\nan extreme. The Muse had grown so weak as to be unable to dictate\neven a little blank verse, and the indisposition had so far affected\nher mind that she had no memory of Parnassus, but deliriously\nmaintained that she had been born in the home counties--nay, in the\nneighbourhood of Uxbridge. Her every phrase was a deplorable\ncommonplace, and, on the physician applying a stethoscope and\nbegging her to attempt some verse, she could give us nothing better\nthan a sonnet upon the expansion of the Empire. Her weakness was\nsuch that she could do no more than awake, and that feebly, while\nshe professed herself totally unable to arise, to expand, to soar,\nto haunt, or to perform any of those exercises which are proper to\nher profession.\n\nWhen his examination was concluded the doctor took me aside and\nasked me upon what letters the patient had recently fed. I told him\nupon the daily Press, some of the reviews, the telegrams from the\nlatest seat of war, and occasionally a debate in Parliament. At this\nhe shook his head and asked whether too much had not recently been\nasked of her. I admitted that she had done a very considerable\namount of work for so young a Muse in the past year, though its\nquality was doubtful, and I hastened to add that I was the less to\nblame as she had wasted not a little of her powers upon others\nwithout asking my leave; notably upon the knife-boy and the cook.\n\nThe doctor was then good enough to write out a prescription in Latin\nand to add such general recommendations as are commonly of more\nvalue than physic. She was to keep her bed, to be allowed no modern\nliterature of any kind, unless Milton and Swift may be admitted as\nmoderns, and even these authors and their predecessors were to be\nadmitted in very sparing quantities. If any signs of inversion,\narchaism, or neologistic tendencies appeared he was to be summoned\nat once; but of these (he added) he had little fear. He did not\ndoubt that in a few weeks we should have her up and about again, but\nhe warned me against letting her begin work too soon.\n\n\"I would not,\" he said, \"permit her to undertake any effort until\nshe can inspire within one day of twelve hours at least eighteen\nquatrains, and those lucid, grammatical, and moving. As for single\nlines, tags, fine phrases, and the rest, they are no sign whatever\nof returning health, if anything of the contrary.\"\n\nHe also begged that she might not be allowed any Greek or Latin for\nten days, but I reassured him upon the matter by telling him that\nshe was totally unacquainted with those languages--at which he\nexpressed some pleasure but even more astonishment.\n\nAt last he told me that he was compelled to be gone; the season had\nbeen very hard, nor had he known so general a breakdown among the\nMuses of his various clients.\n\nI thought it polite as I took him to the door to ask after some of\nhis more distinguished patients; he was glad to say that the\nArchbishop of Armagh's was very vigorous indeed, in spite of the age\nof her illustrious master. He had rarely known a more inventive or\ncourageous female, but when, as I handed him into his carriage, I\nasked after that of Mr. Kipling, his face became suddenly grave; and\nhe asked me, \"Have you not heard?\"\n\n\"No,\" said I; but I had a fatal presentiment of what was to follow,\nand indeed I was almost prepared for it when he answered in solemn\ntones:\n\n\"She is dead.\"\n\n\n\n\nON A DOG AND A MAN ALSO\n\n\nThere lives in the middle of the Weald upon the northern edge of a\nsmall wood where a steep brow of orchard pasture goes down to a\nlittle river, a Recluse who is of middle age and possessed of all\nthe ordinary accomplishments; that is, French and English literature\nare familiar to him, he can himself compose, he has read his\nclassical Latin and can easily decipher such Greek as he has been\ntaught in youth. He is unmarried, he is by birth a gentleman, he\nenjoys an income sufficient to give him food and wine, and has for\ncompanion a dog who, by the standard of dogs, is somewhat more\nelderly than himself.\n\nThis dog is called Argus, not that he has a hundred eyes nor even two,\nindeed he has but one; for the other, or right eye, he lost the sight\nof long ago from luxury and lack of exercise. This dog Argus is neither\nsmall nor large; he is brown in colour and covered--though now but\npartially--with curly hair. In this he resembles many other dogs, but\nhe differs from most of his breed in a further character, which is\nthat by long association with a Recluse he has acquired a human manner\nthat is unholy. He is fond of affected poses. When he sleeps it is with\nthat abandonment of fatigue only naturally to be found in mankind. He\nwatches sunsets and listens mournfully to music. Cooked food is dearer\nto him than raw, and he will eat nuts--a monstrous thing in a dog and\nproof of corruption.\n\nNevertheless, or, rather, on account of all this, the dog Argus is\nexceedingly dear to his master, and of both I had the other day a\nsingular revelation when I set out at evening to call upon my\nfriend.\n\nThe sun had set, but the air was still clear and it was light enough\nto have shot a bat (had there been bats about and had one had a gun)\nwhen I knocked at the cottage door and opened it. Right within, one\ncomes to the first of the three rooms which the Recluse possesses,\nand there I found him tenderly nursing the dog Argus, who lay\ngroaning in the arm-chair and putting on all the airs of a Christian\nman at the point of death.\n\nThe Recluse did not even greet me, but asked me only in a hurried\nway how I thought the dog Argus looked. I answered gravely and in a\nlow tone so as not to disturb the sufferer, that as I had not seen\nhim since Tuesday, when he was, for an elderly dog, in the best of\nhealth, he certainly presented a sad contrast, but that perhaps he\nwas better than he had been some few hours before, and that the\nRecluse himself would be the best judge of that.\n\nMy friend was greatly relieved at what I said, and told me that he\nthought the dog was better, compared at least with that same\nmorning; then, whether you believe it or not, he took him by the\nleft leg just above the paw and held it for a little time as though\nhe were feeling a pulse, and said, \"He came back less than twenty-four\nhours ago!\" It seemed that the dog Argus, for the first time in fourteen\nyears, had run away, and that for the first time in perhaps twenty or\nthirty years the emotion of loss had entered into the life of the\nRecluse, and that he had felt something outside books and outside\nthe contemplation of the landscape about his hermitage.\n\nIn a short time the dog fell into a slumber, as was shown by a\nnumber of grunts and yaps which proved his sleep, for the dog Argus\nis of that kind which hunts in dreams. His master covered him\nreverently rather than gently with an Indian cloth and, still\nleaving him in the armchair, sat down upon a common wooden chair\nclose by and gazed pitifully at the fire. For my part I stood up and\nwondered at them both, and wondered also at that in man by which he\nmust attach himself to something, even if it be but a dog, a\npolitician, or an ungrateful child.\n\nWhen he had gazed at the fire a little while the Recluse began to\ntalk, and I listened to him talking:\n\n\"Even if they had not dug up so much earth to prove it I should have\nknown,\" said he, \"that the Odyssey was written not at the beginning\nof a civilisation nor in the splendour of it, but towards its close.\nI do not say this from the evening light that shines across its\npages, for that is common to all profound work, but I say it because\nof the animals, and especially because of the dog, who was the only\none to know his master when that master came home a beggar to his\nown land, before his youth was restored to him, and before he got\nback his women and his kingship by the bending of his bow, and\nbefore he hanged the housemaids and killed all those who had\ndespised him.\"\n\n\"But how,\" said I (for I am younger than he), \"can the animals in\nthe poem show you that the poem belongs to a decline?\"\n\n\"Why,\" said he, \"because at the end of a great civilisation the air\ngets empty, the light goes out of the sky, the gods depart, and men\nin their loneliness put out a groping hand, catching at the\nfriendship of, and trying to understand, whatever lives and suffers\nas they do. You will find it never fail that where a passionate\nregard for the animals about us, or even a great tenderness for\nthem, is to be found there is also to be found decay in the State.\"\n\n\"I hope not,\" said I. \"Moreover, it cannot be true, for in the\nThirteenth Century, which was certainly the healthiest time we ever\nhad, animals were understood; and I will prove it to you in several\ncarvings.\"\n\nHe shrugged his shoulders and shook his head, saying, \"In the rough\nand in general it is true; and the reason is the reason I have given\nyou, that when decay begins, whether of a man or of a State, there\ncomes with it an appalling and a torturing loneliness in which our\nenergies decline into a strong affection for whatever is constantly\nour companion and for whatever is certainly present upon earth. For\nwe have lost the sky.\"\n\n\"Then if the senses are so powerful in a decline of the State there\nshould come at the same time,\" said I, \"a quick forgetfulness of the\nhuman dead and an easy change of human friendship?\"\n\n\"There does,\" he answered, and to that there was no more to be said.\n\n\"I know it by my own experience,\" he continued. \"When, yesterday, at\nsunset, I looked for my dog Argus and could not find him, I went out\ninto the wood and called him: the darkness came and I found no trace\nof him. I did not hear him barking far off as I have heard him\nbefore when he was younger and went hunting for a while, and three\ntimes that night I came back out of the wild into the warmth of my\nhouse, making sure he would have returned, but he was never there.\nThe third time I had gone a mile out to the gamekeeper's to give him\nmoney if Argus should be found, and I asked him as many questions\nand as foolish as a woman would ask. Then I sat up right into the\nnight, thinking that every movement of the wind outside or of the\ndrip of water was the little pad of his step coming up the\nflagstones to the door. I was even in the mood when men see unreal\nthings, and twice I thought I saw him passing quickly between my\nchair and the passage to the further room. But these things are\nproper to the night and the strongest thing I suffered for him was\nin the morning.\n\n\"It was, as you know, very bitterly cold for several days. They\nfound things dead in the hedgerows, and there was perhaps no running\nwater between here and the Downs. There was no shelter from the\nsnow. There was no cover for my friend at all. And when I was up at\ndawn with the faint light about, a driving wind full of sleet filled\nall the air. Then I made certain that the dog Argus was dead, and\nwhat was worse that I should not find his body: that the old dog had\ngot caught in some snare or that his strength had failed him through\nthe cold, as it fails us human beings also upon such nights,\nstriking at the heart.\n\n\"Though I was certain that I would not see him again yet I went on\nfoolishly and aimlessly enough, plunging through the snow from one\nspinney to another and hoping that I might hear a whine. I heard\nnone: and if the little trail he had made in his departure might\nhave been seen in the evening, long before that morning the drift\nwould have covered it.\n\n\"I had eaten nothing and yet it was near noon when I returned,\npushing forward to the cottage against the pressure of the storm,\nwhen I found there, miserably crouched, trembling, half dead, in the\nlee of a little thick yew beside my door, the dog Argus; and as I\ncame his tail just wagged and he just moved his ears, but he had not\nthe strength to come near me, his master.\"\n\n[Greek: ourae men rh ho g esaene kai ouata kabbalen ampho, asson d\nouket epeita dunaesato oio anaktos elthemen.]\n\n\"I carried him in and put him here, feeding him by force, and I have\nrestored him.\"\n\nAll this the Recluse said to me with as deep and as restrained\nemotion as though he had been speaking of the most sacred things, as\nindeed, for him, these things were sacred.\n\nIt was therefore a mere inadvertence in me, and an untrained habit\nof thinking aloud, which made me say:\n\n\"Good Heavens, what will you do when the dog Argus dies?\"\n\nAt once I wished I had not said it, for I could see that the Recluse\ncould not bear the words. I looked therefore a little awkwardly\nbeyond him and was pleased to see the dog Argus lazily opening his\none eye and surveying me with torpor and with contempt. He was\ncertainly less moved than his master.\n\nThen in my heart I prayed that of these two (unless The God would\nmake them both immortal and catch them up into whatever place is\nbetter than the Weald, or unless he would grant them one death\ntogether upon one day) that the dog Argus might survive my friend,\nand that the Recluse might be the first to dissolve that long\ncompanionship. For of this I am certain, that the dog would suffer\nless; for men love their dependents much more than do their\ndependents them; and this is especially true of brutes; for men are\nnearer to the gods.\n\n\n\n\nON TEA\n\n\nWhen I was a boy--\n\nWhat a phrase! What memories! O! Noctes Coenasque De\u00fbm! Why, then,\nis there something in man that wholly perishes? It is against sound\nreligion to believe it, but the world would lead one to imagine it.\nThe Hills are there. I see them as I write. They are the cloud or\nwall that dignified my sixteenth year. And the river is there, and\nflows by that same meadow beyond my door; from above Coldwatham the\nsame vast horizon opens westward in waves of receding crests more\nchangeable and more immense than is even our sea. The same sunsets\nat times bring it all in splendour, for whatever herds the western\nclouds together in our stormy evenings is as stable and as vigorous\nas the County itself. If, therefore, there is something gone, it is\nI that have lost it.\n\nCertainly something is diminished (the Priests and the tradition of\nthe West forbid me to say that the soul can perish), certainly\nsomething is diminished--what? Well, I do not know its name, nor has\nanyone known it face to face or apprehended it in this life, but the\nsense and influence--alas! especially the memory of It, lies in the\nwords \"When I was a boy,\" and if I write those words again in any\ndocument whatsoever, even in a lawyer's letter, without admitting at\nonce a full-blooded and galloping parenthesis, may the Seven Devils\nof Sense take away the last remnant of the joy they lend me.\n\nWhen I was a boy there was nothing all about the village or the\nwoods that had not its living god, and all these gods were good. Oh!\nHow the County and its Air shone from within; what meaning lay in\nunexpected glimpses of far horizons; what a friend one was with the\nclouds!\n\nWell, all I can say to the Theologians is this:\n\n\"I will grant you that the Soul does not decay: you know more of\nsuch flimsy things than I do. But you, on your side, must grant me\nthat there is Something which does not enter into your systems. That\nhas perished, and I mean to mourn it all the days of my life. Pray\ndo not interfere with that peculiar ritual.\"\n\nWhen I was a boy I knew Nature as a child knows its nurse, and Tea I\ndenounced for a drug. I found to support this fine instinct many\narguments, all of which are still sound, though not one of them\nwould prevent me now from drinking my twentieth cup. It was\nintroduced late and during a corrupt period. It was an exotic. It\nwas a sham exhilarant to which fatal reactions could not but attach.\nIt was no part of the Diet of the Natural Man. The two nations that\nalone consume it--the English and the Chinese--are become, by its\nbaneful influence on the imagination, the most easily deceived in\nthe world. Their politics are a mass of bombastic illusions. Also it\ndries their skins. It tans the liver, hardens the coats of the\nstomach, makes the brain feverishly active, rots the nerve-springs;\nall that is still true. Nevertheless I now drink it, and shall drink\nit; for of all the effects of Age none is more profound than this:\nthat it leads men to the worship of some one spirit less erect than\nthe Angels. A care, an egotism, an irritability with regard to\ndetails, an anxious craving, a consummate satisfaction in the\nperformance of the due rites, an ecstasy of habit, all proclaim the\nsenile heresy, the material Religion. I confess to Tea.\n\nAll is arranged in this Cult with the precision of an ancient creed.\nThe matter of the Sacrifice must come from China. He that would\ndrink Indian Tea would smoke hay. The Pot must be of metal, and the\nmetal must be a white metal, not gold or iron. Who has not known the\nacidity and paucity of Tea from a silver-gilt or golden spout? The\nPot must first be warmed by pouring in a little _boiling_ water\n(the word _boiling_ should always be underlined); then the\nwater is poured away and a few words are said. Then the Tea is put\nin and unrolls and spreads in the steam. Then, in due order, on\nthese expanding leaves _Boiling_ Water is largely poured and\nthe god arises, worthy of continual but evil praise and of the\nthanks of the vicious, a Deity for the moment deceitfully kindly to\nmen. Under his influence the whole mind receives a sharp vision of\npower. It is a phantasm and a cheat. Men can do wonders through\nwine; through Tea they only think themselves great and clear--but\nthat is enough if one has bound oneself to that strange idol and\nlearnt the magic phrase on His Pedestal, [Greek: ARISTON MEN TI],\nfor of all the illusions and dreams men cherish none is so grandiose\nas the illusion of conscious power within.\n\n * * * * *\n\nWell, then, it fades.... I begin to see that this cannot continue\n... of Tea it came, inconsecutive and empty; with the influence of\nTea dissolving, let these words also dissolve.... I could wish it\nhad been Opium, or Haschisch, or even Gin; you would have had\nsomething more soaring for your money.... _In vino Veritas. In\nAqua satietas. In_ ... What is the Latin for Tea? What! Is there\nno Latin word for Tea? Upon my soul, if I had known that I would\nhave let the vulgar stuff alone.\n\n\n\n\nON THEM\n\n\nI do not like Them. It is no good asking me why, though I have\nplenty of reasons. I do not like Them. There would be no particular\npoint in saying I do not like Them if it were not that so many\npeople doted on Them, and when one hears Them praised, it goads one\nto expressing one's hatred and fear of Them.\n\nI know very well that They can do one harm, and that They have\noccult powers. All the world has known that for a hundred thousand\nyears, more or less, and every attempt has been made to propitiate\nThem. James I. would drown Their mistress or burn her, but\n_They_ were spared. Men would mummify Them in Egypt, and\nworship the mummies; men would carve Them in stone in Cyprus, and\nCrete and Asia Minor, or (more remarkable still) artists, especially\nin the Western Empire, would leave Them out altogether; so much was\nTheir influence dreaded. Well, I yield so far as not to print Their\nname, and only to call Them \"They\", but I hate Them, and I'm not\nafraid to say so.\n\nIf you will take a little list of the chief crimes that living\nbeings can commit you will find that They commit them all. And They\nare cruel; cruelty is even in Their tread and expression. They are\nhatefully cruel. I saw one of Them catch a mouse the other day (the\ncat is now out of the bag), and it was a very much more sickening\nsight, I fancy, than ordinary murder. You may imagine that They\ncatch mice to eat them. It is not so. They catch mice to torture them.\nAnd what is worse, They will teach this to Their children--Their\nchildren who are naturally innocent and fat, and full of goodness,\nare deliberately and systematically corrupted by Them; there is\ndiabolism in it.\n\nOther beings (I include mankind) will be gluttonous, but gluttonous\nspasmodically, or with a method, or shamefacedly, or, in some way or\nanother that qualifies the vice; not so They. They are gluttonous\nalways and upon all occasions, and in every place and for ever. It\nwas only last Vigil of All Fools' Day when, myself fasting, I filled\nup the saucer seven times with milk and seven times it was emptied,\nand there went up the most peevish, querulous, vicious complaint and\ndemand for an eighth. They will eat some part of the food of all\nthat are in the house. Now even a child, the most gluttonous one\nwould think of all living creatures, would not do that. It makes a\nselection, _They_ do not. _They_ will drink beer. This is not a theory;\nI know it; I have seen it with my own eyes. They will eat special foods;\nThey will even eat dry bread. Here again I have personal evidence of\nthe fact; They will eat the dog's biscuits, but never upon any occasion\nwill They eat anything that has been poisoned, so utterly lacking are\nThey in simplicity and humility, and so abominably well filled with\ncunning by whatever demon first brought their race into existence.\n\nThey also, alone of all creation, love hateful noises. Some beings\nindeed (and I count Man among them) cannot help the voice with which\nthey have been endowed, but they know that it is offensive, and are\nat pains to make it better; others (such as the peacock or the\nelephant) also know that their cry is unpleasant. They therefore use\nit sparingly. Others again, the dove, the nightingale, the thrush,\nknow that their voices are very pleasant, and entertain us with them\nall day and all night long; but They know that Their voices are the\nmost hideous of all the sounds in the world, and, knowing this, They\nperpetually insist upon thrusting those voices upon us, saying, as\nit were, \"I am giving myself pain, but I am giving you more pain,\nand therefore I shall go on.\" And They choose for the place where\nthis pain shall be given, exact and elevated situations, very close\nto our ears. Is there any need for me to point out that in every\ncity they will begin their wicked jar just at the time when its\ninhabitants must sleep? In London you will not hear it till after\nmidnight; in the county towns it begins at ten; in remote villages\nas early as nine.\n\nTheir Master also protects them. They have a charmed life. I have\nseen one thrown from a great height into a London street, which when\nIt reached it It walked quietly away with the dignity of the Lost\nWorld to which It belonged.\n\nIf one had the time one could watch Them day after day, and never\nsee Them do a single kind or good thing, or be moved by a single\nvirtuous impulse. They have no gesture for the expression of\nadmiration, love, reverence or ecstasy. They have but one method of\nexpressing content, and They reserve that for moments of physical\nrepletion. The tail, which is in all other animals the signal for\njoy or for defence, or for mere usefulness, or for a noble anger, is\nwith Them agitated only to express a sullen discontent.\n\nAll that They do is venomous, and all that They think is evil, and\nwhen I take mine away (as I mean to do next week--in a basket), I\nshall first read in a book of statistics what is the wickedest part\nof London, and I shall leave It there, for I know of no one even\namong my neighbours quite so vile as to deserve such a gift.\n\n\n\n\nON RAILWAYS AND THINGS\n\n\nRailways have changed the arrangement and distribution of crowds and\nsolitude, but have done nothing to disturb the essential contrast\nbetween them.\n\nThe more behindhand of my friends, among whom I count the weary men\nof the towns, are ceaselessly bewailing the effect of railways and\nthe spoiling of the country; nor do I fail, when I hear such\ncomplaints, to point out their error, courteously to hint at their\nsheep-like qualities, and with all the delicacy imaginable to let\nthem understand they are no better than machines repeating worn-out\nformulae through the nose. The railways and those slow lumbering\nthings the steamboats have not spoilt our solitudes, on the contrary\nthey have intensified the quiet of the older haunts, they have\ncreated new sanctuaries, and (crowning blessing) they make it easy\nfor us to reach our refuges.\n\nFor in the first place you will notice that new lines of travel are\nlike canals cut through the stagnant marsh of an old civilisation,\ndraining it of populace and worry, and concentrating upon themselves\nthe odious pressure of humanity.\n\nYou know (to adopt the easy or conversational style) that you and I\nbelong to a happy minority. We are the sons of the hunters and the\nwandering singers, and from our boyhood nothing ever gave us greater\npleasure than to stand under lonely skies in forest clearings, or to\nfind a beach looking westward at evening over unfrequented seas. But\nthe great mass of men love companionship so much that nothing seems\nof any worth compared with it. Human communion is their meat and\ndrink, and so they use the railways to make bigger and bigger hives\nfor themselves.\n\nNow take the true modern citizen, the usurer. How does the usurer\nsuck the extremest pleasure out of his holiday? He takes the train\npreferably at a very central station near the Strand, and (if he can\nchoose his time) on a foggy and dirty day; he picks out an express\nthat will take him with the greatest speed through the Garden of Eden,\nnor does he begin to feel the full savour of relaxation till a row of\nabominable villas' appears on the southern of what were once the\ndowns; these villas stand like the skirmishers of a foul army deployed:\nhe is immediately whirled into Brighton and is at peace. There he has\nhis wish for three days; there he can never see anything but houses,\nor, if he has to walk along the sea, he can rest his eye on herds of\nunhappy people and huge advertisements, and he can hear the newspaper\nboys telling lies (perhaps special lies he has paid for) at the top of\ntheir voices; he can note as evening draws on the pleasant glare of gas\nupon the street mud and there pass him the familiar surroundings of\nservility, abject poverty, drunkenness, misery, and vice. He has his\nmusic-hall on the Saturday evening with the sharp, peculiar finish of\nthe London accent in the patriotic song, he has the London paper on\nSunday to tell him that his nastiest little Colonial War was a crusade,\nand on Monday morning he has the familiar feeling that follows his\nexcesses of the previous day.... Are you not glad that such men and\ntheir lower-fellows swarm by hundreds of thousands into the \"resorts\"?\nDo you not bless the railways that take them so quickly from one Hell\nto another.\n\nNever let me hear you say that the railways spoil a countryside;\nthey do, it is true, spoil this or that particular place--as, for\nexample, Crewe, Brighton, Stratford-on-Avon--but for this\ndisadvantage they give us I know not how many delights. What is more\nEnglish than the country railway station? I defy the eighteenth\ncentury to produce anything more English, more full of home and rest\nand the nature of the country, than my junction. Twenty-seven trains\na day stop at it or start from it; it serves even the expresses.\nSmith's monopoly has a bookstall there; you can get cheap Kipling\nand Harmsworth to any extent, and yet it is a theme for English\nidylls. The one-eyed porter whom I have known from childhood; the\nstation-master who ranges us all in ranks, beginning with the Duke\nand ending with a sad, frayed and literary man; the little chaise in\nwhich the two old ladies from Barlton drive up to get their paper of\nan evening, the servant from the inn, the newsboy whose mother keeps\na sweetshop--they are all my village friends. The glorious Sussex\naccent, whose only vowel is the broad \"a\", grows but more rich and\nemphatic from the necessity of impressing itself upon foreign\nintruders. The smoke also of the train as it skirts the Downs is\npart and parcel of what has become (thanks to the trains) our\nencloistered country life; the smoke of the trains is a little\nsmudge of human activity which permits us to match our incomparable\nseclusion with the hurly-burly from which we have fled. Upon my\nsoul, when I climb up the Beacon to read my book on the warm turf,\nthe sight of an engine coming through the cutting is an emphasis of\nmy selfish enjoyment. I say \"There goes the Brighton train\", but the\nimage of Brighton, with its Anglo-Saxons and its Vision of Empire,\ndoes not oppress me; it is a far-off thing; its life ebbs and flows\nalong that belt of iron to distances that do not regard me.\n\nConsider this also with regard to my railway: it brings me what I\nwant in order to be perfect in my isolation. Those books discussing\nProblems: whether or not there is such an idea as right; the\ninconvenience of being married; the worry of being Atheist and yet\nliving upon a clerical endowment,--these fine discussions come from\na library in a box by train and I can torture myself for a shilling,\nwhereas, before the railways, I should have had to fall back on the\n_Gentleman's Magazine_ and the County History. In the way of\nnewspapers it provides me with just the companionship necessary to a\nhermitage. Often and often, after getting through one paper, I\nstroll down to the junction and buy fifteen others, and so enjoy the\nfruits of many minds.\n\nThanks to my railway I can sit in the garden of an evening and read\nmy paper as I smoke my pipe, and say, \"Ah! That's Buggin's work. I\nremember him well; he worked for Rhodes.... Hullo! Here's Simpson at\nit again; since when did they buy _him_?...\" And so forth. I lead\nmy pastoral life, happy in the general world about me, and I serve,\nas sauce to such healthy meat, the piquant wickedness of the town;\nnor do I ever note a cowardice, a lie, a bribery, or a breach of\ntrust, a surrender in the field, or a new Peerage, but I remember\nthat my newspaper could not add these refining influences to my life\nbut for the _railway_ which I set out to praise at the beginning of\nthis and intend to praise manfully to the end.\n\nYet another good we owe to railways occurs to me. They keep the\nsmall towns going.\n\nDon't pester me with \"economics\" on that point; I know more\neconomics than you, and I say that but for the railways the small\ntowns would have gone to pieces. There never yet was a civilisation\ngrowing richer and improving its high roads in which the small towns\ndid not dwindle. The village supplied the local market with bodily\nnecessaries; the intellectual life, the civic necessities had to go\ninto the large towns. It happened in the second and third centuries\nin Italy; it happened in France between Henri IV and the Revolution;\nit was happening here before 1830.\n\nTake those little paradises Ludlow and Leominster; consider Arundel,\nand please your memory with the admirable s of Whitchurch; grow\ncontented in a vision of Ledbury, of Rye, or of Abingdon, or of\nBeccles with its big church over the river, or of Newport in the\nIsle of Wight, or of King's Lynn, or of Lymington--you would not\nhave any of these but for the railway, and there are 1800 such in\nEngland--one for every tolerable man.\n\nValognes in the Cotentin, Bourg-d'Oysan down in the Dauphin\u00e9 in its\nvast theatre of upright hills, St. Julien in the Limousin,\nAubusson-in-the-hole, Puy (who does not connect beauty with the\nword?), Mansle in the Charente country--they had all been half dead\nfor over a century when the railway came to them and made them\njolly, little, trim, decent, self-contained, worthy, satisfactory,\ngenial, comforting and human [Greek: politeiae], with clergy, upper\nclass, middle class, poor, soldiers, yesterday's news, a college,\nanti-Congo men, fools, strong riders, old maids, and all that makes\na state. In England the railway brought in that beneficent class,\nthe gentlemen; in France, that still more beneficent class, the\nHaute Bourgeoisie.\n\nI know what you are going to say; you are going to say that there\nwere squires before the railways in England. Pray have you\nconsidered how many squires there were to go round? About half a\ndozen squires to every town, that is (say) four gentlemen, and of\nthose four gentlemen let us say two took some interest in the place.\nIt wasn't good enough ... and heaven help the country towns now if\nthey had to depend on the great houses! There would be a smart dog-cart\nonce a day with a small (vicious and servile) groom in it, an actor, a\nforeign money-lender, a popular novelist, or a newspaper owner jumping\nout to make his purchases and driving back again to his host's within\nthe hour. No, no; what makes the country town is the Army, the Navy,\nthe Church, and the Law--especially the retired ones.\n\nThen think of the way in which the railways keep a good man's\ninfluence in a place and a bad man's out of it. Your good man loves\na country town, but he must think, and read, and meet people, so in\nthe last century he regretfully took a town house and had his little\nhouse in the country as well. Now he lives in the country and runs\nup to town when he likes.\n\nHe is always a permanent influence in the little city--especially if\nhe has but \u00a3400 a year, which is the normal income of a retired\ngentleman (yes, it is so, and if you think it is too small an\nestimate, come with me some day and make an inquisitorial tour of my\ntown). As for the vulgar and cowardly man, he hates small towns\n(fancy a South African financier in a small town!), well, the\nrailway takes him away. Of old he might have had to stay there or\nstarve, now he goes to London and runs a rag, or goes into\nParliament, or goes to dances dressed up in imitation of a soldier;\nor he goes to Texas and gets hanged--it's all one to me. He's out of\nmy town.\n\nAnd as the railways have increased the local refinement and virtue,\nso they have ennobled and given body to the local dignitary. What\nwould the Bishop of Caen (he calls himself Bishop of Lisieux and\nBayeux, but that is archaeological pedantry); what, I say, would the\nBishop of Caen be without his railway? A Phantom or a Paris magnate.\nWhat the Mayor of High Wycombe? Ah! what indeed! But I cannot waste\nany more of this time of mine in discussing one aspect of the\nrailway; what further I have to say on the subject shall be\npresented in due course in my book on _The Small Town of\nChristendom_ [Footnote: _The Small Town of Christendom: an\nAnalytical Study_. With an Introduction by Joseph Reinach. Ulmo\net Cie. \u00a325 nett.] I will close this series of observations with a\nlittle list of benefits the railway gives you, many of which would\nnot have occurred to you but for my ingenuity, some of which you may\nhave thought of at some moment or other, and yet would never have\nretained but for my patient labour in this.\n\nThe railway gives you seclusion. If you are in an express alone you\nare in the only spot in Western Europe where you can be certain of\ntwo or three hours to yourself. At home in the dead of night you may\nbe wakened by a policeman or a sleep-walker or a dog. The heaths are\npopulous. You cannot climb to the very top of Helvellyn to read your\nown poetry to yourself without the fear of a tourist. But in the\ncorner of a third-class going north or west you can be sure of your\nown company; the best, the most sympathetic, the most brilliant in\nthe world.\n\nThe railway gives you sharp change. And what we need in change is\nsurely keenness. For instance, if one wanted to go sailing in the\nold days, one left London, had a bleak drive in the country, got\nnearer and nearer the sea, felt the cold and wet and discomfort\ngrowing on one, and after half a day or a day's gradual introduction\nto the thing, one would at last have got on deck, wet and wretched,\nand half the fun over. Nowadays what happens? Why, the other day, a\nrich man was sitting in London with a poor friend; they were\ndiscussing what to do in three spare days they had. They said \"let\nus sail.\" They left London in a nice warm, comfortable, rich-padded,\nswelly carriage at four, and before dark they were letting\neverything go, putting on the oilies, driving through the open in\nfront of it under a treble-reefed storm jib, praying hard for their\nlives in last Monday's gale, and wishing to God they had stayed at\nhome--all in the four hours. That is what you may call piquant, it\nbraces and refreshes a man.\n\nFor the rest I cannot detail the innumerable minor advantages of\nrailways; the mild excitement which is an antidote to gambling; the\nshaking which (in moderation) is good for livers; the meeting\nfamiliarly with every kind of man and talking politics to him; the\ndelight in rapid motion; the luncheon-baskets; the porters; the\nsolid guard; the strenuous engine-driver (note this next time you\ntravel--it is an accurate observation). And of what other kind of\nmodern thing can it be said that more than half pay dividends?\nThinking of these things, what sane and humorous man would ever\nsuggest that a part of life, so fertile in manifold and human\npleasure, should ever be bought by the dull clique who call\nthemselves \"the State\", and should yield under such a scheme yet\n_more_, yet _larger_, yet _securer_ salaries to the younger sons.\n\n\n\n\nON CONVERSATIONS IN TRAINS\n\n\nI might have added in this list I have just made of the advantages\nof Railways, that Railways let one mix with one's fellow-men and\nhear their continual conversation. Now if you will think of it,\nRailways are the only institutions that give us that advantage. In\nother places we avoid all save those who resemble us, and many men\nbecome in middle age like cabinet ministers, quite ignorant of their\nfellow-citizens. But in Trains, if one travels much, one hears every\nkind of man talking to every other and one perceives all England.\n\nIt is on this account that I have always been at pains to note what\nI heard in this way, especially the least expected, most startling,\nand therefore most revealing dialogues, and as soon as I could to\nwrite them down, for in this way one can grow to know men.\n\nThus I have somewhere preserved a hot discussion among some miners\nin Derbyshire (voters, good people, voters remember) whether the\nUnited States were bound to us as a colony \"like Egypt.\" And I once\nheard also a debate as to whether the word were Horizon or Horizon;\nthis ended in a fight; and the Horizon man pushed the Horizon man\nout at Skipton, and wouldn't let him get into the carriage again.\n\nThen again I once heard two frightfully rich men near Birmingham\narguing why England was the richest and the Happiest Country in the\nworld. Neither of these men was a gentleman but they argued politely\nthough firmly, for they differed profoundly. One of them, who was\nalmost too rich to walk, said it was because we minded our own\naffairs, and respected property and were law-abiding. This (he said)\nwas the cause of our prosperity and of the futile envy with which\nforeigners regarded the homes of our working men. Not so the other:\n_he_ thought that it was the Plain English sense of Duty that\ndid the trick: he showed how this was ingrained in us and appeared\nin our Schoolboys and our Police: he contrasted it with Ireland, and\nhe asked what else had made our Criminal Trials the model of the\nworld? All this also I wrote down.\n\nThen also once on a long ride (yes, \"ride\". Why not?) through\nLincolnshire I heard two men of the smaller commercial or salaried\nkind at issue. The first, who had a rather peevish face, was looking\ngloomily out of window and was saying, \"Denmark has it: Greece has\nit--why shouldn't we have it? Eh? America has it and so's Germany--why\nshouldn't we have it?\" Then after a pause he added, \"Even France has\nit--why haven't we got it?\" He spoke as though he wouldn't stand it\nmuch longer, and as though France were the last straw.\n\nThe other man was excitable and had an enormous newspaper in his\nhand, and he answered in a high voice, \"'Cause we're too sensible,\nthat's why! 'Cause we know what we're about, we do.\"\n\nThe other man said, \"Ho! Do we?\"\n\nThe second man answered, \"Yes: we do. What made England?\"\n\n\"Gord,\" said the first man.\n\nThis brought the second man up all standing and nearly carried away\nhis fore-bob-stay. He answered slowly--\n\n\"Well ... yes ... in a manner of speaking. But what I meant to say\nwas like this, that what made England was Free Trade!\" Here he\nslapped one hand on to the other with a noise like that of a pistol,\nand added heavily: \"And what's more, I can prove it.\"\n\nThe first man, who was now entrenched in his position, said again,\n\"Ho! Can you?\" and sneered.\n\nThe second man then proved it, getting more and more excited. When\nhe had done, all the first man did was to say, \"You talk\nfoolishness.\"\n\nThen there was a long silence: very strained. At last the Free\nTrader pulled out a pipe and filled it at leisure, with a light sort\nof womanish tobacco, and just as he struck a match the Protectionist\nshouted out, \"No you don't! This ain't a smoking compartment. I\nobject!\" The Free Trader said, \"O! that's how it is, is it?\" The\nProtectionist answered in a lower voice and surly, \"Yes: that's\nhow.\"\n\nThey sat avoiding each other's eyes till we got to Grantham. I had\nno idea that feeling could run so high, yet neither of them had a\nreal grip on the Theory of International Exchange.\n\nBut by far the most extraordinary conversation and perhaps the most\nilluminating I ever heard, was in a train going to the West Country\nand stopping first at Swindon.\n\nIt passed between two men who sat in corners facing each other.\n\nThe one was stout, tall, and dressed in a tweed suit. He had a gold\nwatch-chain with a little ornament on it representing a pair of\ncompasses and a square. His beard was brown and soft. His eyes were\nvery sodden. When he got in he first wrapped a rug round and round\nhis legs, then he took off his top hat and put on a cloth cap, then\nhe sat down.\n\nThe other also wore a tweed suit and was also stout, but he was not\nso tall. His watch-chain also was of gold (but of a different\npattern, paler, and with no ornament hung on it). His eyes also were\nsodden. He had no rug. He also took off his hat but put no cap upon\nhis head. I noticed that he was rather bald, and in the middle of\nhis baldness was a kind of little knob. For the purposes of this\nrecord, therefore, I shall give him the name \"Bald,\" while I shall\ncall the other man \"Cap.\"\n\nI have forgotten, by the way, to tell you that Bald had a very large\nnose, at the end of which a great number of little veins had\ncongested and turned quite blue.\n\nCAP (_shuts up Levy's paper, \"The Daily Telegraph,\" and opens\nHarmsworth's \"Daily Mail,\" Shuts that up and looks fixedly at_ BALD):\nI ask your pardon ... but isn't your name Binder?\n\nBALD (_his eyes still quite sodden_): That is my name. Binder's my\nname. (_He coughs to show breeding_.) Why! (_his eyes getting a\ntrifle less sodden_) if you aren't Mr. Mowle! Well, Mr. Mowle, sir,\nhow are you?\n\nCAP (_with some dignity_): Very well, thank you, Mr. Binder.\nHow, how's Mrs. Binder and the kids? All blooming?\n\nBALD: Why, yes, thank you, Mr. Mowle, but Mrs. Binder still has\nthose attacks (_shaking his head_). Abdominal (_continuing to\nshake his head_). Gastric. Something cruel.\n\nCAP: They do suffer cruel, as you say, do women, Mr. Binder\n(_shaking his head too--but more slightly_). This indigestion--ah!\n\nBALD (_more brightly_): Not married yet, Mr. Mowle?\n\nCAP (_contentedly and rather stolidly_): No, Mr. Binder. Nor\nnot inclined to neither. (_Draws a great breath._) I'm a single\nman, Mr. Binder, and intend so to adhere. (_A pause to think._)\nThat's what I call (_a further pause to get the right phrase_)\n\"single blessedness.\" Yes, (_another deep breath_) I find life\nworth living, Mr. Binder.\n\nBALD (_with great cunning_): That depends upon the liver.\n(_Roars with laughter._)\n\nCAP (_laughing a good deal too, but not so much as_ BALD): Ar!\nThat was young Cobbler's joke in times gone by.\n\nBALD (_politely_): Ever see young Cobbler now, Mr. Mowle?\n\nCAP (_with importance_): Why yes, Mr. Binder; I met him at the\nThersites' Lodge down Brixham way--only the other day. Wonderful\nbrilliant he was ... well, there ... (_his tone changes_) he\nwas sitting next to me--(_thoughtfully_)--as, might be here--(_putting\nHarmsworth's paper down to represent Young Cobbler_)--and here like,\nwould be Lord Haltingtowres.\n\nBALD (_his manner suddenly becoming very serious_): He's a\nfine man, he is! One of those men I respect.\n\nCAP (_with still greater seriousness_): You may say that, Mr.\nBinder. No respecter of persons--talks to me or you or any of them\njust the same.\n\nBALD (_vaguely_): Yes, they're a fine lot! (_Suddenly_)\nSo's Charlie Beresford!\n\nCAP (_with more enthusiasm than he had yet shown_): I say ditto\nto that, Mr. Binder! (_Thinking for a few moments of the\ncharacteristics of Lord Charles Beresford._) It's pluck--that's\nwhat it is--regular British pluck (_Grimly_) That's the kind of\nman--no favouritism.\n\nBALD: Ar! it's a case of \"Well done, Condor!\"\n\nCAP: Ar! you're right there, Mr. Binder.\n\nBALD (_suddenly pulling a large flask out of his pocket and\nspeaking very rapidly_): Well, here's yours, Mr. Mowle. (_He\ndrinks out of it a quantity of neat whisky, and having drunk it rubs\nthe top of his flask with his sleeve and hands it over politely to_)\nCAP.\n\nCap (_having drunk a lot of neat whisky also, rubbed his sleeve\nover it, screwed on the little top and giving that long gasp which\nthe occasion demands_): Yes, you're right there--\"Well done.\nCondor.\"\n\nAt this point the train began to go slowly, and just as it stopped\nat the station I heard Cap begin again, asking Bald on what occasion\nand for what services Lord Charles Beresford had been given his\ntitle.\n\nFull of the marvels of this conversation I got out, went into the\nwaiting-room and wrote it all down. I think I have it accurately\nword for word.\n\nBut there happened to me what always happens after all literary\neffort; the enthusiasm vanished, the common day was before me. I\nwent out to do my work in the place and to meet quite ordinary\npeople and to forget, perhaps, (so strong is Time) the fantastic\nbeings in the train. In a word, to quote Mr. Binyon's admirable\nlines:\n\n \"The world whose wrong\n Mocks holy beauty and our desire returned.\"\n\n\n\n\nON THE RETURN OF THE DEAD\n\n\nThe reason the Dead do not return nowadays is the boredom of it.\n\nIn the old time they would come casually, as suited them, without\nfuss and thinly, as it were, which is their nature; but when such\nvisits were doubted even by those who received them and when new and\nfalse names were given them the Dead did not find it worth while. It\nwas always a trouble; they did it really more for our sakes than for\ntheirs and they would be recognised or stay where they were.\n\nI am not certain that they might not have changed with the times and\ncome frankly and positively, as some urged them to do, had it not\nbeen for Rabelais' failure towards the end of the Boer war. Rabelais\n(it will be remembered) appeared in London at the very beginning of\nthe season in 1902. Everybody knows one part of the story or\nanother, but if I put down the gist of it here I shall be of\nservice, for very few people have got it quite right all through,\nand yet that story alone can explain why one cannot get the dead to\ncome back at all now even in the old doubtful way they did in the\n'80's and early '90's of the last century.\n\nThere is a place in heaven where a group of writers have put up a\ncolonnade on a little hill looking south over the plains. There are\nthrones there with the names of the owners on them. It is a sort of\nClub.\n\nRabelais was quarrelling with some fool who had missed fire with a\nmedium and was saying that the modern world wanted positive\nunmistakable appearances: he said he ought to know, because he had\nbegun the modern world. Lucian said it would fail just as much as\nany other way; Rabelais hotly said it wouldn't. He said he would\ncome to London and lecture at the London School of Economics and\nestablish a good solid objective relationship between the two\nworlds. Lucian said it would end badly. Rabelais, who had been\ndrinking, lost his temper and did at once what he had only been\nboasting he would do. He materialised at some expense, and he\nannounced his lecture. Then the trouble began, and I am honestly of\nopinion that if we had treated the experiment more decently we\nshould not have this recent reluctance on the part of the Dead to\npay us reasonable attention.\n\nIn the first place, when it was announced that Rabelais had returned\nto life and was about to deliver a lecture at the London School of\nEconomics, Mrs. Whirtle, who was a learned woman, with a well-deserved\nreputation in the field of objective psychology, called it a rumour\nand discredited it (in a public lecture) on these three grounds:\n\n(_a_) That Rabelais being dead so long ago would not come back\nto life now.\n\n(_b_) That even if he did come back to life it was quite out of\nhis habit to give lectures.\n\n(_c_) That even if he had come back to life and did mean to\nlecture, he would never lecture at the London School of Economics,\nwhich was engaged upon matters principally formulated since\nRabelais' day and with which, moreover, Rabelais' \"essentially\nsynthetical\" mind would find a difficulty in grappling.\n\nAll Mrs. Whirtle's audience agreed with one or more of these\npropositions except Professor Giblet, who accepted all three saving\nand excepting the term \"synthetical\" as applied to Rabelais' mind.\n\"For,\" said he, \"you must not be so deceived by an early use of the\nInducto-Deductive method as to believe that a sixteenth-century man\ncould be, in any true sense, synthetical.\" And this judgment the\nProfessor emphasized by raising his voice suddenly by one octave.\nHis position and that of Mrs. Whirtle were based upon that thorough\nsummary of Rabelais' style in Mr. Effort's book on French\nliterature: each held a sincere position, nevertheless this cold\nwater thrown on the very beginning of the experiment did harm.\n\nThe attitude of the governing class did harm also. Lady Jane Bird saw\nthe announcement on the placards of the evening papers as she went\nout to call on a friend. At tea-time a man called Wantage-Verneyson,\nwho was well dressed, said that he knew all about Rabelais, and a\ngroup of people began to ask questions together: Lady Jane herself\ndid so. Mr. Wantage-Verneyson is (or rather was, alas!) the second\ncousin of the Duke of Durham (he is--or rather was, alas!--the son of\nLord and Lady James Verneyson, now dead), and he said that Rabelais\nwas written by Urquhart a long time ago; this was quite deplorable\nand did infinite harm. He also said that every educated man had read\nRabelais, and that he had done so. He said it was a protest against\nRome and all that sort of thing. He added that the language was\ndifficult to understand. He further remarked that it was full of\nfootnotes, but that he thought these had been put in later by scholars.\nCross-questioned on this he admitted that he did not see what scholars\ncould want with Rabelais. On hearing this and the rest of his\ninformation several ladies and a young man of genial expression began\nto doubt in their turn.\n\nA Hack in Grub Street whom Painful Labour had driven to Despair and\nMysticism read the announcement with curiosity rather than\namazement, fully believing that the Great Dead, visiting as they do\nthe souls, may also come back rarely to the material cities of men.\nOne thing, however, troubled him, and that was how Rabelais, who had\nslept so long in peace beneath the Fig Tree of the Cemetery of St.\nPaul, could be risen now when his grave was weighed upon by No. 32\nof the street of the same name. Howsoever, he would have guessed\nthat the alchemy of that immeasurable mind had in some way got rid\nof the difficulty, and really the Hack must be forgiven for his\nfaith, since one learned enough to know so much about sites, history\nand literature, is learned enough to doubt the senses and to accept\nthe Impossible; unfortunately the fact was vouched for in eight\nnewspapers of which he knew too much and was not accepted in the\nonly sheet he trusted. So he doubted too.\n\nJohn Bowles, of Lombard Street, read the placards and wrought\nhimself up into a fury saying, \"In what other country would these\ncursed Boers be allowed to come and lecture openly like this? It is\nenough to make one excuse the people who break up their meetings.\"\nHe was a little consoled, however, by the thought that his country\nwas so magnanimous, and in the calmer mood of self-satisfaction went\nso far as to subscribe \u00a35 to a French newspaper which was being\nfounded to propagate English opinions on the Continent. He may be\nneglected.\n\nPeter Grierson, attorney, was so hurried and overwrought with the\nwork he had been engaged on that morning (the lending of \u00a31323 to a\nwidow at 5 1\/4 per cent., [which heaven knows is reasonable!] on\nsecurity of a number of shares in the London and North-Western\nRailway) that he misread the placard and thought it ran \"Rabelais\nlecture at the London School Economics\"; disturbed for a moment at\nthe thought of so much paper wasted in time of war for so paltry an\nannouncement, he soon forgot about the whole business and went off\nto \"The Holborn,\" where he had his lunch comfortably standing up at\nthe buffet, and then went and worked at dominoes and cigars for two\nhours.\n\nSir Judson Pennefather, Cabinet Minister and Secretary of State for\nPublic Worship, Literature and the Fine Arts--\n\nBut what have I to do with all these; absurd people upon whom the\nnews of Rabelais' return fell with such varied effect? What have you\nand I to do with men and women who do not, cannot, could not, will\nnot, ought not, have not, did, and by all the thirsty Demons that\nserve the lamps of the cavern of the Sibyl, _shall_ not count\nin the scheme of things as worth one little paring of Rabelais'\nlittle finger nail? What are they that they should interfere with\nthe great mirific and most assuaging and comfortable feast of wit to\nwhich I am now about to introduce you!--for know that I take you now\ninto the lecture-hall and put you at the feet of the past-master of\nall arts and divinations (not to say crafts and homologisings and\nintegrativeness), the Teacher of wise men, the comfort of an\nafflicted world, the uplifter of fools, the energiser of the\nlethargic, the doctor of the gouty, the guide of youth, the\ncompanion of middle age, the _vade mecum_ of the old, the\npleasant introducer of inevitable death, yea, the general solace of\nmankind. Oh! what are you not now about to hear! If anywhere there\nare rivers in pleasant meadows, cool heights in summer, lovely\nladies discoursing upon smooth lawns, or music skilfully befingered\nby dainty artists in the shade of orange groves, if there is any\nleft of that wine of Chinon from behind the _Grille_ at four\nfrancs a bottle (and so there is, I know, for I drank it at the last\nReveillon by St. Gervais)--I say if any of these comforters of the\nliving anywhere grace the earth, you shall find my master Rabelais\ngiving you the very innermost and animating spirit of all these good\nthings, their utter flavour and their saving power in the\nquintessential words of his incontestably regalian lips. So here,\nthen, you may hear the old wisdom given to our wretched generation\nfor one happy hour of just living and we shall learn, surely in this\ncase at least, that the return of the Dead was admitted and the\nGreat Spirits were received and honoured.\n\n * * * * *\n\nBut alas! No. (which is not a _nominativus pendens_, still less\nan anacoluthon but a mere interjection). Contrariwise, in the place\nof such a sunrise of the mind, what do you think we were given? The\nsight of an old man in a fine red gown and with a University cap on\nhis head hurried along by two policemen in the Strand and followed\nby a mob of boys and ruffians, some of whom took him for Mr. Kruger,\nwhile others thought he was but a harmless mummer. And the\nmagistrate (who had obtained his position by a job) said these\nsimple words: \"I do not know who you are in reality nor what foreign\nname mask under your buffoonery, but I do know on the evidence of\nthese intelligent officers, evidence upon which I fully rely and\nwhich you have made no attempt to contradict, you have disgraced\nyourself and the hall of your kind hosts and employers by the use of\nlanguage which I shall not characterise save by telling you that it\nwould be comprehensible only in a citizen of the nation to which you\nhave the misfortune to belong. Luckily you were not allowed to\nproceed for more than a moment with your vile harangue which (if I\nunderstand rightly) was in praise of wine. You will go to prison for\ntwelve months. I shall not give you the option of a fine: but I can\npromise you that if you prefer to serve with the gallant K. O.\nFighting Scouts your request will be favourably entertained by the\nproper authorities.\"\n\nLong before this little speech was over Rabelais had disappeared,\nand was once more with the immortals cursing and swearing that he\nwould not do it again for 6,375,409,702 sequins, or thereabouts, no,\nnor for another half-dozen thrown in as a makeweight.\n\nThere is the whole story.\n\nI do not say that Rabelais was not over-hasty both in his appearance\nand his departure, but I do say that if the Physicists (and notably\nMrs. Whirtle) had shown more imagination, the governing class a\nwider reading, and the magistracy a trifle more sympathy with the\ndifference of tone between the sixteenth century and our own time,\nthe deplorable misunderstanding now separating the dead and the\nliving would never have arisen; for I am convinced that the Failure\nof Rabelais' attempt has been the chief cause of it.\n\n\n\n\nON THE APPROACH OF AN AWFUL DOOM\n\n\nMy dear little Anglo-Saxons, Celt-Iberians and Teutonico-Latin\noddities---The time has come to convey, impart and make known to you\nthe dreadful conclusions and horrible prognostications that flow,\nhappen, deduce, derive and are drawn from the truly abominable\nconditions of the social medium in which you and I and all poor\ndevils are most fatally and surely bound to draw out our miserable\nexistence.\n\nNote, I say \"existence\" and not \"existences.\" Why do I say\n\"existence\", and not \"existences\"? Why, with a fine handsome plural\nready to hand, do I wind you up and turn you off, so to speak, with\na piffling little singular not fit for a half-starved newspaper\nfellow, let alone a fine, full-fledged, intellectual and well-read\nvegetarian and teetotaller who writes in the reviews? Eh? Why do I\nsay \"existence\"?--speaking of many, several and various persons as\nthough they had but one mystic, combined and corporate personality\nsuch as Rousseau (a fig for the Genevese!) portrayed in his\n_Contrat Social_ (which you have never read), and such as\nHobbes, in his _Leviathan_ (which some of you have heard of),\nought to have premised but did not, having the mind of a lame,\nhalting and ill-furnished clockmaker, and a blight on him!\n\nWhy now \"existence\" and not \"existences\"? You may wonder; you may\nask yourselves one to another mutually round the tea-table putting\nit as a problem or riddle. You may make a game of it, or use it for\ngambling, or say it suddenly as a catch for your acquaintances when\nthey come up from the suburbs. It is a very pretty question and\nwould have been excellently debated by Thomas Aquinas in the\nJacobins of St. Jacques, near the Parloir aux Bourgeois, by the gate\nof the University; by Albertus Magnus in the Cordeliers, hard by the\nCollege of Bourgoyne; by Pic de la Mirandole, who lived I care not a\nrap where and debated I know not from Adam how or when; by Lord\nBacon, who took more bribes in a day than you and I could compass in\na dozen years; by Spinoza, a good worker of glass lenses, but a\nphilosopher whom I have never read nor will; by Coleridge when he\nwas not talking about himself nor taking some filthy drug; by John\nPilkington Smith, of Norwood, Drysalter, who has, I hear, been\nlately horribly bitten by the metaphysic; and by a crowd of others.\n\nBut that's all by the way. Let them debate that will, for it leads\nnowhere unless indeed there be sharp revelation, positive\ndeclaration and very certain affirmation to go upon by way of Basis\nor First Principle whence to deduce some sure conclusion and\nirrefragable truth; for thus the intellect walks, as it were, along\na high road, whereas by all other ways it is lurching and stumbling\nand boggling and tumbling in I know not what mists and brambles of\nthe great bare, murky twilight and marshy hillside of philosophy,\nwhere I also wandered when I was a fool and unoccupied and lacking\nexercise for the mind, but from whence, by the grace of St. Anthony\nof Miranella and other patrons of mine, I have very happily\nextricated myself. And here I am in the parlour of the \"Bugle\" at\nYarmouth, by a Christian fire, having but lately come off the sea\nand writing this for the edification and confirmation of honest\nsouls.\n\nWhat, then, of the question, _Quid de quuerendo? Quantum?\nQualiter? Ubi? Cur? Quid? Quando? Quomodo? Quum? Sive an non?_\n\nAh! There you have it. For note you, all these interrogative\ncategories must be met, faced, resolved and answered exactly--or you\nhave no more knowledge of the matter than the _Times_ has of\neconomics or the King of the Belgians of thorough-Bass. Yea, if you\nmiss, overlook, neglect, or shirk by reason of fatigue or indolence,\nso much as one tittle of these several aspects of a question you\nmight as well leave it altogether alone and give up analysis for\nselling stock, as did the Professor of Verbalism in the University\nof Adelaide to the vast solace and enrichment of his family.\n\nFor by the neglect of but one of these final and fundamental\napproaches to the full knowledge of a question the world has been\nirreparably, irretrievably and permanently robbed of the certain\nreply to, and left ever in the most disastrous doubt upon, this most\nimportant and necessary matter--namely, _whether real existence\ncan be predicated of matter._\n\nFor Anaxagoras of Syracuse, that was tutor to the Tyrant Machion,\nbeing in search upon this question for a matter of seventy-two\nyears, four months, three days and a few odd hours and minutes, did,\nin extreme old age, as he was walking by the shore of the sea, hit,\nas it were in a flash, upon six of the seven answers, and was able\nin one moment, after so much delay and vexatious argument for and\nagainst with himself, to resolve the problem upon the points of\n_how, why, when, where, how much_, and _in what_, matter might or might\nnot be real, and was upon the very nick of settling the last little\npoint--namely, _sive an non_ (that is, whether it _were_ real or no)--when,\nas luck would have it, or rather, as his own beastly appetite and senile\ngreed would have it, he broke off sharp at hearing the dinner-gong or\nbell, or horn, or whatever it was--for upon these matters the King was\nindifferent (_de minimis non curat rex_), and so am I--and was poisoned\neven as he sat at table by the agents of Pyrrhus.\n\nBy this accident, by this mere failure upon _one_ of the Seven\nAnswers, it has been since that day never properly decided whether\nor no this true existence was or was not predicable of matter; and\nsome believing matter to be there have treated it pompously and\ngiven it reverence and adored it in a thousand merry ways, but\nothers being confident it was not there have starved and fallen off\nedges and banged their heads against corners and come plump against\nhigh walls; nor can either party convince the other, nor can the\ndoubts of either be laid to rest, nor shall it from now to the Day\nof Doom be established whether there is a Matter or is none; though\nmany learned men have given up their lives to it, including\nProfessor Britton, who so despaired of an issue that he drowned\nhimself in the Cam only last Wednesday. But what care I for him or\nany other Don?\n\nSo there we are and an answer must be found, but upon my soul I\nforget to what it hangs, though I know well there was some question\npropounded at the beginning of this for which I cared a trifle at\nthe time of asking it and you I hope not at all. Let it go the way\nof all questions, I beg of you, for I am very little inclined to\nseek and hunt through all the heap that I have been tearing through\nthis last hour with Pegasus curvetting and prancing and flapping his\nwings to the danger of my seat and of the cities and fields below\nme.\n\nCome, come, there's enough for one bout, and too much for some. No\ngood ever came of argument and dialectic, for these breed only angry\ngestures and gusty disputes (_de gustibus non disputandum_) and\nthe ruin of friendships and the very fruitful pullulation of\nDictionaries, textbooks and wicked men, not to speak of\nIntellectuals, Newspapers, Libraries, Debating-clubs, bankruptcies,\nmadness, _Petitiones elenchi_ and ills innumerable.\n\nI say live and let live; and now I think of it there was something\nat the beginning and title of this that dealt with a warning to ward\nyou off a danger of some kind that terrified me not a little when I\nsat down to write, and that was, if I remember right, that a friend\nhad told me how he had read in a book that the damnable Brute\nCAPITAL was about to swallow us all up and make slaves of us and\nthat there was no way out of it, seeing that it was fixed, settled\nand grounded in economics, not to speak of the procession of the\nEquinox, the Horoscope of Trimegistus, and _Old Moore's\nAlmanack_. Oh! Run, Run! The Rich are upon us! Help! Their hot\nbreath is on our necks! What jaws! What jaws!\n\nWell, what must be must be, and what will be will be, and if the\nRich are upon us with great open jaws and having power to enslave\nall by the very fatal process of unalterable laws and at the bidding\nof Blind Fate as she is expounded by her prophets who live on milk\nand newspapers and do woundily talk Jew Socialism all day long; yet\nis it proved by the same intellectual certitude and irrefragable\nmethod that we shall not be caught before the year 1938 at the\nearliest and with luck we may run ten years more: why then let us\nmake the best of the time we have, and sail, ride, travel, write,\ndrink, sing and all be friends together; and do you go about doing\ngood to the utmost of your power, as I heartily hope you will,\nthough from your faces I doubt it hugely. A blessing I wish you all.\n\n\n\n\nON A RICH MAN WHO SUFFERED\n\n\nOne cannot do a greater service now, when a dangerous confusion of\nthought threatens us with an estrangement of classes, than to\ndistinguish in all we write between Capitalism--the result of a\nblind economic development--and the persons and motives of those who\nhappen to possess the bulk of the means of Production.\n\nCapitalism may or may not have been a Source of Evil to Modern\nCommunities--it may have been a necessary and even a beneficent\nphase in that struggle upward from the Brute which marks our\nprogress from Gospel Times until the present day--but whether it has\nbeen a good or a bad phase in Economic Evolution, it is not\nScientific and it is not English to confuse the system with the\nliving human beings attached to it, and to contrast \"Rich\" and\n\"Poor,\" insisting on the supposed luxury and callousness of the one\nor the humiliations and sufferings of the other.\n\nTo expose the folly--nay, the wickedness--of that attitude I have\nbut to take some very real and very human case of a rich man--a very\nrich man--who suffered and suffered deeply merely _as_ a man:\none whose suffering wealth did not and could not alleviate.\n\nOne very striking example of this human bond I am able to lay before\nyou, because the gentleman in question has, with fine human\nsympathy, permitted his story to be quoted.\n\nThe only stipulation he made with me was first that I should conceal\nreal names and secondly that I should write the whole in as\njournalistic and popular a method as possible, so that his very\nlegitimate grievance in the matter I am about to describe should be\nas widely known as possible and also in order to spread as widely as\npossible the lesson it contains that _the rich also are men_.\n\nTo change all names etc., a purely mechanical task, I easily\nachieved. Whether I have been equally successful in my second object\nof catching the breezy and happy style of true journalism it is for\nmy readers to judge. I can only assure them that my intentions are\npure.\n\n * * * * *\n\nI have promised my friend to set down the whole matter as it\noccurred.\n\n\"The Press,\" he said to me, \"is the only vehicle left by which one\ncan bring pressure to bear upon public opinion. I hope you can do\nsomething for me.... You write, I believe\", he added, \"for the\npapers?\"\n\nI said I did.\n\n\"Well,\" he answered, \"you fellows that write for the newspapers have\na great advantage ...!\"\n\nAt this he sighed deeply, and asked me to come and have lunch with\nhim at his club, which is called \"The Ragamuffins\" for fun, and is\nfull of jolly fellows. There I ate boiled mutton and greens, washed\ndown with an excellent glass, or maybe a glass and a half, of\nBelgian wine--a wine called Chateau Bollard.\n\nI noticed in the room Mr. Cantor, Mr. Charles, Sir John Ebbsmith,\nMr. May, Mr. Ficks, \"Joe\" Hesketh, Matthew Fircombe, Lord Boxgrove,\nold Tommy Lawson, \"Bill\", Mr. Compton, Mr. Annerley, Jeremy (the\ntrainer), Mr. Mannering, his son, Mr. William Mannering, and his\nnephew Mr. \"Kite\" Mannering, Lord Nore, Pilbury, little Jack Bowdon,\nBaxter (\"Horrible\" Baxter) Bayney, Mr. Claversgill, the solemn old\nDuke of Bascourt (a Dane), Ephraim T. Seeber, Algernon Gutt,\nFeverthorpe (whom that old wit Core used to call \"_Feather_thorpe\"),\nand many others with whose names I will not weary the reader, for he\nwould think me too reminiscent and digressive were I to add to the list\n\"Cocky\" Billings, \"Fat Harry\", Mr. Muntzer, Mr. Eartham, dear, courteous,\nold-world Squire Howle, and that prime favourite, Lord Mann. \"\"\nCourthorpe, Ring, the Coffee-cooler, and Harry Sark, with all the\nForfarshire lot, also fell under my eye, as did Maxwell, Mr. Gam----\n\nHowever, such an introduction may prove overlong for the complaint I\nhave to publish. I have said enough to show the position my friend\nholds. Many of my readers on reading this list will guess at once\nthe true name of the club, and may also come near that of my\ndistinguished friend, but I am bound in honour to disguise it under\nthe veil of a pseudonym or _nom de guerre_; I will call him Mr.\nQuail.\n\nMr. Quail, then, was off to shoot grouse on a moor he had taken in\nMull for the season; the house and estate are well known to all of\nus; I will disguise the moor under the pseudonym or _nom de\nguerre_ of \"Othello\". He was awaited at \"Othello\" on the evening\nof the eleventh; for on the one hand there is an Act most strictly\nobserved that not a grouse may be shot until the dawn of August\n12th, and on the other a day passed at \"Othello\" with any other\noccupation but that of shooting would be hell.\n\nMr. Quail, therefore, proposed to travel to \"Othello\" by way of\nGlasgow, taking the 9.47 at St. Pancras on the evening of the\n10th--last Monday--and engaging a bed on that train.\n\nIt is essential, if a full, Christian and sane view is to be had of\nthis relation, that the reader should note the following details:--\n\nMr. Quail had _engaged_ the bed. He had sent his cheque for it\na week before and held the receipt signed \"T. Macgregor,\nSuperintendent\".\n\nTrue, there was a notice printed very small on the back of the\nreceipt saying the company would not be responsible in any case of\ndisappointment, overcrowding, accident, delay, robbery, murder, or\nthe Act of God; but my friend Mr. Quail very properly paid no\nattention to that rubbish, knowing well enough (he is a J.P.) that a\nman cannot sign himself out of his common-law rights.\n\nIn order to leave ample time for the train, my friend Mr. Quail\nordered dinner at eight--a light meal, for his wife had gone to the\nEngadine some weeks before. At nine precisely he was in his carriage\nwith his coachman on the box to drive his horses, his man Mole also,\nand Piggy the little dog in with him. He knows it was nine, because\nhe asked the butler what time it was as he left the dining-room, and\nthe butler answered \"Five minutes to nine, my Lord\"; moreover, the\nclock in the dining-room, the one on the stairs and his own watch,\nall corroborated the butler's statement.\n\nHe arrived at St. Pancras. \"If,\" as he sarcastically wrote to the\ncompany, \"your _own clocks_ are to be trusted,\" at 9.21.\n\nSo far so good. He had twenty-six minutes to spare. On his carriage\ndriving up to the station he was annoyed to discover an enormous\nseething mob through which it was impossible to penetrate, swirling\nround the booking office and behaving with a total lack of\ndiscipline which made the confusion ten thousand times worse than it\nneed have been.\n\n\"I wish,\" said Mr. Quail to me later, with some heat, \"I wish I\ncould have put some of those great hulking brutes into the ranks for\na few months! Believe me, conscription would work wonders!\" Mr.\nQuail himself holds a commission in the Yeomanry, and knows what he\nis talking about. But that is neither here nor there. I only mention\nit to show what an effect this anarchic mob produced upon a man of\nMr. Quail's trained experience.\n\nHis man Mole had purchased the tickets in the course of the day;\nunfortunately, on being asked for them he confessed in some\nconfusion to having mislaid them.\n\nMr. Quail was too well bred to make a scene. He quietly despatched his\nman Mole to the booking office with orders to get new tickets while\nhe waited for him at an appointed place near the door. He had not been\nthere five minutes, he had barely seen his man struggle through the\npress towards the booking office, when a hand was laid upon his\nshoulder and a policeman told him in an insolent and surly tone to\n\"move out of it.\" Mr. Quail remonstrated, and the policeman--who, I am\nassured, was only a railway servant in disguise--_bodily and physically_\nforced him from the doorway.\n\nTo this piece of brutality Mr. Quail ascribes all his subsequent\nmisfortunes. Mr. Quail was on the point of giving his card, when he\nfound himself caught in an eddy of common people who bore him off\nhis feet; nor did he regain them, in spite of his struggles, until\nhe was tightly wedged against the wall at the further end of the\nroom.\n\nMr. Quail glanced at his watch, and found it to be twenty minutes to\nten. There were but seven minutes left before his train would start,\nand his appointment with his man, Mole, was hopelessly missed unless\nhe took the most immediate steps to recover it.\n\nMr. Quail is a man of resource; he has served in South Africa, and\nis a director of several companies. He noticed that porters pushing\nheavy trollies and crying \"By your leave\" had some chance of forging\nthrough the brawling welter of people. He hailed one such; and\nstretching, as best he could, from his wretched fix, begged him to\nreach the door and tell his man Mole where he was. At the same time--as\nthe occasion was most urgent (for it was now 9.44)--he held out half a\nsovereign. The porter took it respectfully enough, but to Mr. Quail's\nhorror the menial had no sooner grasped the coin than he made off in\nthe opposite direction, pushing his trolley indolently before him and\ncrying \"By your leave\" in a tone that mingled insolence with a coarse\nexultation.\n\nMr. Quail, now desperate, fought and struggled to be free--there\nwere but two minutes left--and he so far succeeded as to break\nthrough the human barrier immediately in front of him. It may be he\nused some necessary violence in this attempt; at any rate a woman of\nthe most offensive appearance raised piercing shrieks and swore that\nshe was being murdered.\n\nThe policeman (to whom I have before alluded) came jostling through\nthe throng, seized Mr. Quail by the collar, and crying \"What!\nAgain?\" treated him in a manner which (in the opinion of Mr. Quail's\nsolicitor) would (had Mr. Quail retained his number) have warranted\na criminal prosecution.\n\nMeanwhile Mr. Quail's man Mole was anxiously looking for him, first\nat the refreshment bar, and later at the train itself. Here he was\nstartled to hear the Guard say \"Going?\" and before he could reply he\nwas (according to his own statement) thrust into the train which\nimmediately departed, and did not stop till Peterborough; there the\nfaithful fellow assures us he alit, returning home in the early\nhours of the morning.\n\nMr. Quail himself was released with a torn coat and collar, his\neye-glasses smashed, his watch-chain broken, and smarting under a\nwarning from the policeman not to be caught doing it again.\n\nHe went home in a cab to find every single servant out of the house,\njunketing at some music-hall or other, and several bottles of wine,\nwith a dozen glasses, standing ready for them against their return,\non his own study table.\n\nThe unhappy story need not be pursued. Like every misfortune it bred\na crop of others, some so grievous that none would expose them to\nthe public eye, and one consequence remote indeed but clearly\ntraceable to that evening nearly dissolved a union of seventeen\nyears. I do not believe that any one of those who are for ever\npresenting to us the miseries of the lower classes, would have met a\ndisaster of this sort with the dignity and the manliness of my\nfriend, and I am further confident that the recital of his suffering\nhere given will not have been useless in the great debate now\nengaged as to the function of wealth in our community.\n\n\n\n\nON A CHILD WHO DIED\n\n\nThere was once a little Whig....\n\nUgh! The oiliness, the public theft, the cowardice, the welter of\nsin! One cannot conceive the product save under shelter and in the\nmidst of an universal corruption.\n\nWell, then, there was once a little Tory. But stay; that is not a\npleasant thought....\n\nWell, then there was once a little boy whose name was Joseph, and\nnow I have launched him, I beg you to follow most precisely all that\nhe said, did and was, for it contains a moral. But I would have you\nbear me witness that I have withdrawn all harsh terms, and have\ncalled him neither Whig nor Tory. Nevertheless I will not deny that\nhad he grown to maturity he would inevitably have been a politician.\nAs you will be delighted to find at the end of his short biography,\nhe did not reach that goal. He never sat upon either of the front\nbenches. He never went through the bitter business of choosing his\nparty and then ratting when he found he had made a mistake. He never\nso much as got his hand into the public pocket. Nevertheless read\nhis story and mark it well. It is of immense purport to the State.\n\n * * * * *\n\nWhen little Joseph was born, his father (who could sketch remarkably\nwell and had rowed some years before in his College boat) was\ncongratulated very warmly by his friends. One lady wrote to him:\n\"_Your_ son cannot fail to add distinction to an already famous\nname\"--for little Joseph's father's uncle had been an Under\nSecretary of State. Then another, the family doctor, said heartily,\n\"Well, well, all doing excellently; another Duggleton\" (for little\nJoseph's father's family were Duggletons) \"and one that will keep\nthe old flag flying.\"\n\nLittle Joseph's father's aunt whose husband had been the Under\nSecretary, wrote and said she was longing to see the _last\nDuggleton_, and hinted that a Duggleton the more was sheer gain\nto This England which Our Fathers Made. His father put his name down\nthat very day for the Club and met there Baron Urscher, who promised\nevery support \"if God should spare him to the time when he might\nwelcome another Duggleton to these old rooms.\" The baron then\nrecalled the names of Charlie Fox and Beau Rimmel, that was to say,\nBrummel. He said an abusive word or two about Mr. Gladstone, who was\nthen alive, and went away.\n\nLittle Joseph for many long weeks continued to seem much like\nothers, and if he had then died (as some cousins hoped he would, and\nas, indeed, there seemed to be a good chance on the day that he\nswallowed the pebble at Bournemouth) I should have no more to write\nabout. There would be an end of little Joseph so far as you and I\nare concerned; and as for the family of Duggleton, why any one but\nthe man who does Society Notes in the _Evening Yankee_ should\nwrite about them I can't conceive.\n\nWell, but little Joseph did not die--not just then, anyhow. He lived\nto learn to speak, and to talk, and to put out his tongue at\nvisitors, let alone interrupting his parents with unpleasing remarks\nand telling lies. It was early observed that he did all these things\nwith a _je-ne-scais-quoy_ and a _verve_ quite different from the manner\nof his little playmates. When one day he moulded out, flattened and\nunshaped the waxen nose of a doll of his, it was apparent to all that\nit had been very skilfully done, and showed a taste for modelling,\nand the admiration this excited was doubled when it was discovered\nthat he had called the doll \"Aunt Garry\". He took also to drawing\nthings with a pencil as early as eight years old, and for this talent\nhis father's house was very suitable, for Mrs. Duggleton had nice\nLouis XV furniture, all white and gold, and a quaint new brown-paper\nmedium on her walls. Colour, oddly enough, little Joseph could not\npretend to; but he had a remarkably fine ear, and was often heard,\nbefore he was ten years old, singing some set of words or other over\nand over again very loudly upon the staircase to a few single notes.\n\nIt seems incredible, but it is certainly true, that he even composed\n_verses_ at the age of eleven, wherein \"land\" and \"strand\",\n\"more\" and \"shore\" would frequently recur, the latter being commonly\nassociated with England, to which, his beloved country, the\nintelligent child would add the epithet \"old\".\n\nHe was, a short time after this, discovered playing upon words and\nwould pun upon \"rain\" and \"reign\", as also upon \"Wales\" the country\n(or rather province, for no patriot would admit a Divided Crown) and\n\"Whales\"--the vast Oceanic or Thalassic mammals that swim in Arctic\nwaters.\n\nHe asked questions that showed a surprising intelligence and at the\nsame time betrayed a charming simplicity and purity of mind. Thus he\nwould cross-examine upon their recent movements ladies who came to\ncall, proving them very frequently to have lied, for he was puzzled\nlike most children by the duplicity of the gay world. Or again, he\nwould ask guests at the dinner table how old they were and whether\nthey liked his father and mother, and this in a loud and shrill way\nthat provoked at once the attention and amusement of the select\ncoterie (for coterie it was) that gathered beneath his father's\nroof.\n\nAs is so often the case with highly strung natures, he was morbidly\nsensitive in his self-respect. Upon one occasion he had invented\nsome boyish nickname or other for an elderly matron who was present\nin his mother's drawing-room, and when that lady most forcibly urged\nhis parent to chastise him he fled to his room and wrote a short\nnote in pencil forgiving his dear mamma her intimacy with his\nenemies and announcing his determination to put an end to his life.\nHis mother on discovering this note pinned to her chair gave way to\nvery natural alarm and rushed upstairs to her darling, with whom she\nremonstrated in terms deservedly severe, pointing out the folly and\nwickedness of self-destruction and urging that such thoughts were\nunfit for one of his tender years, for he was then barely thirteen.\n\nThis incident and many others I could quote made a profound\nimpression upon the Honourable Mr. and Mrs. Duggleton, who, by the\ntime of their son's adolescence, were convinced that Providence had\nentrusted them with a vessel of no ordinary fineness. They discussed\nthe question of his schooling with the utmost care, and at the age\nof fifteen sent \"little Joseph\", as they still affectionately called\nhim, to the care of the Rev. James Filbury, who kept a small but\nexceedingly expensive school upon the banks of the River Thames.\n\nThe three years that he spent at this establishment were among the\nhappiest in the life of his father's private secretary, and are\nstill remembered by many intimate friends of the family.\n\nHe was twice upon the point of securing the prize for Biblical\nstudies and did indeed take that for French and arithmetic. Mr.\nFilbury assured his father that he had the very highest hopes of his\ncareer at the University. \"Joseph,\" he wrote, \"is a fine, highly\ntempered spirit, one to whom continual application is difficult, but\nwho is capable of high flights of imagination not often reached by\nour sturdy English boyhood.... I regret that I cannot see my way to\nreducing the charge for meat at breakfast. Joseph's health is\nexcellent, and his scholarship, though by no means ripe, shows\npromise of that ...\" and so forth.\n\nI have no space to give the letter in full; it betrays in every line\nthe effect this gifted youth had produced upon one well acquainted\nwith the marks of future greatness;--for Mr. Filbury had been the\ntutor and was still the friend of the Duke of Buxton, the sometime\nform-master of the present Bishop of Lewes and the cousin of the\nlate Joshua Lambkin of Oxford.\n\nLittle Joseph's entry into college life abundantly fulfilled the\nexpectations held of him. The head of his college wrote to his\ngreat-aunt (the wife of the Under Secretary of State) \"... he has\nsomething in him of what men of Old called prophecy and we term\ngenius ...\", old Dr. Biddlecup the Dean asked the boy to dinner, and\nafterwards assured his father that little Joseph was the image of\nWilliam Pitt, whom he falsely pretended to have seen in childhood,\nand to whom the Duggletons were related through Mrs. Duggleton's\ngrandmother, whose sister had married the first cousin of the\nSaviour of Europe.\n\nDr. Biddlecup was an old man and may not have been accurate in his\nhistorical pretensions, but the main truth of what he said was\ncertain, for Joseph resembled the great statesman at once in his\nphysical appearance, for he was sallow and had a turned-up nose: in\nhis gifts: in his oratory which was ever remarkable at the social\nclubs and wines--and alas! in his fondness for port.\n\nIndeed, little Joseph had to pay the price of concentrating in\nhimself the genius of three generations, he suffered more than\none of the temptations that assault men of vigorous imagination. He\nkept late hours, drank--perhaps not always to excess but always\nover-frequently--and gambled, if not beyond his means, at least with\na feverish energy that was ruinous to his health. He fell desperately\nill in the fortnight before his schools, but he was granted an\n_aegrotat_, a degree equivalent in his case to a First Class in\nHonours, and he was asked by one or other of the Colleges to compete\nfor a Fellowship; it was, however, given to another candidate.\n\nAfter this failure he went home, and on his father's advice,\nattempted political work; but the hurry and noise of an election\ndisgusted him, and it is feared that his cynical and highly\nepigrammatic speeches were another cause of his defeat.\n\nSir William Mackle, who had watched the boy with the tenderest\ninterest and listened to his fancied experiences with a father's\npatience, ordered complete rest and change, and recommended the\nSouth of France; he was sent thither with a worthless friend or\nrather dependent, who permitted the lad to gamble and even to borrow\nmoney, and it was this friend to whom Sir William (in his letter to\nthe Honourable Mr. Duggleton acknowledging receipt of his cheque)\nattributed the tragedy that followed.\n\n\"Had he not,\" wrote the distinguished physician, \"permitted our poor\nJoseph to borrow money of him; had he resolutely refused to drink\nwine at dinner; had he locked Joseph up in his room every evening at\nthe opening hour of the Casino, we should not have to deplore the\nloss of one of England's noblest.\" Nor did the false friend make\nthings easier for the bereaved father by suggesting ere twelve short\nmonths had elapsed that the sums Joseph had borrowed of him should\nbe repaid.\n\nJoseph, one fatal night, somewhat heated by wine, had heard a\nFrenchman say to an Italian at his elbow certain very outrageous\nthings about one Mazzini. The pair were discussing a local\nbookmaker, but the boy, whose passion for Italian unity is now well\nknown, imagined that the Philosopher and Statesman was in question;\nhe fell into such a passion and attacked these offensive foreigners\nwith such violence as to bring on an attack from which he did not\nrecover: his grave now whitens the hillside of the Monte Resorto (in\nFrench Mont-resort).\n\nHe left some fifty short poems in the manner of Shelley, Rossetti\nand Swinburne, and a few in an individual style that would surely\nhave developed with age. These have since been gathered into a\nvolume and go far to prove the truth of his father's despairing cry:\n\"Joseph,\" the poor man sobbed as he knelt by the insanitary\ncurtained bed on which the body lay, \"Joseph would have done for the\nname of Duggleton in literature what my Uncle did for it in\npolitics.\"\n\nHis portrait may be found in _Annals of the Rutlandshire\nGentry_, a book recently published privately by subscriptions of\ntwo guineas, payable to the gentleman who produced that handsome\nvolume.\n\n\n\n\n\nON A LOST MANUSCRIPT\n\n\nIf this page does not appal you, nothing will.\n\nIf these first words do not fill you with an uneasy presentiment of\ndoom, indeed, indeed you have been hitherto blessed in an ignorance\nof woe.\n\nIt is lost! What is lost? The revelation this page was to afford.\nThe essay which was to have stood here upon page 127 of my book: the\nnoblest of them all.\n\nThe words you so eagerly expected, the full exposition which was to\nhave brought you such relief, is not here.\n\nIt was lost just after I wrote it. It can never be re-written; it is\ngone.\n\nMuch depended upon it; it would have led you to a great and to a\nrapidly acquired fortune; but you must not ask for it. You must turn\nyour mind away. It cannot be re-written, and all that can take its\nplace is a sort of dirge for departed and irrecoverable things.\n\n\"Lugete o Veneres Cupidinesque,\" which signifies \"Mourn oh! you\npleasant people, you spirits that attend the happiness of mankind\":\n\"et quantum est hominum venustiorum,\" which signifies \"and you such\nmortals as are chiefly attached to delightful things.\" _Passer_, etc.,\nwhich signifies my little, careful, tidy bit of writing, _mortuus est_,\nis lost. I lost it in a cab.\n\nIt was a noble and accomplished thing. Pliny would have loved it who\nsaid: \"Ea est stomachi mei natura ut nil nisi merum atque totum\nvelit,\" which signifies \"such is the character of my taste that it\nwill tolerate nothing but what is absolute and full.\" ... It is no\nuse grumbling about the Latin. The nature of great disasters calls\nout for that foundational tongue. They roll as it were (do the great\ndisasters of our time) right down the emptiness of the centuries\nuntil they strike the walls of Rome and provoke these sonorous\nechoes worthy of mighty things.\n\nIt was to have stood here instead of this, its poor apologist. It\nwas to have filled these lines, this space, this very page. It is\nnot here. You all know how, coming eagerly to a house to see someone\ndearly loved, you find in their place on entering a sister or a\nfriend who makes excuses for them; you all know how the mind grows\nblank at the news and all nature around one shrivels. It is a worse\nemptiness than to be alone. So it is with me when I consider this as\nI write it, and then think of That Other which should have taken its\nplace; for what I am writing now is like a little wizened figure\ndressed in mourning and weeping before a deserted shrine, but That\nOther which I have lost would have been like an Emperor returned\nfrom a triumph and seated upon a throne.\n\nIndeed, indeed it was admirable! If you ask me where I wrote it, it\nwas in Constantine, upon the Rock of Cirta, where the storms come\nbowling at you from Mount Atlas and where you feel yourself part of\nthe sky. At least it was there in Cirta that I blocked out the\nthing, for efforts of that magnitude are not completed in one place\nor day. It was in Cirta that I carved it into form and gave it a\ngeneral life, upon the 17th of January, 1905, sitting where long ago\nMassinissa had come riding in through the only gate of the city,\nsitting his horse without stirrups or bridle. Beside me, as I wrote,\nan Arab looked carefully at every word and shook his head because he\ncould not understand the language; but the Muses understood and\nApollo, which were its authors almost as much as I. How graceful it\nwas and yet how firm! How generous and yet how particular! How easy,\nhow superb, and yet how stuffed with dignity! There ran through it,\nhalf-perceived and essential, a sort of broken rhythm that never\ndescended to rhetoric, but seemed to enliven and lift up the order\nof the words until they were filled with something approaching\nmusic; and with all this the meaning was fixed and new, the order\nlucid, the adjectives choice, the verbs strong, the substantives\nmeaty and full of sap. It combined (if I may say so with modesty)\nall that Milton desired to achieve, with all that Bacon did in the\nmodelling of English.... And it is gone. It will never be seen or\nread or known at all. It has utterly disappeared nor is it even\npreserved in any human memory--no, not in my own.\n\nI kept it for a year, closely filing, polishing, and emending it\nuntil one would have thought it final, and even then I continued to\ndevelop and to mould it. It grew like a young tree in the corner of\na fruitful field and gave an enduring pleasure. It never left me by\nnight or by day; it crossed the Pyrenees with me seven times and the\nMediterranean twice. It rode horses with me and was become a part of\nmy habit everywhere. In trying to ford the Sousseyou I held it high\nout of the water, saving it alone, and once by a camp fire I woke\nand read it in the mountains before dawn. My companions slept on\neither side of me. The great brands of pine glowed and gave me\nlight; there was a complete silence in the forest except for the\nnoise of water, and in the midst of such spells I was so entranced\nby the beauty of the thing that when I had done my reading I took a\ndead coal from the fire and wrote at the foot of the paper: \"There\nis not a word which the most exuberant could presume to add, nor one\nwhich the most fastidious would dare to erase.\" All that glory has\nvanished.\n\nI know very well what the cabman did. He looked through the trap-door\nin the top of the roof to see if I had left anything behind. It was\nin Vigo Street, at the corner, that the fate struck. He looked and\nsaw a sheet or two of paper--something of no value. He crumpled it up\nand threw it away, and it joined the company which men have not been\nthought worthy to know. It went to join Calvus and the dreadful books\nof the Sibyl, and those charred leaves which were found on the floor\nwhere Chatterton lay dead.\n\nI went three times to Scotland Yard, allowing long intervals and\ntorturing myself with hope. Three times my hands thought to hold it,\nand three times they closed on nothingness. A policeman then told me\nthat cabmen very rarely brought him written things, but rather\nsticks, gloves, rings, purses, parcels, umbrellas, and the crushed\nhats of drunken men, not often verse or prose; and I abandoned my\nquest.\n\nThere are some reading this who may think me a trifle too fond and\nmay doubt the great glory to which I testify here. They will\nremember how singularly the things we no longer possess rise upon\nthe imagination and enlarge themselves, and they will quote that\npathetic error whereby the dead become much dearer to us when we can\nno longer smile into their faces or do them the good we desire. They\nwill suggest (most tenderly) that loss and the enchantment of memory\nhave lent a thought too much of radiance and of harmony to what was\ncertainly a noble creation of the mind, but still human and shot\nwith error.\n\nTo such a criticism I cannot reply, I have no longer, alas! the best\nof replies, the Thing Itself, the Achievement: and not having that I\nhave nothing. I am without weapons. Who shall convince of\npersonality, of beauty, or of holiness, unless they be seen and\nfelt? So it is with letters, and if I am not believed--or even if I\nam--it is of little moment, for the beloved object is rapt away.\n\nIts matter--if one can say that anything so manifold and exalted had\na mere subject--its matter was the effect of the piercing of the\nSuez Canal upon coastwise trade in the Mediterranean, but it is\nprofane to bring before the general gaze a title which can tell the\nworld nothing of the iridescence and vitality it has lost.\n\nI will not console myself with the uncertain guess that things\nperished are in some way recoverable beyond the stars, nor hope to\nsee and read again the artistry and the result whose loss I have\nmourned in these lines; but if, as the wisest men imagine, there is\na place of repose for whatever most deserves it among the shades,\nthere either I or others worthier may read what will never be read\nby living eyes or praised by living lips again. It may be so. But\nthe loss alone is certain.\n\n\n\n\nON A MAN WHO WAS PROTECTED BY ANOTHER MAN\n\n\nThere was once a man called Mahmoud. He had other names, such as\nAli, Akbar, and Shmaeil, and so forth, with which I will not trouble\nyou, because in very short stories it is important not to confuse\nthe mind. I have been assured of this by many authorities, some of\nwhom make a great deal of money by short stories, and all of whom\nknow a great deal about the way in which they ought to be written.\n\nNow I come to think of it, I very much doubt whether this is a short\nstory at all, for it has no plot so far and I do not see any plot\ndeveloping. No matter. The thing is to say what one has to say\nhumbly but fully. Providence will look after the rest.\n\nSo, as I was saying, there was a man called Mahmoud. He lived in a\ncountry entirely made of sand. There were hills which on the maps\nwere called mountains, but when you came to look at them they were\nonly a lot more sand, and there was nothing about them except an\naspect of sand heaped up. You may say, \"How, then, did Mahmoud build\na house?\" He did not. He lived in a tent. \"But,\" you continue, \"what\ndid he do about drinking?\" Well, it was Mahmoud's habit to go to a\nplace where he knew that by scratching a little he would find bad\nwater, and there he would scratch a little and find it, and, being\nan abstemious man, he needed but a drop.\n\nThe sun in Mahmoud's country was extremely hot. It stood right up\nabove one's head and looked like the little thing that you get in\nthe focus of a burning glass. The sun made it almost impossible to\nmove, except in the early morning or at evening, and even during the\nnight it was not particularly cool. It never rained in this place.\n\nThere were no rivers and no trees. There was no grass, and the only\nanimal was a camel. The camel was content to eat a kind of scrub\nthat grew here and there on the sand, and it drank the little water\nMahmoud could afford it, and was permanently happy. So was Mahmoud.\nBeneath him the sand sloped down until it met the sea, which was\ntepid on account of the great heat, and in which were a lot of fish,\npearls, and other things. Every now and then Mahmoud would force a\nson or domestic of his to go down and hoick out a pearl, and this\npearl he would exchange for something that he absolutely needed,\nsuch as a new tent or a new camel, and then he went on living the\nway he had been living before.\n\nNow, one day there came to this part of the world a man called\nSmith. He was dressed as you and I are, in trousers and a coat and\nboots, and he had a billycock hat on. He had a foolish, anxious\nface. He did not keep his word particularly; and he was exceedingly\nfond of money. He had spent most of his life accumulating all sorts\nof wealth in a great bag, and he landed with this bag in Mahmoud's\ncountry, and Mahmoud was as polite to him as the heat would allow.\nThen Mahmoud said to him:\n\n\"You appear to be a very rich man.\"\n\nAnd Smith said:\n\n\"I am,\" and opened his bag and showed a great quantity of things. So\nMahmoud was pleased and astonished, and fussed a good deal\nconsidering the climate, and got quite a quantity of pearls out of\nthe sea, and gave them to Smith, who let him have a gun, but a bad\none; and he, Smith, retained a good rifle. Then Smith sat down and\nwaited for about six months, living on the provisions he had brought\nin his bag, until Mahmoud said to him:\n\n\"What have you come to do here?\"\n\nAnd Smith said:\n\n\"Why, to tell you the honest truth, I have come to protect you.\"\n\nSo Mahmoud thought a long time, smoking a pipe, because he did not\nunderstand a word of what Smith had said. Then Mahmoud said:\n\n\"All right, protect away,\" and after that there was a silence for\nabout another six months, and nothing had happened.\n\nMahmoud did not mind being protected, because it made no difference\nto him, and after a certain time he had got all he wanted out of\nSmith, and was tired of bothering about the pearls. So he and Smith\njust lived side by side doing nothing in particular, except that\nSmith went on protecting and that Mahmoud went on being protected.\nBut while Mahmoud was perfectly content to be protected till\nDoomsday, being an easy-going kind of fellow, Smith was more and\nmore put out. He was a trifle irritable by nature. The climate did\nnot suit him. He drank beer and whisky and other things quite\ndangerous under such a sun, and he came out all over like the\nmeasles. He tried to pass the time riding on a camel. At first he\nthought it great sport, but after a little he got tired of that\nalso. He began to write poetry, all about Mahmoud, and as Mahmoud\ncould not read it did not much matter. Then he wrote poetry about\nhimself, making out Mahmoud to be excessively fond of him, and this\npoetry he read to himself, and it calmed him; but as Mahmoud did not\nknow about this poetry, Smith got bored with it, and, his irritation\nincreasing, he wrote more poetry, showing Mahmoud to be a villain\nand a serf, and showing himself, Smith, to be under a divine\nmission.\n\nNow, just when things had come to this unpleasant state Mahmoud got\nup and shook himself and began skipping and dancing outside the door\nof his tent and running round and round it very fast, and waving his\nhands in the air, and shouting incongruous things.\n\nSmith was exceedingly annoyed by this. He had never gone on like\nthat himself, and he did not see why Mahmoud should. But Mahmoud had\nlived there a good deal longer than Smith had, and he knew that it\nwas absolutely necessary. There were stories of people in the past\nwho had felt inclined to go on like this and had restrained\nthemselves with terrible consequences. So Mahmoud went on worse than\never, running as fast as he could out into the sand, shouting,\nleaping into the air, and then running back again as fast as he\ncould, and firing off his gun and calling upon his god.\n\nSmith, whose nerves were at the last stretch, asked Mahmoud savagely\nwhat he was about. To this Mahmoud gave no reply, save to twirl\nround rapidly upon one foot and to fall down foaming at the mouth.\nSmith, therefore, losing all patience, said to Mahmoud:\n\n\"If you do not stop I will shoot you by way of protecting you\nagainst yourself.\"\n\nMahmoud did not know what the word protected meant, but he\nunderstood the word shoot, and shouting with joy, he blew off\nSmith's hat with his gun, and said:\n\n\"A fight! a fight!\"\n\nFor he loved fighting when he was in this mood, while Smith detested\nit.\n\nSmith, however, remembered that he had come there to protect\nMahmoud; he set his teeth, aimed with his rifle, fired at Mahmoud,\nand missed.\n\nMahmoud was so surprised at this that he ran at Smith, and rolled\nhim over and over on the ground. Then they unclenched, both very\nmuch out of breath, and Smith said:\n\n\"Will you or will you not be protected?\"\n\nMahmoud said he should be delighted. Moreover, he said that he had\ngiven his word that he would be protected, and that he was not a man\nto break his word.\n\nAfter that he took Smith by the hand and shook it up and down for\nabout five minutes, until Smith was grievously put out.\n\nWhen they were friends again. Smith said to Mahmoud:\n\n\"Will you not go down into the sea and get me some more pearls?\"\n\n\"No,\" said Mahmoud, \"I am always very exhausted after these\nattacks.\"\n\nThen Smith sat down by the seashore and began to cry, thinking of\nhis home and of the green trees and of the North, and he wrote\nanother poem about the burden that he had borne, and of what a great\nman he was and how he went all over the world protecting people, and\nhow brave he was, and how Mahmoud also was very brave, but how he\nwas much braver than Mahmoud. Then he said:\n\n\"Mahmoud, I am going away back to my distant home, unless you will\nget me more pearls.\"\n\nBut Mahmoud said:\n\n\"I cannot get you any more pearls because it is too hot, and if only\nyou will stop you can go on doing some protecting, which, upon my\nsoul, I do like better than anything in the world.\"\n\nAnd even as he said this he began jumping about and shouting strange\nthings and waving his gun, and Smith at once went away.\n\nThen Mahmoud sat down sadly by the sea, and thought of how Smith had\nprotected him, and how now all that was passed and the old\nmonotonous life would begin again. But Smith went home, and all his\nneighbours asked how it was that he protected so well, and he wrote\na book to enlighten them, called _How I Protected Mahmoud_.\nThen all his neighbours read this book and went out in a great boat\nto do something of the same kind. And Smith could not refrain from\nsmiling.\n\nMahmoud, however, by his lonely shore, regretted more and more this\nepisode in his dull life, and he wept when he remembered the\nfantastic Smith, who had such an enormous number of things in his\nbag and who had protected him; and he also wrote a poem, which is\nrather difficult to understand in connection with the business, but\nwhich to him exactly described it. And the poem went like this;\nhaving no metre and no rhyming, and being sung to three notes and a\nquarter in a kind of wail:\n\n\"When the jackal and the lion meet it is full moon; it is full moon\nand the gazelles are abroad.\"\n\n\"Why are the gazelles abroad when the jackal and the lion meet: when\nit is full moon in the desert and there is no wind?\"\n\n\"There is no wind because the gazelles are abroad, the moon is at\nthe full, and the lion and the jackal are together.\"\n\n\"Where is he that protected me and where is the great battle and the\nshouts and the feasting afterwards, and where is that bag?\"\n\n\"But we dwell in the desert always, and men do not visit us, and the\nlion and the jackal have met, and it is full moon, O gazelles!\"\n\nMahmoud was so pleased with this song that he wrote it down, a thing\nhe only did with one song out of several thousands, for he wrote\nwith difficulty, but I think it a most ridiculous song, and I far\nprefer Smith's, though you would never know it had to do with the\nsame business.\n\n\n\n\nON NATIONAL DEBTS (WHICH ARE IMAGINARIES AND TRUE NOTHINGS OF STATE)\n\n\nOne day Peter and Paul--I knew them both, the dear fellows: Peter\nperhaps a trifle wild, Paul a little priggish, but that is no\nmatter--one day, I say, Peter and Paul (who lived together in rooms off\nSouthampton Row, Bloomsbury, a very delightful spot) were talking\nover their mutual affairs.\n\n\"My dear Paul,\" said Peter, \"I wish I could persuade you to this\nexpenditure. It will be to our mutual advantage. Come now, you have\nten thousand a year of your own and I with great difficulty earn a\nhundred; it is surprising that you should make the fuss you do.\nBesides which you well know that this feeding off packing-cases is\nirksome; we really need a table and it will but cost ten pounds.\"\n\nTo all this Paul listened doubtfully, pursing up his lips, joining\nthe tips of his fingers, crossing his legs and playing the solemn\nfool generally.\n\n\"Peter,\" said he, \"I mislike this scheme of yours. It is a heavy\noutlay for a single moment. It would disturb our credit, and yours\nespecially, for your share would come to five pounds and you would\nhave to put off paying the Press-Cutting agency to which you\nfoolishly subscribe. No; there is an infinitely better way than this\ncrude idea of paying cash down in common. I will lend the whole sum\nof ten pounds to our common stock and we will each pay one pound a\nyear as interest to myself for the loan. I for my part will not\nshirk my duty in the matter of this interest and I sincerely trust\nyou will not shirk yours.\"\n\nPeter was so delighted with this arrangement that his gratitude knew\nno bounds. He would frequently compliment himself in private on the\nadvantage of living with Paul, and when he went out to see his\nfriends it was with the jovial air of the Man with the Bottomless\nPurse, for he did not feel the pound a year he had to pay, and Paul\nalways seemed willing to undertake similar expenses on similar\nterms. He purchased a bronze over-mantel, he fitted the rooms with\nelectric light, he bought (for the common use) a large prize dog for\n\u00a356, and he was for ever bringing in made dishes, bottles of wine\nand what not, all paid for by this lending of his. The interest\nincreased to \u00a320 and then to \u00a330 a year, but Paul was so rigorously\nhonest, prompt and exact in paying himself the interest that Peter\ncould not bear to be behindhand or to seem less punctual and upright\nthan his friend. But so high a proportion of his small income going\nin interest left poor Peter but a meagre margin for himself and he\nhad to dine at Lockhart's and get his clothes ready made, which (to\na refined and sensitive soul such as his) was a grievous trial.\n\nSome little time after a Fishmonger who had attained to Cabinet rank\nwas married to the daughter of a Levantine and London was in\nconsequence illuminated. Paul said to Peter in his jovial way, \"It\nis imperative that we should show no meanness upon this occasion. We\nare known for the most flourishing and well-to-do pair of bachelors\nin the neighbourhood, and I have not hesitated (for I know I had\nyour consent beforehand) to go to Messrs. Brock and order an immense\nquantity of fireworks for the balcony on this auspicious occasion.\nNot a word. The loan is mine and very freely do I make it to our\nMutual Position.\"\n\nSo that night there was an illumination at their flat, and the\ncentre-piece was a vast combination of roses, thistles, shamrocks,\nleeks, kangaroos, beavers, schamboks, and other national emblems,\nand beneath it the motto, \"United we stand, divided we fall: Peter\nand Paul,\" in flaming letters two feet high.\n\nPeter was after this permanently reduced to living upon rice and to\nmending his own clothes; but he could easily see how fair the\narrangement was, and he was not the man to grumble at a free\ncontract. Moreover, he was expecting a rise in salary from the\neditor of the _Hoot_, in which paper he wrote \"Woman's World\",\nand signed it \"Emily\".\n\nAt the close of the year Peter had some difficulty in meeting the\ninterest, though Paul had, with true business probity, paid his on\nthe very day it fell due. Peter therefore approached Paul with some\nlittle diffidence and hesitation, saying:\n\n\"Paul: I trust you will excuse me, but I beg you will be so very\ngood as to see your way, if possible, to granting me an extension of\ntime in the matter of paying my interest.\"\n\nPaul, who was above everything regular and methodical, replied:\n\n\"Hum, chrm, chrum, chrm. Well, my dear Peter, it would not be\ngenerous to press you, but I trust you will remember that this money\nhas not been spent upon my private enjoyment. It has gone for the\nglory of our Mutual Position; pray do not forget that, Peter; and\nremember also that if you have to pay interest, so have I, so have\nI. We are all in the same boat, Peter, sink or swim; sink or\nswim....\" Then his face brightened, he patted Peter genially on the\nshoulder and added: \"Do not think me harsh, Peter. It is necessary\nthat I should keep to a strict, business-like way of doing things,\nfor I have a large property to manage; but you may be sure that my\nfriendship for you is of more value to me than a few paltry\nsovereigns. I will lend you the sum you owe to the interest on the\nCommon Debt, and though in strict right you alone should pay the\ninterest on this new loan I will call half of it my own and you\nshall pay but \u00a31 a year on it for ever.\"\n\nPeter's eyes swam with tears at Paul's generosity, and he thanked\nhis stars that his lot had been cast with such a man. But when Paul\ncame again with a grave face and said to him, \"Peter, my boy, we\nmust insure at once against burglars: the underwriters demand a\nhundred pounds,\" his heart broke, and he could not endure the\nthought of further payments. Paul, however, with the quiet good\nsense that characterised him, pointed out the necessity of the\npayment and, eyeing Peter with compassion for a moment, told him\nthat he had long been feeling that he (Peter) had been unfairly\ntaxed. \"It is a principle\" (said Paul) \"that taxation should fall\nupon men in proportion to their ability to pay it. I am determined\nthat, whatever happens, you shall in future pay but a third of the\ninterest that may accrue upon further loans.\" It was in vain that\nPeter pointed out that, in his case, even a thirtieth would mean\nstarvation; Paul was firm and carried his point.\n\nThe wretched Peter was now but skin and bone, and his earning power,\nsmall as it had ever been, was considerably lessened. Paul began to\nfear very seriously for his invested funds: he therefore kept up\nPeter's spirits as best he could with such advice as the following:--\n\n\"Dear Peter, do not repine; your lot is indeed hard, but it has its\nsilver lining. You are the member of a partnership famous among all\nother bachelor-residences for its display of fireworks and its fine\nfurniture. So valuable is the room in which you live that the\ninsurance alone is the wonder and envy of our neighbours. Consider\nalso how firm and stable these loans make our comradeship. They give\nme a stake in the rooms and furnish a ready market for the spare\ncapital of our little community. The interest WE pay upon the fund\nis an evidence of our social rank, and all London stares with\nastonishment at the flat of Peter and Paul, which can without an\neffort buy such gorgeous furniture at a moment's notice.\"\n\nBut, alas! these well-meant words were of no avail. On a beautiful\nspring day, when all the world seemed to be holding him to the joys\nof living, Peter passed quietly away in his little truckle bed,\nunattended even by a doctor, whose fees would have necessitated a\nloan the interest of which he could never have paid.\n\nPaul, on the death of Peter, gave way at first to bitter\nrecrimination. \"Is this the way,\" he said, \"that you repay years of\nunstinted generosity? Nay, is this the way you meet your sacred\nobligations? You promised upon a thousand occasions to pay your\nshare of the interest for ever, and now like a defaulter you abandon\nyour post and destroy half the revenue of our firm by one\nintempestive and thoughtless act! Had you but possessed a little\nproperty which, properly secured, would continue to meet the claims\nyou had incurred, I had not blamed you. But a man who earns all that\nhe possesses has no right to pledge himself to perpetual payment\nunless he is prepared to live for ever!\"\n\nNobler thoughts, however, succeeded this outburst, and Paul threw\nhimself upon the bed of his Departed Friend and moaned. \"Who now\nwill pay me an income in return for my investments? All my fortune\nis sunk in this flat, though I myself pay the interest never so\nregularly, it will not increase my fortune by one farthing! I shall\nas I live consume a fund which will never be replenished, and within\na short time I shall be compelled to work for my living!\"\n\nMaddened by this last reflection, he dashed into the street, hurried\nnorthward through-the-now-rapidly-gathering-darkness, and drowned\nhimself in the Regent's Canal, just where it runs by the Zoological\nGardens, under the bridge that leads to the cages of the larger\npachyderms.\n\nThus miserably perished Peter and Paul, the one in the thirtieth,\nthe other in the forty-seventh year of his age, both victims to\ntheir ignorance of _Mrs. Fawcett's Political Economy for the\nYoung_, the _Nicomachean Ethics_, Bastiat's _Economic Harmonies, The\nFourth Council of Lateran on Unfruitful Loans and Usury, The Speeches\nof Sir Michael Hicks-Beach and Mr. Brodrick (now Lord Midleton), The\nSermons of St. Thomas Aquinas_, under the head \"Usuria,\"\nMr. W. S. Lilly's First _Principles in Politics_, and other works\ntoo numerous to mention.\n\n\n\n\nON LORDS\n\n\n\"_Saepe miratus sum_,\" I have often wondered why men were\nblamed for seeking to know men of title. That a man should be blamed\nfor the acceptance of, or uniformity with, ideals not his own is\nright enough; but a man who simply reveres a Lord does nothing so\ngrave: and why he should not revere such a being passes my\ncomprehension.\n\nThe institution of Lords has for its object the creation of a high\nand reverend class; well, a man looks up to them with awe or\nexpresses his reverence and forthwith finds himself accused! Get rid\nof Lords by all means, if you think there should be none, but do not\ncome pestering me with a rule that no Lord shall be considered while\nyou are making them by the bushel for the special purpose of being\nconsidered--_ad considerandum_ as Quintillian has it in his\nhighly Quintillianarian essay on I forget what.\n\nI have heard it said that what is blamed in snobs, _snobinibus\nquid reatumst_, is not the matter but the manner of their\nworship. Those who will have it so maintain that we should pay to\nrank a certain discreet respect which must not be marred by crude\nexpression. They compare snobbishness to immodesty, and profess that\nthe pleasure of acquaintance with the great should be so enjoyed\nthat the great themselves are but half-conscious of the homage\noffered them: this is rather a subtle and finicky critique of what\nis in honest minds a natural restraint.\n\nI knew a man once--Chatterley was his name, Shropshire his county,\nand racing his occupation--who said that a snob was blamed for the\noffence he gave to Lords themselves. Thus we do well (said this man\nChatterley) to admire beautiful women, but who would rush into a\nroom and exclaim loudly at the ladies it contained? So (said this\nman Chatterley) is it with Lords, whom we should never forget, but\nwhom we should not disturb by violent affection or by too persistent\na pursuit.\n\nThen there was a nasty drunken chap down Wapping way who had seen\nbetter days; he had views on dozens of things and they were often\nworth listening to, and one of his fads was to be for ever preaching\nthat the whole social position of an aristocracy resided in a veil\nof illusion, and that hands laid too violently on this veil would\ntear it. It was only by a sort of hypnotism, he said, that we\nregarded Lords as separate from ourselves. It was a dream, and a\nrough movement would wake one out of it. Snobbishness (he said) did\nviolence to this sacred film of faith and might shatter it, and\nhence (he pointed out) was especially hated by Lords themselves. It\nwas interesting to hear as a theory and delivered in those\nsurroundings, but it is exploded at once by the first experience of\nHigh Life and its solid realities.\n\nThere is yet another view that to seek after acquaintance with men\nof position in some way hurts one's own soul, and that to strain\ntowards our superiors, to mingle our society with their own, is\nunworthy, because it is destructive of something peculiar to\nourselves. But surely there is implanted in man an instinct which\nleads him to all his noblest efforts and which is, indeed, the\nmotive force of religion, the instinct by which he will ever seek to\nattain what he sees to be superior to him and more worthy than the\nthings of his common experience. It seems to be proper, therefore,\nthat no man should struggle against the very natural attraction\nwhich radiates from superior rank, and I will boldly affirm that he\ndoes his country a good service who submits to this force.\n\nThe just appetite for rank gives rise to two kinds of duty, one or\nthe other of which each of us in his sphere is bound to regard.\nThere is first for much the greater part of men the duty of showing\nrespect and deference to men of title, by which I do not mean only\nLords absolute (which are Barons, Viscounts, Earls, Marquises and\nDukes), but also Lords in gross, that is the whole body of lords,\nincluding lords by courtesy, ladies, their wives and mothers,\nhonourables and cousins--especially heirs of Lords, and to some\nextent Baronets as well. Secondly, there is the duty of those few\nwithin whose power it lies to become Lords, Lords to become, lest\nthe aristocratic element in our Constitution should decline. The\nmost obvious way of doing one's duty in this regard if one is\nwealthy is to purchase a peerage, or a Baronetcy at the least, and\nwhen I consider how very numerous are the fortunes to which a sum of\ntwenty or thirty thousand pounds is not really a sacrifice, and how\nfew of their possessors exercise a tenacious effort to acquire rank\nby the disbursement of money, I cannot but fear for the future of\nthe country! It is no small sign of our times that we should read so\ncontinually of large bequests to public charities made by men who\nhave had every opportunity for entering the Upper House but who\npreferred to remain unnoted in the North of England and to leave\ntheir posterity no more dignified than they were themselves.\n\nThere is a yet more restricted class to whom it is open to become\nLords by sheer merit. The one by gallant conduct in the field,\nanother by a pretty talent for verse, a third by scientific\nresearch. And if any of my readers happen to be a man of this kind\nand yet hesitate to undertake the effort required of him, I would\npoint out that our Constitution in its wisdom adds certain very\nmaterial advantages to a peerage of this kind. It is no excuse for a\nman of military or scientific eminence to say that his income would\nnot enable him to maintain such a dignity. Parliament is always\nready to vote a sufficient grant of money, and even were it not so,\nit is quite possible to be a Lord and yet to be but poorly provided\nwith the perishable goods of this world, as is very clearly seen in\nthe case of no fewer than eighty-two Barons, fourteen Earls, and\nthree dukes, a list of whom I had prepared for printing in these\ndirections but have most unfortunately mislaid.\n\nAgain, even if one's private means be small, and if Parliament by\nsome neglect omit to endow one's new splendour, the common sense of\nEngland will come to the help of any man so situated if he is worth\nhis salt. He will with the greatest ease obtain positions of\nresponsibility and emolument, notably upon the directorate of public\ncompanies, and can often, if he finds his salary insufficient,\npersuade his fellow-directors to increase it, whether by threatening\nthem with exposure or by some other less drastic and more convivial\nmeans.\n\nIf after reading these lines there is anyone who still doubts the\nattitude that an honest man should take upon this matter, it is\nenough to point out in conclusion how Providence itself appears to\nhave designed the whole hierarchy of Lords with a view to tempting\nman higher and ever higher. Thus, if some reader of this happens to\nbe a baron, he might think perhaps that it is not worth a further\neffort to receive another grade of distinction. He would be wrong,\nfor such an advance gives a courtesy title to his daughters; one\nmore step and the same benefit accrues to his sons. After that there\nis indeed a hiatus, nor have I ever been able to see what advantage\nis held out to the viscount who desires to become a marquis--unless,\nindeed, it be marquises that become viscounts. Anyhow, it is the\nlatter title which is the less English and the less manly and which\nI am glad to hear it is proposed to abolish by a short, one-clause\nbill in the next Session of Parliament. Above these, the dukes in\nthe titles of their wives and the mode in which they are addressed\nstand alone. There is, therefore, no stage in a man's upward\nprogress upon this ancient and glorious ladder where he will not\nfind some great reward for the toil of ascending. In view of these\nthings, I for my part hope, in common with many another, that the\nfoolish pledge given some years ago when the Liberal Party was in\nopposition, that it would create no more Lords, will be revised now\nthat it has to consider the responsibilities of office; a revision\nfor which there is ample precedent in the case of other pledges\nwhich were as rashly made but of which a reconsideration has been\nfound necessary in practice.\n\nNOTE.--_I find I am wrong upon Viscounts, but as I did not\ndiscover this until my book was in the press I cannot correct it.\nThe remainder of the matter is accurate enough, and may be relied on\nby the student._\n\n\n\n\nON JINGOES: IN THE SHAPE OF A WARNING\n\nBEING\n\n\nThe sad and lamentable history of Jack Bull, son of the late John\nBull, India Merchant, wherein it will be seen how this prosperous\nmerchant left an heir that ran riot with 'Squires, trainbands, Black\nmen, and Soldiers, and squandered all his substance, so that at last\nhe came to selling penny tokens in front of the Royal Exchange in\nThreadneedle Street, and is now very miserably writing for the\npapers.\n\nJohn Bull, whom I knew very well, drove a great trade in tea, cotton\ngoods, and bombazine, as also in hardware, all manner of cutlery,\ngood and bad, and especially sea-coal, and was very highly respected\nin the City of London, of which he was twice Sheriff and once Lord\nMayor. When he went abroad some begged of him, and to these he would\ngive a million or so at a time openly in the street, so that a crowd\nwould gather and cry, \"Lord! what a generous fellow is this Mr.\nBull!\" Some, again, of better station would pluck his sleeve and\ntake him aside into Broad Street Corner or Mansion House Court, and\nsay, \"Mr. Bull, a word in your ear. I have more paper about than I\ncare for in these hard times, and I could pay you handsomely for a\nshort loan.\" These always found Mr. Bull willing and ready, sure and\nsilent, and, withal, cheaper at a discount than any other. For\nbuying cloth all came to Bull; and for buying other wares his house\nwas preferred to those of Frog and Hans and the rest, because he was\ncourteous and ready, always to be found in his office (which was\nnear the Wool-pack in Leaden Hall Street, next to Mr. Marlow's, the\nMethodist preacher), and moreover he was very attentive to little\nthings. This last habit he would call the soul of business. In such\nfashion Mr. Bull had accumulated a sum of five hundred thousand\nmillion pounds, or thereabouts, and when he died the neighbours said\nthis and that spiteful thing about his son Jack whom he had trained\nup to the business, making out that _they knew more than they\ncared to say_, that _Jack was not John_, that _they had heard of Pride\ngoing before a fall_, and so much tittle-tattle as jealousy will breed.\nBut they were very much disappointed in their malice, for this same\nJack went sturdily to work and trod in his father's steps, so that\nhis wealth increased even beyond what he had inherited, and he had at\nlast more risks upon the sea in one way and another than any other\nmerchant in the City. And if you would know how Jack (who was, to\ntell the truth, more flighty and ill-informed than his father) came to\ngo so wisely, it was thus: Old John had left him a few directions writ\nup in pencil on the mantelpiece, which ran in this way:---\n\n1. Never go into an adventure unless the feeling of your neighbours\nbe with you.\n\n2. Spend no more than you earn--nay, put by every year.\n\n3. Put out no money for show in your business but only for use, save\nonly on the occasion of the Lord Mayor's Show, your taking of an\noffice, or on the occasion of public holidays, as, when the King's\nwife or daughter lies in.\n\n4. Live and let live, for be sure your business can only thrive on\nthe condition that others do also.\n\n5. Vex no man at your door; buy and sell freely.\n\n6. Do not associate with Drunkards, Brawlers and Poets; and God's\nblessing be with you.\n\nNow when Jack was grown to about thirty years old, he came, most\nunfortunately, upon a certain Sir John Snipe, Bart., that was a very\nscandalous young squire of Oxfordshire, and one that had published\nfive lyrics and a play (enough to warn any Bull against him), who\nspoke to him somewhat in this fashion:---\n\n\"La! Jack, what a pity you and I should live so separate! I'll be\nbound you're the best fellow in the world, the very backbone of the\ncountry. To be sure there's a silly old-fashioned lot of Lumpkins in\nour part that will have it you're no gentleman, but I say, 'Gentle\nis as Gentle does,' and fair play's a jewel. I will enter your\ncounting-house as soon as drink to you, as I do here.\"\n\nWhereat Jack cried--\n\n\"God 'a' mercy, a very kind gentleman! Be welcome to my house. Pray\ntake it as your own. I think you may count me one of you? Eh? Be\nseated. Come, how can I serve you?\": and at last he had this\nJackanapes taking a handsome salary for doing nothing.\n\nWhen Jack's friends would reproach him and say, \"Oh, Jack, Jack,\nbeware this fine gentleman; he will be your ruin,\" Jack would\nanswer, \"A plague on all levellers,\" or again, \"What if he be a\ngentleman? So that he have talent 'tis all I seek,\" or yet further,\n\"Well, gentle or simple, thank God he's an honest Englishman.\"\nWhereat Jack added to the firm, Isaacs of Hamburg, Larochelle of\nCanada, Warramugga of Van Dieman's Land, Smuts Bieken of the Cape of\nGood Hope, and the Maharajah of Mahound of the East Indies that was\na plaguey devilish-looking black fellow, pock-marked, and with a\nterrible great paunch to him.\n\nSo things went all to the dogs with poor Jack, that would hear no\nsense or reason from his father's old friends, but was always seen\narm in arm with Sir John Snipe, Warra Mugga, the Maharajah and the\nrest; drinking at the sign of the \"Beerage,\" gambling and dicing at\n\"The Tape,\" or playing fisticuffs at the \"Lord Nelson,\" till at last\nhe quarrelled with all the world but his boon companions and, what\nwas worse, boasted that his father's brother's son, rich Jonathan\nSpare, was of the company. So if he met some dirty dog or other in\nthe street he would cry, \"Come and sup to-night, you shall meet\nCousin Jonathan!\" and when no Jonathan was there he would make a\nthousand excuses saying, \"Excuse Jonathan, I pray you, he has\nmarried a damned Irish wife that keeps him at home\"; or, \"What!\nJonathan not come? Oh! we'll wait awhile. He never fails, for we are\nlike brothers!\" and so on; till his companions came to think at last\nthat he had never met or known Jonathan; which was indeed the case.\n\nAbout this time he began to think himself too fine a gentleman to\nlive over the shop as his father had done, and so asked Sir John\nSnipe where he might go that was more genteel; for he still had too\nmuch sense to ask any of those other outlandish fellows' advice in\nsuch a matter. At last, on Snipe's bespeaking, he went to Wimbledon,\nwhich is a vastly smart suburb, and there, God knows, he fell into a\nthousand absurd tricks so that many thought he was off his head.\n\nHe hired a singing man to stand before his door day and night\nsinging vulgar songs out of the street in praise of Dick Turpin and\nMolly Nog, only forcing him to put in his name of Jack Bull in the\nplace of the Murderer or Oyster Wench therein celebrated.\n\nHe would drink rum with common soldiers in the public-houses and\nthen ask them in to dinner to meet gentlemen, saying \"These are\nheroes and gentlemen, which are the two first kinds of men,\" and\nthey would smoke great pipes of tobacco in his very dining-room to\nthe general disgust.\n\nHe would run out and cruelly beat small boys unaware, and when he\nhad nigh killed them he would come back and sit up half the night\nwriting an account of how he had fought Tom Mauler of Bermondsey and\nbeaten him in a hundred and two rounds, which (he would add) no man\nliving but he could do.\n\nHe would hang out of his window a great flag with a challenge on it\n\"to all the people of Wimbledon assembled, or to any of them\nsingly,\" and then he would be seen at his front gate waving a great\nred flag and gnawing a bone like a dog, saying that he loved Force\nonly, and would fight all and any.\n\nWhen he received any print, newspaper, book or pamphlet that praised\nany but himself, he would throw it into the fire in a kind of\nfrenzy, calling God to witness that he was the only person of\nconsequence in the world, that it was a horrible shame that he was\nso neglected, and Lord knows what other rubbish.\n\nIn this spirit he quarrelled with all his fellow-underwriters and\nfriends and comrades, and that in the most insolent way. For knowing\nwell that Mr. Frog had a shrew of a wife, he wrote to him daily\nasking \"if he had had a domestic broil of late, and how his poor\nhead felt since it was bandaged.\" To Mr. Hans, who lived in a small\nway and loved gardening, he sent an express \"begging him to mind his\ncabbages and leave gentlemen to their greater affairs.\" To Niccolini\nof Savoy, the little swarthy merchant, he sent indeed a more polite\nnote, but as he said in it \"that he would be very willing to give\nhim charity and help him as he could\" and as he added \"for my father\nit was that put you up in business\" (which was a monstrous lie, for\nFrog had done this) he did but offend. Then to Mr. William Eagle,\nthat was a strutting, arrogant fellow, but willing to be a friend,\nhe wrote every Monday to say that the house of Bull was lost unless\nMr. Eagle would very kindly protect it and every Thursday to\nchallenge him to mortal combat, so that Mr. Eagle (who, to tell the\ntruth, was no great wit, but something of a dullard and moreover\nsuffering from a gathering in the ear, a withered arm, and poor\nblood) gave up his friendship and business with Bull and took to\nmaking up sermons and speeches for orators.\n\nHe would have no retainers but two, whose common names were Hocus\nand Pocus, but as he hated the use of common names and as no one had\nheard of Hocus' lineage (nor did he himself know it) he called him,\nHocus, \"Freedom\" as being a high-sounding and moral name for a\nfootman and Pocus (whose name was of an ordinary decent kind) he\ncalled \"Glory\" as being a good counterweight to Freedom; both these\nwere names in his opinion very decent and well suited for a\ngentleman's servants.\n\nNow Freedom and Glory got together in the apple closet and put it to\neach other that, as their master was evidently mad it would be a\nthousand pities to take no advantage of it, and they agreed that\nwhatever bit of jobbing Hocus Freedom should do, Pocus Glory should\napprove; and contrariwise about. But they kept up a sham quarrel to\nmask this; thus Hocus was for Chapel, Pocus for Church, and it was\nagreed Hocus should denounce Pocus for drinking Port.\n\nThe first fruit of their conspiracy was that Hocus recommended his\nbrother and sister, his two aunts and nieces and four nephews, his\nown six children, his dog, his conventicle-minister, his laundress,\nhis secretary, a friend of whom he had once borrowed five pounds,\nand a blind beggar whom he favoured, to various posts about the\nhouse and to certain pensions, and these Jack Bull (though his\nfortune was already dwindling) at once accepted.\n\nThereupon Pocus loudly reproached Hocus in the servants' hall,\nsaying that the compact had only stood for things in reason, whereat\nHocus took off his coat and offered to \"Take him on,\" and Pocus,\nthinking better of it, managed for his share to place in the\nhousehold such relatives as he could, namely, Cohen to whom he was\nin debt, Bernstein his brother-in-law and all his family of five\nexcept little Hugh that blacked the boots for the Priest, and so was\nalready well provided for.\n\nIn this way poor Jack's fortune went to rack and ruin. The clerks in\nhis office in the City (whom he now never saw) would telegraph to him\nevery making-up day that there was loss that had to be met, but to\nthese he always sent the same reply, namely, \"Sell stock and scrip to\nthe amount\"; and as that phrase was costly, he made a code-word, to\nwit, \"Prosperity,\" stand for it. Till one day they sent word \"There\nis nothing left.\" Then he bethought him how to live on credit, but\nthis plan was very much hampered by his habit of turning in a passion\non all those who did not continually praise him. Did an honest man\nlook in and say, \"Jack, there is a goat eating your cabbages,\" he\nwould fly into a rage and say, \"You lie, Pro-Boer, my cabbages are\nsacred, and Jove would strike the goat dead that dared to eat them,\"\nor if a poor fellow should touch his hat in the street and say,\n\"Pardon, sir, your buttons are awry,\" he would answer, \"Off, villain!\nZounds, knave! Know you not that my Divine buttons are the model of\nthings?\" and so forth, until he fell into a perfect lunacy.\n\nBut of how he came to selling tokens of little leaden soldiers at a\npenny in front of the Exchange, and of how at last he even fell to\nwriting for the papers, I will not tell you; for, _imprimis_,\nit has not happened yet, nor do I think it will, and in the second\nplace I am tired of writing.\n\n\n\n\nON A WINGED HORSE AND THE EXILE WHO RODE HIM\n\n\nIt so happened that one day I was riding my horse Monster in the\nBerkshire Hills right up above that White Horse which was dug they\nsay by this man and by that man, but no one knows by whom; for I was\nseeing England, a delightful pastime, but a somewhat anxious one if\none is riding a horse. For if one is alone one can sleep where one\nchooses and walk at one's ease, and eat what God sends one and spend\nwhat one has; but when one is responsible for any other being\n(especially a horse) there come in a thousand farradiddles, for of\neverything that walks on earth, man (not woman--I use the word in\nthe restricted sense) is the freest and the most unhappy.\n\nWell, then, I was riding my horse and exploring the Island of\nEngland, going eastward of a summer afternoon, and I had so ridden\nalong the ridge of the hills for some miles when I came, as chance\nwould have it, upon a very extraordinary being.\n\nHe was a man like myself, but his horse, which was grazing by his\nside, and from time to time snorting in a proud manner, was quite\nunlike my own. This horse had all the strength of the horses of\nNormandy, all the lightness, grace, and subtlety of the horses of\nBarbary, all the conscious value of the horses that race for rich\nmen, all the humour of old horses that have seen the world and will\nbe disturbed by nothing, and all the valour of young horses who have\ntheir troubles before them, and race round in paddocks attempting to\ndefeat the passing trains. I say all these things were in the horse,\nand expressed by various movements of his body, but the list of\nthese qualities is but a hint of the way in which he bore himself;\nfor it was quite clearly apparent as I came nearer and nearer to\nthis strange pair that the horse before me was very different (as\nperhaps was the man) from the beings that inhabit this island.\n\nWhile he was different in all qualities that I have mentioned--or\nrather in their combination--he also differed physically from most\nhorses that we know, in this, that from his sides and clapt along\nthem in repose was growing a pair of very fine sedate and noble\nwings. So habited, with such an expression and with such gestures of\nhis limbs, he browsed upon the grass of Berkshire, which, if you\nexcept the grass of Sussex and the grass perhaps of Hampshire, is\nthe sweetest grass in the world. I speak of the chalk-grass; as for\nthe grass of the valleys, I would not eat it in a salad, let alone\ngive it to a beast.\n\nThe man who was the companion rather than the master of this\ncharming animal sat upon a lump of turf singing gently to himself\nand looking over the plain of Central England, the plain of the\nUpper Thames, which men may see from these hills. He looked at it\nwith a mixture of curiosity, of memory, and of desire which was very\ninteresting but also a little pathetic to watch. And as he looked at\nit he went on crooning his little song until he saw me, when with\ngreat courtesy he ceased and asked me in the English language\nwhether I did not desire companionship.\n\nI answered him that certainly I did, though not more than was\ncommonly the case with me, for I told him that I had had\ncompanionship in several towns and inns during the past few days,\nand that I had had but a few hours' bout of silence and of\nloneliness.\n\n\"Which period,\" I added, \"is not more than sufficient for a man of\nmy years, though I confess that in early youth I should have found\nit intolerable.\"\n\nWhen I had said this he nodded gravely, and I in my turn began to\nwonder of what age he might be, for his eyes and his whole manner\nwere young, but there was a certain knowledge and gravity in his\nexpression and in the posture of his body which in another might\nhave betrayed middle age. He wore no hat, but a great quantity of\nhis own hair, which was blown about by the light summer wind upon\nthese heights. As he did not reply to me, I asked him a further\nquestion, and said:\n\n\"I see you are gazing upon the plain. Have you interests or memories\nin that view? I ask you without compunction so delicate a question\nbecause it is as open to you to lie as it was to me when I lied to\nthem only yesterday morning, a little beyond Wayland's Cave, telling\nthem that I had come to make sure of the spot where St. George\nconquered the Dragon, though, in truth, I had come for no such\npurpose, and telling them that my name was so-and-so, whereas it was\nnothing of the kind.\"\n\nHe brightened up at this, and said: \"You are quite right in telling\nme that I am free to lie if I choose, and I would be very happy to\nlie to you if there were any purpose in so doing, but there is none.\nI gaze upon this plain with the memories that are common to all men\nwhen they gaze upon a landscape in which they have had a part in the\nyears recently gone by. That is, the plain fills me with a sort of\nlonging, and yet I cannot say that the plain has treated me\nunjustly. I have no complaint against it. God bless the plain!\"\nAfter thinking a few moments, he added: \"I am fond of Wantage;\nWallingford has done me no harm; Oxford gave me many companions; I\nwas not drowned at Dorchester beyond the Little Hills; and the best\nof men gave me a true farewell in Faringdon yonder. Moreover, Cumnor\nis my friend. Nevertheless, I like to indulge in a sort of sadness\nwhen I look over this plain.\"\n\nI then asked him whither he would go next.\n\nHe answered: \"My horse flies, and I am therefore not bound to any\nparticular track or goal, especially in these light airs of summer\nwhen all the heaven is open to me.\"\n\nAs he said this I looked at his mount and noticed that when he shook\nhis skin as horses will do in the hot weather to rid themselves of\nflies, he also passed a little tremor through his wings, which were\nlarge and goose-grey, and, spreading gently under that effort,\nseemed to give him coolness.\n\n\"You have,\" said I, \"a remarkable horse.\"\n\nAt this word he brightened up as men do when something is spoken of\nthat interests them nearly, and he answered: \"Indeed, I have! and I\nam very glad you like him. There is no such other horse to my\nknowledge in England, though I have heard that some still linger in\nIreland and in France, and that a few foals of the breed have been\ndropped of late years in Italy, but I have not seen them.\n\n\"How did you come by this horse?\" said I; \"if it is not trespassing\nupon your courtesy to ask you so delicate a question.\"\n\n\"Not at all; not at all,\" he answered. \"This kind of horse runs wild\nupon the heaths of morning and can be caught only by Exiles: and I\nam one.... Moreover, if you had come three or four years later than\nyou have I should have been able to give you an answer in rhyme, but\nI am sorry to say that a pestilent stricture of the imagination, or\nrather, of the compositive faculty so constrains me that I have not\nyet finished the poem I have been writing with regard to the\ndiscovery and service of this beast.\"\n\n\"I have great sympathy with you,\" I answered, \"I have been at the\nballade of Val-\u00e8s-Dunes since the year 1897 and I have not yet\ncompleted it.\"\n\n\"Well, then,\" he said, \"you will be patient with me when I tell you\nthat I have but three verses completed.\" Whereupon without further\ninvitation he sang in a loud and clear voice the following verse:\n\n _It's ten years ago to-day you turned me out of doors\n To cut my feet on flinty lands and stumble down the shores.\n And I thought about the all in all ..._\n\n\"The '_all in all_,'\" I said, \"is weak.\"\n\nHe was immensely pleased with this, and, standing up, seized me by\nthe hand. \"I know you now,\" he said, \"for a man who does indeed\nwrite verse. I have done everything I could with those three\nsyllables, and by the grace of Heaven I shall get them right in\ntime. Anyhow, they are the stop-gap of the moment, and with your\nleave I shall reserve them, for I do not wish to put words like\n'tumty tum' into the middle of my verse.\"\n\nI bowed to him, and he proceeded:\n\n _And I thought about the all in all, and more than I could tell;\n But I caught a horse to ride upon and rode him very well.\n He had flame behind the eyes of him and wings upon his side--\n And I ride; and I ride!_\n\n\"Of how many verses do you intend this metrical composition to be?\"\nsaid I, with great interest.\n\n\"I have sketched out thirteen,\" said he firmly, \"but I confess that\nthe next ten are so embryonic in this year 1907 that I cannot sing\nthem in public.\" He hesitated a moment, then added: \"They have many\nfine single lines, but there is as yet no composition or unity about\nthem.\" And as he recited the words \"composition\" and \"unity\" he\nwaved his hand about like a man sketching a cartoon.\n\n\"Give me, then,\" said I, \"at any rate the last two.\" For I had\nrapidly calculated how many would remain of his scheme.\n\nHe was indeed pleased to be so challenged, and continued to sing:\n\n _And once atop of Lambourne Down, towards the hill of Clere,\n I saw the host of Heaven in rank and Michael with his spear\n And Turpin, out of Gascony, and Charlemagne the lord,\n And Roland of the Marches with his hand upon his sword\n For fear he should have need of it;--and forty more beside!\n And I ride; and I ride!\n For you that took the all in all..._\n\n\"That again is weak,\" I murmured.\n\n\"You are quite right,\" he said gravely, \"I will rub it out.\" Then he\nwent on:\n\n _For you that took the all in all, the things you left were\n three:\n A loud Voice for singing, and keen Eyes to see,\n And a spouting Well of Joy within that never yet was dried!\n And I ride!_\n\nHe sang this last in so fierce and so exultant a manner that I was\nimpressed more than I cared to say, but not more than I cared to\nshow. As for him, he cared little whether I was impressed or not; he\nwas exalted and detached from the world.\n\nThere were no stirrups upon the beast. He vaulted upon it, and said\nas he did so:\n\n\"You have put me into the mood, and I must get away!\"\n\nAnd though the words were abrupt, he _did_ speak them with such\na grace that I will always remember them!\n\nHe then touched the flanks of his horse with his heels (on which\nthere were no spurs) and at once beating the air powerfully twice or\nthrice with its wings it spurned the turf of Berkshire and made out\nsouthward and upward into the sunlit air, a pleasing and a glorious\nsight.\n\nIn a very little while they had dwindled to a point of light and\nwere soon mixed with the sky. But I went on more lonely along the\ncrest of the hills, very human, riding my horse Monster, a mortal\nhorse--I had almost written a human horse. My mind was full of\nsilence.\n\nSome of those to whom I have related this adventure criticise it by\nthe method of questions and of cross-examination proving that it\ncould not have happened precisely where it did; showing that I left\nthe vale so late in the afternoon that I could not have found this\nman and his mount at the hour I say I did, and making all manner of\ncomments upon the exact way in which the feathers (which they say\nare those of a bird) grew out of the hide of the horse, and so\nforth. There are no witnesses of the matter, and I go lonely, for\nmany people will not believe, and those who do believe believe too\nmuch.\n\n\n\n\nON A MAN AND HIS BURDEN\n\n\nOnce there was a Man who lived in a House at the Corner of a Wood\nwith an excellent landscape upon every side, a village about one\nmile off, and a pleasant stream flowing over chalk and full of\ntrout, for which he used to fish.\n\nThis man was perfectly happy for some little time, fishing for the\ntrout, contemplating the shapes of clouds in the sky, and singing\nall the songs he could remember in turn under the high wood, till\none day he found, to his annoyance, that there was strapped to his\nback a Burden.\n\nHowever, he was by nature of a merry mood, and began thinking of all\nthe things he had read about Burdens. He remembered an uncle of his\ncalled Jonas (ridiculous name) who had pointed out that Burdens,\nespecially if borne in youth, strengthen the upper deltoid muscle,\nexpand the chest, and give to the whole figure an erect and graceful\npoise. He remembered also reading in a book upon \"Country Sports\"\nthat the bearing of heavy weights is an excellent training for all\nother forms of exercise, and produces a manly and resolute carriage,\nvery useful in golf, cricket and Colonial wars. He could not forget\nhis mother's frequent remark that a Burden nobly endured gave\nfirmness, and at the same time elasticity, to the character, and\naltogether he went about his way taking it as kindly as he could;\nbut I will not deny that it annoyed him.\n\nIn a few days he discovered that during sleep, when he lay down, the\nBurden annoyed him somewhat less than at other times, though the\nmemory of it never completely left him. He would therefore sleep for\na very considerable number of hours every day, sometimes retiring to\nrest as early as nine o'clock, nor rising till noon of the next day.\nHe discovered also that rapid and loud conversation, adventure,\nwine, beer, the theatre, cards, travel, and so forth made him forget\nhis Burden for the time being, and he indulged himself perhaps to\nexcess in all these things. But when the memory of his Burden would\nreturn to him after each indulgence, whether working in his garden,\nor fishing for trout, or on a lonely walk, he began reluctantly to\nadmit that, on the whole, he felt uncertainty and doubt as to\nwhether the Burden was really good for him.\n\nIn this unpleasing attitude of mind he had the good fortune one day\nto meet with an excellent Divine who inhabited a neighbouring\nparish, and was possessed of no less a sum than \u00a329,000. This\nEcclesiastic, seeing his whilom jocund Face fretted with the Marks\nof Care, put a hand gently upon his shoulder and said:\n\n\"My young friend, I easily perceive that you are put out by this\nBurden which you bear upon your shoulders. I am indeed surprised\nthat one so intelligent should take such a matter so ill. What! Do\nyou not know that burdens are the common lot of humanity? I myself,\nthough you may little suspect it, bear a burden far heavier than\nyours, though, true, it is invisible, and not strapped on to my\nshoulders by gross material thongs of leather, as is yours. The\nworthy Squire of our parish bears one too; and with what manliness!\nwhat ease! what abnegation! Believe me, these other Burdens of which\nyou never hear, and which no man can perceive, are for that very\nreason the heaviest and the most trying. Come, play the man! Little\nby little you will find that the patient sustenance of this Burden\nwill make you something greater, stronger, nobler than you were, and\nyou will notice as you grow older that those who are most favoured\nby the Unseen bear the heaviest of such impediments.\"\n\nWith these last words recited in a solemn, and, as it were, an\ninspired voice, the Hierarch lifted an immense stone from the\nroadway, and placing it on the top of the Burden, so as considerably\nto add to its weight, went on his way.\n\nThe irritation of the Man was already considerable when his family\ncalled upon him--his mother, that is, his younger sister, his cousin\nJane, and her husband--and after they had eaten some of his food and\ndrunk some of his beer they all sat out in the garden with him and\ntalked to him somewhat in this manner:\n\n\"We really cannot pity you much, for ever since you were a child\nwhatever evil has happened to you has been your own doing, and\nprobably this is no different from the rest.... What can have\npossessed you to get putting upon your back an ugly, useless, and\ndangerous great Burden! You have no idea how utterly out of fashion\nyou seem, stumbling about the roads like a clodhopper, and going up\nand downstairs as though you were on the treadmill.... For the\nLord's sake, at least have the decency to stay at home and not to\ndisgrace the family with your miserable appearance!\"\n\nHaving said so much they rose, and adding to his burden a number of\nleaden weights they had brought with them, went on their way and\nleft him to his own thoughts.\n\nYou may well imagine that by this time the irritation of the Man had\ngone almost past bearing. He would quarrel with his best friends,\nand they, in revenge, would put something more on to the burden,\ntill he felt he would break down. It haunted his dreams and filled\nmost of his waking thoughts, and did all those things which burdens\nhave been discovered to do since the beginning of time, until at\nlast, though very reluctantly, he determined to be rid of it.\n\nUpon hearing of this resolution his friends and acquaintances raised\na most fearful hubbub; some talked of sending for the police, others\nof restraining him by force, and others again of putting him into an\nasylum, but he broke away from them all, and, making for the open\nroad, went out to see if he could not rid himself of this abominable\nstrain.\n\nOf himself he could not, for the Burden was so cunningly strapped on\nthat his hands could not reach it, and there was magic about it, and\na spell; but he thought somewhere there must be someone who could\ntell him how to cast it away.\n\nIn the very first ale-house he came to he discovered what is common\nto such places, namely, a batch of politicians, who laughed at him\nvery loudly for not knowing how to get rid of burdens. \"It is done,\"\nthey said, \"by the very simple method of paying one of us to get on\ntop and undo the straps.\" This the man said he would be very willing\nto do, whereat the politicians, having fought somewhat among\nthemselves for the money, desisted at last in favour of the most\nvulgar, who climbed on to the top of the man's burden, and remained\nthere, viewing the landscape and commenting in general terms upon\nthe nature of public affairs, and when the man complained a little,\nthe politician did but cuff him sharply on the side of the head to\nteach him better manners.\n\nYet a little further on he met with a Scientist, who told him in\nEnglish Greek a clear and simple method of getting rid of the\nburden, and, since the Man did not seem to understand, he lost his\ntemper, and said, \"Come, let me do it,\" and climbed up by the side\nof the Politician. Once there the Scientist confessed that the\nproblem was not so easy as he had imagined.\n\n\"But,\" said he, \"now that I am here, you may as well carry me, for\nit will be no great additional weight, and meanwhile I will spend\nmost of my time in trying to set you free.\"\n\nAnd the third man he met was a Philosopher with quiet eyes; a person\nwhose very gestures were profound. Taking by the hand the Man, now\nfevered and despairing, he looked at him with a mixture of\ncomprehension and charity, and he said:\n\n\"My poor fellow, your eyes are very wild and staring and bloodshot.\nHow little you understand the world!\" Then he smiled gently, and\nsaid, \"Will you never learn?\"\n\nAnd without another word he climbed up on the top of the burden and\nseated himself by the side of the other two.\n\nAfter this the man went mad.\n\nThe last time I saw him he was wandering down the road with his\nburden very much increased. He was bearing not only these original\nthree, but some Kings and Tax-gatherers and Schoolmasters, several\nFortune-tellers, and an Old Admiral. He was blind, and they were\ngoading him. But as he passed me he smiled and gibbered a little,\nand told me it was in the nature of things, and went on downward\nstumbling.\n\n_This Parable I think, as I re-read it, demands a KEY, lest it\nprove a stumbling-block to the muddle-headed and a perplexity to the\nfoolish. Here then is the KEY:_--\n\n_The_ MAN _is a_ MAN. _His_ BURDEN _is that Burden\nwhich men often feel themselves to be bearing as they advance from\nyouth to manhood. The_ RELATIVES _(his mother, his sister, his\ncousins, etc.) are a Man's_ RELATIVES _and the little weights\nthey add to the_ BURDEN _are the little additional weights a\nMan's_ RELATIVES _commonly add to his burden. The_ PARSON\n_represents a_ PARSON, _and the_ POLITICIAN, _the_\nPHILOSOPHER, _the_ SCIENTIST, _the_ KINGS, _the_ TAX-GATHERERS _and the_\nOLD ADMIRAL, _stand severally for an_ OLD ADMIRAL, TAX-GATHERERS,\nPOLITICIANS, PHILOSOPHERS, SCIENTISTS _and_ KINGS.\n\n_The_ POLITICIANS _who fight for the_ MONEY\n_represent_ POLITICIANS, _and the_ MONEY _they struggle\nfor is the_ MONEY _for which Politicians do ceaselessly jostle\nand barge one another. The_ MOST VULGAR _in whose favour the\nothers desist, represents the_ MOST VULGAR _who, among Politicians,\ninvariably obtains the largest share of whatever public money is going._\n\n_The_ MADNESS _of the Man at the end, stands for the_ MADNESS\n_which does as a fact often fall upon Men late in life if their\nBurdens are sufficiently increased._\n\n_I trust that with this Key the Parable will be clear to all._\n\n\n\n\nON A FISHERMAN AND THE QUEST OF PEACE\n\n\nIn that part of the Thames where the river begins to feel its life\nbefore it knows its name the counties play with it upon either side.\nIt is not yet a boundary. The parishes upon the northern bank are\nsometimes as truly Wiltshire as those to the south. The men upon the\nfarms that look at each other over the water are close neighbours;\nthey use the same words and the way they build their houses is the\nsame. Between them runs the beginning of the Thames.\n\nFrom the surface of the water the whole prospect is sky, bounded by\nreeds; but sitting up in one's canoe one sees between the reeds\ndistant hills to the southward, or, on the north, trees in groups,\nand now and then the roofs of a village; more often the lonely group\nof a steading with a church close by.\n\nFloating down this stream quite silently, but rather swiftly upon a\nsummer's day, I saw on the bank to my right a very pleasant man. He\nwas perhaps a hundred yards or two hundred ahead of me when I first\ncaught sight of him, and perceived that he was a clergyman of the\nChurch of England. He was fishing.\n\nHe was dressed in black, even his hat was black (though it was of\nstraw), but his collar was of such a kind as his ancestors had worn,\nturned down and surrounded by a soft white tie. His face was clear\nand ruddy, his eyes honest, his hair already grey, and he was gazing\nintently upon the float; for I will not conceal it that he was\nfishing in that ancient manner with a float shaped like a sea-buoy\nand stuck through with a quill. So fish the yeomen to this day in\nNorthern France and in Holland. Upon such immutable customs does an\nancient State repose, which, if they are disturbed, there is danger\nof its dissolution.\n\nAs I so looked at him and rapidly approached him I took care not to\ndisturb the water with my paddle, but to let the boat glide far from\nhis side, until in the pleasure of watching him, I got fast upon the\nfurther reeds. There she held and I, knowing that the effort of\ngetting her off would seriously stir the water, lay still. Nor did I\nspeak to him, though he pleased me so much, because a friend of mine\nin Lambourne had once told me that of all things in Nature what a\nfish most fears is the voice of a man.\n\nHe, however, first spoke to me in a sort of easy tone that could\nfrighten no fish. He said \"Hullo!\"\n\nI answered him in a very subdued voice, for I have no art where\nfishes are concerned, \"Hullo!\"\n\nThen he asked me, after a good long time, whether his watch was\nright, and as he asked me he pulled out his, which was a large,\nthick, golden watch, and looked at it with anxiety and dread. He\nasked me this, I think, because I must have had the look of a tired\nman fresh from the towns, and with the London time upon him, and yet\nI had been for weeks in no town larger than Cricklade: moreover, I\nhad no watch. Since, none the less, it is one's duty to uplift,\nsustain, and comfort all one's fellows I told him that his watch was\nbut half a minute fast, and he put it back with a greater content\nthan he had taken it out; and, indeed, anyone who blames me for what\nI did in so assuring him of the time should remember that I had\nother means than a watch for judging it. The sunlight was already\nfull of old kindness, the midges were active, the shadow of the\nreeds on the river was of a particular colour, the haze of a\nparticular warmth; no one who had passed many days and nights\ntogether sleeping out and living out under this rare summer could\nmistake the hour.\n\nIn a little while I asked him whether he had caught any fish. He\nsaid he had not actually caught any, but that he would have caught\nseveral but for accidents, which he explained to me in technical\nlanguage. Then he asked me in his turn where I was going to that\nevening. I said I had no object before me, that I would sleep when I\nfelt sleepy, and wake when I felt wakeful, and that I would so drift\ndown Thames till I came to anything unpleasant, when it was my\ndesign to leave my canoe at once, to tie it up to a post, and to go\noff to another place, \"for,\" I told him, \"I am here to think about\nPeace, and to see if She can be found.\" When I said this his face\nbecame moody, and, as though such portentous thoughts required\naction to balance them, he strained his line, lifted his float\nsmartly from the water (so that I saw the hook flying through the\nair with a quarter of a worm upon it), and brought it down far up\nthe stream. Then he let it go slowly down again as the water carried\nit, and instead of watching it with his steady and experienced eyes\nhe looked up at me and asked me if, as yet, I had come upon any clue\nto Peace, that I expected to find Her between Cricklade and Bablock\nHythe. I answered that I did not exactly expect to find Her, that I\nhad come out to think about Her, and to find out whether She could\nbe found. I told him that often and often as I wandered over the\nearth I had clearly seen Her, as once in Auvergne by Pont-Gibaud,\nonce in Terneuzen, several times in Hazlemere, Hampstead, Clapham,\nand other suburbs, and more often than I could tell in the Weald:\n\"but seeing Her,\" said I, \"is one thing and holding Her is another.\nI hardly propose to follow all Her ways, but I do propose to\nconsider Her nature until I know so much as to be able to discover\nHer at last whenever I have need, for I am convinced by this time\nthat nothing else is worth the effort of a man ... and I think I\nshall achieve my object somewhere between here and Bablock Hythe.\"\n\nHe told me without interest that there was nothing attractive in the\npursuit or in its realisation.\n\nI answered with equal promptitude that the whole of attraction was\nsummed up in it: that to nothing else did we move by nature, and to\nnothing else were we drawn but to Peace. I said that a completion\nand a fulfilment were vaguely demanded by a man even in very early\nyouth, that in manhood the desire for them became a passion and in\nearly middle age so overmastering and natural a necessity that all\nwho turned aside from it and attempted to forget it were justly\ndespised by their fellows and were some of them money-makers, some\nof them sybarites, but all of them perverted men, whose hard eyes,\nweak mouths, and fear of every trial sufficiently proved the curse\nthat was upon them. I told him as heatedly as one can speak lying\nback in a canoe to a man beyond a little river that he, being older\nthan I, should know that everything in a full man tended towards\nsome place where expression is permanent and secure; and then I told\nhim that since I had only seen such a place far off as it were, but\nnever lived in, I had set forth to see if I might think out the way\nto it, \"and I hope,\" I said, \"to finish the problem not so far down\nas Bablock Hythe, but nearer by, towards New Bridge or even higher,\nby Kelmscott.\"\n\nHe asked me, after a little space, during which he took off the\nremnant of the worm and replaced it by a large new one, whether when\nI said \"Peace\" I did not really mean \"Harmony.\"\n\nAt this phrase a suspicion rose in my mind; it seemed to me that I\nknew the school that had bred him, and that he and I should be\nacquainted. So I was appeased and told him I did not mean Harmony,\nfor Harmony suggested that we had to suit ourselves to the things\naround us or to get suited to them. I told him what I was after was\nno such German Business, but something which was Fruition and more\nthan Fruition--full power to create and at the same time to enjoy, a\nco-existence of new delight and of memory, of growth, and yet of\nforeknowledge and an increasing reverence that should be\nincreasingly upstanding, and high hatred as well as high love\njustified; for surely this Peace is not a lessening into which we\nsink, but an enlargement which we merit and into which we rise and\nenter--\"and this,\" I ended, \"I am determined to obtain before I get\nto Bablock Hythe.\"\n\nHe shook his head determinedly and said my quest was hopeless.\n\n\"Sir,\" said I, \"are you acquainted with the Use of Sarum?\"\n\n\"I have read it,\" he said, \"but I do not remember it well.\" Then,\nindeed, indeed I knew that he was of my own University and of my own\ncollege, and my heart warmed to him as I continued:\n\n\"It is in Latin; but, after all, that was the custom of the time.\"\n\n\"Latin,\" he answered, \"was in the Middle Ages a universal tongue.\"\n\n\"Do you know,\" said I, \"that passage which begins 'Illam Pacem----'?\"\n\nAt this moment the float, which I had almost forgotten but which he\nin the course of our speeches had more and more remembered, began to\nbob up and down violently, and, if I may so express myself, the\nPhilosopher in him was suddenly swamped by the Fisherman. He struck\nwith the zeal and accuracy of a conqueror; he did something\ndexterous with his rod, flourished the line and landed a\nmagnificent--ah! There the whole story fails, for what on earth was\nthe fish?\n\nHad it been a pike or a trout I could have told it, for I am well\nacquainted with both; but this fish was to me as a human being is to\na politician: this fish was to me unknown....\n\n\n\n\nON A HERMIT WHOM I KNEW\n\n\nIn a valley of the Apennines, a little before it was day, I went\ndown by the side of a torrent wondering where I should find repose;\nfor it was now some hours since I had given up all hope of\ndiscovering a place for proper human rest and for the passing of the\nnight, but at least I hoped to light upon a dry bed of sand under\nsome overhanging rock, or possibly of pine needles beneath closely\nwoven trees, where one might get sleep until the rising of the sun.\n\nAs I still trudged, half expectant and half careless, a man came up\nbehind me, walking quickly as do mountain men: for throughout the\nworld (I cannot tell why) I have noticed that the men of the\nmountains walk quickly and in a sprightly manner, arching the foot,\nand with a light and general gait as though the hills were waves and\nas though they were in thought springing upon the crests of them.\nThis is true of all mountaineers. They are but few.\n\nThis man, I say, came up behind me and asked me whether I were going\ntowards a certain town of which he gave me the name, but as I had\nnot so much as heard of this town I told him I knew nothing of it. I\nhad no map, for there was no good map of that district, and a bad\nmap is worse than none. I knew the names of no towns except the\nlarge towns on the coast. So I said to him:\n\n\"I cannot tell anything about this town, I am not making towards it.\nBut I desire to reach the sea coast, which I know to be many hours\naway, and I had hoped to sleep overnight under some roof or at least\nin some cavern, and to start with the early morning; but here I am,\nat the end of the night, without repose and wondering whether I can\ngo on.\"\n\nHe answered me:\n\n\"It is four hours to the sea coast, but before you reach it you will\nfind a lane branching to the right, and if you will go up it (for it\nclimbs the hill) you will find a hermitage. Now by the time you are\nthere the hermit will be risen.\"\n\n\"Will he be at his prayers?\" said I.\n\n\"He says no prayers to my knowledge,\" said my companion lightly;\n\"for he is not a hermit of that kind. Hermits are many and prayers\nare few. But you will find him bustling about, and he is a very\nhospitable man. Now as it so happens that the road to the sea coast\nbends here round along the foot of the hills, you will, in his\ncompany, perceive the port below you and the populace and the high\nroad, and yet you will be saving a good hour in distance of time,\nand will have ample rest before reaching your vessel, if it is a\nvessel indeed that you intend to take.\"\n\nWhen he had said these things I thanked him and gave him a bit of\nsausage and went along my way, for as he had walked faster than me\nbefore our meeting and while I was still in the dumps, so now I\nwalked faster than him, having received good news.\n\nAll happened just as he had described. The dawn broke behind me over\nthe noble but sedate peaks of the Apennines; it first defined the\nheights against the growing colours of the sun, it next produced a\ngeneral warmth and geniality in the air about me; it last displayed\nthe downward opening of the valley, and, very far off, a plain that\nsloped towards the sea.\n\nInvigorated by the new presence of the day I went forward more\nrapidly, and came at last to a place where a sculptured panel made\nout of marble, very clever and modern, and representing a mystery,\nmarked the division between two ways; and I took the lane to my\nright as my companion of the night hours had advised me.\n\nFor perhaps a mile or a little more the lane rose continually\nbetween rough walls intercepted by high banks of thorn, with here\nand there a vineyard, and as it rose one had between the breaches of\nthe wall glimpses of an ever-growing sea: for, as one rose, the sea\nbecame a broader and a broader belt, and the very distant islands,\nwhich at first had been but little clouds along the horizon, stood\nout and became parts of the landscape, and, as it were, framed all\nthe bay.\n\nThen at last, when I had come to the height of the hill, to where it\nturned a corner and ran level along the escarpment of the cliffs\nthat dominated the sea plain, I saw below me a considerable stretch\nof country, between the fall of the ground and the distant shore,\nand under the daylight which was now full and clear one could\nperceive that all this plain was packed with an intense cultivation,\nwith houses, happiness and men.\n\nFar off, a little to the northward, lay the mass of a town; and\nstretching out into the Mediterranean with a gesture of command and\nof desire were the new arms of the harbour.\n\nTo see such things filled me with a complete content. I know not\nwhether it be the effect of long vigil, or whether it be the effect\nof contrast between the darkness and the light, but certainly to\ncome out of a lonely night spent on the mountains, down with the\nsunlight into the civilisation of the plain, is, for any man that\ncares to undergo the suffering and the consolation, as good as any\nexperience that life affords. Hardly had I so conceived the view\nbefore me when I became aware, upon my right, of a sort of cavern,\nor rather a little and carefully minded shrine, from which a\ngreeting proceeded.\n\nI turned round and saw there a man of no great age and yet of a\nvenerable appearance. He was perhaps fifty-five years old, or\npossibly a little less, but he had let his grey-white hair grow\nlongish and his beard was very ample and fine. It was he that had\naddressed me. He sat dressed in a long gown in a modern and rather\nluxurious chair at a low long table of chestnut wood, on which he\nhad placed a few books, which I saw were in several languages and\ntwo of them not only in English, but having upon them the mark of an\nEnglish circulating library which did business in the great town at\nour feet. There was also upon the table a breakfast ready of white\nbread and honey, a large brown coffee-pot, two white cups, and some\ngoat's milk in a bowl of silver. This meal he asked me to share.\n\n\"It is my custom,\" he said, \"when I see a traveller coming up my\nmountain road to get out a cup and a plate for him, or, if it is\nmidday, a glass. At evening, however, no one ever comes.\"\n\n\"Why not?\" said I.\n\n\"Because,\" he answered, \"this lane goes but a few yards further\nround the edge of the cliff, and there it ends in a precipice; the\nlittle platform where we are is all but the end of the way. Indeed,\nI chose it upon that account, seeing, when I first came here, that\nfrom its height and isolation it was well fitted for my retreat.\"\n\nI asked him how long ago that was, and he said nearly twenty years.\nFor all that time, he added, he had lived there, going down into the\nplain but once or twice in a season and having for his rare\ncompanions those who brought him food and the peasants on such days\nas they toiled up to work at their plots towards the summit; also,\nfrom time to time, a chance traveller like myself. But these, he\nsaid, made but poor companions, for they were usually such as had\nmissed their way at the turning and arrived at that high place of\nhis out of breath and angry. I assured him that this was not my\ncase, for a man had told me in the night how to find his hermitage\nand I had come of set purpose to see him. At this he smiled.\n\nWe were now seated together at table eating and talking so, when I\nasked him whether he had a reputation for sanctity and whether the\npeople brought him food. He answered with a little hesitation that\nhe had a reputation, he thought, for necromancy rather than anything\nelse, and that upon this account it was not always easy to persuade\na messenger to bring him the books in French and English which he\nordered from below, though these were innocent enough, being, as a\nrule, novels written by women or academicians, records of travel,\nthe classics of the Eighteenth Century, or the biographies of aged\nstatesmen. As for food, the people of the place did indeed bring it\nto him, but not, as in an idyll, for courtesy; contrariwise, they\ndemanded heavy payment, and his chief difficulty was with bread;\nfor stale bread was intolerable to him. In the matter of religion he\nwould not say that he had none, but rather that he had several\nreligions; only at this season of the year, when everything was\nfresh, pleasant and entertaining, he did not make use of any of\nthem, but laid them all aside. As this last saying of his had no\nmeaning for me I turned to another matter and said to him:\n\n\"In any solitude contemplation is the chief business of the soul.\nHow, then, do you, who say you practise no rites, fill up your\nloneliness here?\"\n\nIn answer to this question he became more animated, spoke with a\nsort of laugh in his voice, and seemed as though he were young again\nand as though my question had aroused a whole lifetime of good\nmemories.\n\n\"My contemplation,\" he said, not without large gestures, \"is this\nwide and prosperous plain below: the great city with its harbour and\nceaseless traffic of ships, the roads, the houses building, the\nfields yielding every year to husbandry, the perpetual activities of\nmen. I watch my kind and I glory in them, too far off to be\ndisturbed by the friction of individuals, yet near enough to have a\ndaily companionship in the spectacle of so much life. The mornings,\nwhen they are all at labour, I am inspired by their energy; in the\nnoons and afternoons I feel a part of their patient and vigorous\nendurance; and when the sun broadens near the rim of the sea at\nevening, and all work ceases, I am filled with their repose. The\nlights along the harbour front in the twilight and on into the\ndarkness remind me of them when I can no longer see their crowds and\nmovements, and so does the music which they love to play in their\nrecreation after the fatigues of the day, and the distant songs\nwhich they sing far into the night.\n\n\"I was about thirty years of age, and had seen (in a career of\ndiplomacy) many places and men; I had a fortune quite insufficient\nfor a life among my equals. My youth had been, therefore, anxious,\nhumiliated, and worn when, upon a feverish and unhappy holiday taken\nfrom the capital of this State, I came by accident to the cave and\nplatform which you see. It was one of those days in which the air\nexhales revelation, and I clearly saw that happiness inhabited the\nmountain corner. I determined to remain for ever in so rare a\ncompanionship, and from that day she has never abandoned me. For a\nlittle while I kept a touch with the world by purchasing those\nnewspapers in which I was reported shot by brigands or devoured by\nwild beasts, but the amusement soon wearied me, and now I have\nforgotten the very names of my companions.\"\n\nWe were silent then until I said: \"But some day you will die here\nall alone.\"\n\n\"And why not?\" he answered calmly. \"It will be a nuisance for those\nwho find me, but I shall be indifferent altogether.\"\n\n\"That is blasphemy,\" says I.\n\n\"So says the priest of St. Anthony,\" he immediately replied--but\nwhether as a reproach, an argument, or a mere commentary I could not\ndiscover.\n\nIn a little while he advised me to go down to the plain before the\nheat should incommode my journey. I left him, therefore, reading a\nbook of Jane Austen's, and I have never seen him since.\n\nOf the many strange men I have met in my travels he was one of the\nmost strange and not the least fortunate. Every word I have written\nabout him is true.\n\n\n\n\nOF AN UNKNOWN COUNTRY\n\n\nTen years ago, I think, or perhaps a little less or perhaps a little\nmore, I came in the Euston Road--that thoroughfare of Empire--upon a\nyoung man a little younger than myself whom I knew, though I did not\nknow him very well. It was drizzling and the second-hand booksellers\n(who are rare in this thoroughfare) were beginning to put out the\nwaterproof covers over their wares. This disturbed my acquaintance,\nbecause he was engaged upon buying a cheap book that should really\nsatisfy him.\n\nNow this was difficult, for he had no hobby, and the book which\nshould satisfy him must be one that should describe or summon up,\nor, it is better to say, hint at--or, the theologians would say,\nreveal, or the Platonists would say _recall_--the Unknown Country,\nwhich he thought was his very home.\n\nI had known his habit of seeking such books for two years, and had\nhalf wondered at it and half sympathised. It was an appetite partly\nsatisfied by almost any work that brought to him the vision of a\nplace in the mind which he had always intensely desired, but to\nwhich, as he had then long guessed, and as he is now quite certain,\nno human paths directly lead. He would buy with avidity travels to\nthe moon and to the planets, from the most worthless to the best. He\nloved Utopias and did not disregard even so prosaic a category as\nbooks of real travel, so long as by exaggeration or by a glamour in\nthe style they gave him a full draught of that drug which he\ndesired. Whether this satisfaction the young man sought was a\nsatisfaction in illusion (I have used the word \"drug\" with\nhesitation), or whether it was, as he persistently maintained, the\nsatisfaction of a memory, or whether it was, as I am often tempted\nto think, the satisfaction of a thirst which will ultimately be\nquenched in every human soul I cannot tell. Whatever it was, he\nsought it with more than the appetite with which a hungry man seeks\nfood. He sought it with something that was not hunger but passion.\n\nThat evening he found a book.\n\nIt is well known that men purchase with difficulty second-hand books\nupon the stalls, and that in some mysterious way the sellers of\nthese books are content to provide a kind of library for the poorer\nand more eager of the public, and a library admirable in this, that\nit is accessible upon every shelf and exposes a man to no control,\nexcept that he must not steal, and even in this it is nothing but\nthe force of public law that interferes. My friend therefore would\nin the natural course of things have dipped into the book and left\nit there; but a better luck persuaded him. Whether it was the\nbeginning of the rain or a sudden loneliness in such terrible\nweather and in such a terrible town, compelling him to seek a more\npermanent companionship with another mind, or whether it was my\nsudden arrival and shame lest his poverty should appear in his\nrefusing to buy the book--whatever it was, he bought that same. And\nsince he bought the Book I also have known it and have found in it,\nas he did, the most complete expression that I know of the Unknown\nCountry, of which he was a citizen--oddly a citizen, as I then\nthought, wisely as I now conceive.\n\nAll that can best be expressed in words should be expressed in\nverse, but verse is a slow thing to create; nay, it is not really\ncreated: it is a secretion of the mind, it is a pearl that gathers\nround some irritant and slowly expresses the very essence of beauty\nand of desire that has lain long, potential and unexpressed, in the\nmind of the man who secretes it. God knows that this Unknown Country\nhas been hit off in verse a hundred times. If I were perfectly sure\nof my accents I would quote two lines from the Odyssey in which the\nUnknown Country stands out as clear as does a sudden vision from a\nmountain ridge when the mist lifts after a long climb and one sees\nbeneath one an unexpected and glorious land; such a vision as greets\na man when he comes over the Saldeu into the simple and secluded\nRepublic of the Andorrans. Then, again, the Germans in their idioms\nhave flashed it out, I am assured, for I remember a woman telling me\nthat there was a song by Schiller which exactly gave the revelation\nof which I speak. In English, thank Heaven, emotion of this kind,\nemotion necessary to the life of the soul, is very abundantly\nfurnished. As, who does not know the lines:\n\n Blessed with that which is not in the word\n Of man nor his conception: Blessed Land!\n\nThen there is also the whole group of glimpses which Shakespeare\namused himself by scattering as might a man who had a great oak\nchest full of jewels and who now and then, out of kindly fun, poured\nout a handful and gave them to his guests. I quote from memory, but\nI think certain of the lines run more or less like this:\n\n Look how the dawn in russet mantle clad\n Stands on the steep of yon high eastern hill.\n\nAnd again:\n\n Night's candles are burnt out, and jocund day\n Stands tiptoe on the misty mountain tops.\n\nWhich moves me to digress.... How on earth did any living man pull\nit off as well as that? I remember arguing with a man who very\ngenuinely thought the talent of Shakespeare was exaggerated in\npublic opinion, and discovering at the end of a long wrangle that he\nwas not considering Shakespeare as a poet. But as a poet, then, how\non earth did he manage it?\n\nKeats did it continually, especially in the _Hyperion_. Milton\ndoes it so well in the Fourth Book of _Paradise Lost_ that I\ndefy any man of a sane understanding to read the whole of that book\nbefore going to bed and not to wake up next morning as though he had\nbeen on a journey. William Morris does it, especially in the verses\nabout a prayer over the corn; and as for Virgil, the poet Virgil, he\ndoes it continually like a man whose very trade it is. Who does not\nremember the swimmer who saw Italy from the top of the wave?\n\nHere also let me digress. How do the poets do it? (I do not mean\nwhere do they get their power, as I was asking just now of\nShakespeare, but how do the words, simple or complex, produce that\neffect?) Very often there is not any adjective, sometimes not any\nqualification at all: often only one subject with its predicate and\nits statement and its object. There is never any detail of\ndescription, but the scene rises, more vivid in colour, more exact\nin outline, more wonderful in influence, than anything we can see\nwith our eyes, except perhaps those things we see in the few moments\nof intense emotion which come to us, we know not whence, and expand\nout into completion and into manhood.\n\nCatullus does it. He does it so powerfully in the opening lines of\n\n_Vesper adest_ ...\n\nthat a man reads the first couplet of that Hymeneal, and immediately\nperceives the Apennines.\n\nThe nameless translator of the Highland song does it, especially\nwhen he advances that battering line--\n\n And we in dreams behold the Hebrides.\n\nThey all do it, bless their hearts, the poets, which leads me back\nagain to the mournful reflection that it cannot be done in prose....\n\nLittle friends, my readers, I wish it could be done in prose, for if\nit could, and if I knew how to do it, I would here present to you\nthat Unknown Country in such a fashion that every landscape which\nyou should see henceforth would be transformed, by the appearing\nthrough it, the shining and uplifting through it, of the Unknown\nCountry upon which reposes this tedious and repetitive world.\n\nNow you may say to me that prose can do it, and you may quote to me\nthe end of the _Pilgrim's Progress_, a very remarkable piece of\nwriting. Or, better still, as we shall be more agreed upon it, the\ngeneral impression left upon the mind by the book which set me\nwriting--Mr. Hudson's _Crystal Age_. I do not deny that prose\ncan do it, but when it does it, it is hardly to be called prose, for\nit is inspired. Note carefully the passages in which the trick is\nworked in prose (for instance, in the story of Ruth in the Bible,\nwhere it is done with complete success), you will perceive an\nincantation and a spell. Indeed this same episode of Ruth in exile\nhas inspired two splendid passages of European verse, of which it is\ndifficult to say which is the more national, and therefore the\ngreatest, Victor Hugo's in the _Legende des Siecles_ or Keats's\nastounding four lines.\n\nThere was a shepherd the other day up at Findon Fair who had come\nfrom the east by Lewes with sheep, and who had in his eyes that\nreminiscence of horizons which makes the eyes of shepherds and of\nmountaineers different from the eyes of other men. He was occupied\nwhen I came upon him in pulling Mr. Fulton's sheep by one hind leg\nso that they should go the way they were desired to go. It happened\nthat day that Mr. Fulton's sheep were not sold, and the shepherd\nwent driving them back through Findon Village, and up on to the high\nDowns. I went with him to hear what he had to say, for shepherds\ntalk quite differently from other men. And when we came on to the\nshoulder of Chanctonbury and looked down upon the Weald, which\nstretched out like the Plains of Heaven, he said to me: \"I never\ncome here but it seems like a different place down below, and as\nthough it were not the place where I have gone afoot with sheep\nunder the hills. It seems different when you are looking down at\nit.\" He added that he had never known why. Then I knew that he, like\nmyself, was perpetually in perception of the Unknown Country, and I\nwas very pleased. But we did not say anything more to each other\nabout it until we got down into Steyning. There we drank together\nand we still said nothing more about it, so that to this day all we\nknow of the matter is what we knew when we started, and what you\nknew when I began to write this, and what you are now no further\ninformed upon, namely, that there is an Unknown Country lying\nbeneath the places that we know, and appearing only in moments of\nrevelation.\n\nWhether we shall reach this country at last or whether we shall not,\nit is impossible to determine.\n\n\n\n\nON A FAERY CASTLE\n\n\nA woman whose presence in English letters will continue to increase\nwrote of a cause to which she had dedicated her life that it was\nlike that Faery Castle of which men became aware when they wandered\nupon a certain moor. In that deserted place (the picture was taken\nfrom the writings of Sir Walter Scott) the lonely traveller heard\nabove him a noise of bugles in the air, and thus a Faery Castle was\nrevealed; but again, when the traveller would reach it, a doom comes\nupon him, and in the act of its attainment it vanishes away.\n\nWe are northern, full of dreams in the darkness; this Castle is\ncaught in glimpses, a misty thing. It is seen a moment--then it\nmixes once again with the mist of our northern air, and when that\nmist has lifted from the heath there is nothing before the watcher\nbut a bare upland open to the wind and roofed only by hurrying\ncloud. Yet in the moment of revelation most certainly the traveller\nperceived it, and the call of its bugle-guard was very clear. He\ncontinues his way perceiving only the things he knows--trees bent by\nthe gale, rude heather, the gravel of the path, and mountains all\naround. In that landscape he has no companion; yet he cannot but be\nhaunted, as he goes, by towers upon which he surely looked, and by\nthe sharp memory of bugle-notes that still seem to startle his\nhearing.\n\nIn our legends of Western Europe this Castle perpetually returns. It\nhas been seen not only on the highlands of Ireland, of Wales, of\nBrittany, of the Asturias, of Normandy, and of Auvergne, but in the\nplains also, and on those river meadows where wealth comes so fast\nthat even simple men early forget the visions of the hills. The\nimagination, or rather the speech, of our race has created or\nrecognised throughout our territory this stronghold which was not\naltogether of the world.\n\nQueen Iseult, as she sat with Tristan in a Castle Garden, towards\nthe end of a summer night, whispered to him: \"Tristan, they say that\nthis Castle is Fa\u00ebry; it is revealed at the sound of a Trumpet, but\npresently it vanishes away,\" and as she said it the bugles rang\ndawn.\n\nRaymond of Saragossa saw this Castle, also, as he came down from the\nwooded hills after he had found the water of life and was bearing it\ntowards the plain. He saw the towers quite clearly and also thought\nhe heard the call upon that downward road at whose end he was to\nmeet with Bramimonde. But he saw it thence only, in the exaltation\nof the summits as he looked over the falling forest to the plain and\nthe Sierra miles beyond. He saw it thence only. Never after upon\neither bank of Ebro could he come upon it, nor could any man assure\nhim of the way.\n\nIn the Story of Val-es-Dunes, Hugh the Fortinbras out of the\nCotentin had a castle of this kind. For when, after the battle, they\ncount the dead, the Priest finds in the sea-grass among other bodies\nthat of this old Lord....\n\n ... and Hugh that trusted in his glass,\n But rode not home the day;\n Whose title was the Fortinbras\n With the Lords of his Array.\n\nThis was that old Hugh the Fortinbras who had been Lord to the\nPriest's father, so that when the battle was engaged the Priest\nwatched him from the opposing rank, and saw him fall, far off, just\nas the line broke and before the men of the Caux country had room to\ncharge. It was easy to see him, for he rode a high horse and was\ntaller than other Normans, and when his horse was wounded....\n\n ... The girth severed and the saddle swung\n And he went down;\n He never more sang winter songs\n In his High Town.\n\n In his High Town that Faery is\n And stands on Harcourt Lea;\n To summon him up his arrier-ban\n His writ beyond the mountain ran.\n My father was his serving-man;\n Although the farm was free.\n Before the angry wars began\n He was a friend to me!\n\n In his High Town that Faery is\n And stands on Harcourt bay;\n The Fisher driving through the night\n Makes harbour by that castle height\n And moors him till the day:\n But with the broadening of the light\n It vanishes away.\n\nSo the Faery Castle comes in by an illusion in the Ballad of the\nBattle of Val-es-Dunes.\n\n * * * * *\n\nWhat is this vision which our race has so symbolised or so seen and\nto which are thus attached its oldest memories? It is the miraculous\nmoment of intense emotion in which whether we are duped or\ntransfigured we are in touch with a reality firmer than the reality\nof this world. The Faery Castle is the counterpart and the example\nof those glimpses which every man has enjoyed, especially in youth,\nand which no man even in the dust of middle age can quite forget. In\nthese were found a complete harmony and satisfaction which were not\nnegative nor dependent upon the absence of discord--such completion\nas criticism may conceive--but as positive as colour or as music,\nand clothed as it were in a living body of joy.\n\nThe vision may be unreal or real, in either case it is valid: if it\nis unreal it is a symbol of the world behind the world. But it is no\nless a symbol; even if it is unreal it is a sudden seeing of the\nplace to which our faces are set during this unbroken marching of\nyears.\n\nOnce on the Sacramento River a little before sunrise I looked\neastward from a boat and saw along the dawn the black edge of the\nSierras. The peaks were as sharp as are the Malvern from the\nCotswold, though they were days and days away. They made a broad\njagged band intensely black against the glow of the sky. I drew them\nso. A tiny corner of the sun appeared between two central peaks:--at\nonce the whole range was suffused with glory. The sun was wholly\nrisen and the mountains had completely disappeared,--in the place\nwhere they had been was the sky of the horizon.\n\nAt another time, also in a boat, I saw beyond a spit of the Tunisian\ncoast, as it seemed a flat island. Through the heat, with which the\nair trembled, was a low gleam of sand, a palm or two, and, less\ncertainly, the flats and domes of a white native village. Our\ncourse, which was to round the point, went straight for this island,\nand, as we approached, it became first doubtful, then flickering,\nthen a play of light upon the waves. It was a mirage, and it had\nmelted into the air.\n\n * * * * *\n\nThere is a part of us, as all the world knows, which is immixed with\nchange and by change only can live. There is another part which lies\nbehind motion and time, and that part is ourselves. This diviner\npart has surely a stronghold which is also an inheritance. It has a\nhome which perhaps it remembers and which certainly it conceives at\nrare moments during our path over the moor.\n\nThis is that Fa\u00ebry Castle. It is revealed at the sound of a trumpet;\nwe turn our eyes, we glance and we perceive it; we strain to reach\nit--in the very effort of our going the doom of human labour falls\nupon us and it vanishes away.\n\nIt is real or unreal. It is unreal like that island which I thought\nto see some miles from Africa, but which was not truly there: for\nthe ship when it came to the place that island had occupied sailed\neasily over an empty sea. It is real, like those high Sierras which\nI drew from the Sacramento River at the turn of the night and which\nwere suddenly obliterated by the rising sun.\n\nWhere the vision is but mirage, even there it is a symbol of our\ngoal; where it stands fast and true, for however brief a moment, it\ncan illumine, and should determine the whole of our lives. For such\nsights are the manifestation of that glory which lies permanent\nbeyond the changing of the world. Of such a sort are the young\npassionate intentions to relieve the burden of mankind, first love,\nthe mood created by certain strains of music, and--as I am willing\nto believe--the Walls of Heaven.\n\n\n\n\nON A SOUTHERN HARBOUR\n\n\nThe ship had sailed northward in an even manner and under a sky that\nwas full of stars, when the dawn broke and the full day quickly\nbroadened over the Mediterranean. With the advent of the light the\nsalt of the sea seemed stronger, and there certainly arose a new\nfreshness in the following air; but as yet no land appeared. Until\nat last, seated as I was alone in the fore part of the vessel, I\nclearly saw a small unchanging shape far off before me, peaked upon\nthe horizon and grey like a cloud. This I watched, wondering what\nits name might be, who lived upon it, or what its fame was; for it\nwas certainly land.\n\nI watched in this manner for some hours--perhaps for two--when the\nisland, now grown higher, was so near that I could see trees upon\nit; but they were set sparsely, as trees are on a dry land, and most\nof them seemed to be thorn trees.\n\nIt was at this moment that a man who had been singing to himself in\na low tone aft came up to me and told me that this island was called\nthe Island of Goats and that there were no men upon it to his\nknowledge, that it was a lonely place and worth little. But by this\ntime there had risen beyond the Island of Goats another and much\nlarger land.\n\nIt lay all along the north in a mountainous belt of blue, and any\nman coming to it for the first time or unacquainted with maps would\nhave said to himself: \"I have found a considerable place.\" And,\nindeed, the name of the island indicates this, for it is called\nMajorca, \"The Larger Land.\" Towards this, past the Island of Goats,\nand past the Strait, we continued to sail with a light breeze for\nhours, until at last we could see on this shore also sparse trees;\nbut most of them were olive trees, and they were relieved with the\ngreen of cultivation up the high mountain sides and with the white\nhouses of men.\n\nThe deck was now crowded with people, most of whom were coming back\nto their own country after an exile in Africa among un-Christian and\ndangerous things. The little children who had not yet known Europe,\nhaving been born beyond the sea, were full of wonder; but their\nparents, who knew the shortness of human life and its trouble, were\nhappy because they had come back at last and saw before them the\nknown jetties and the familiar hills of home. As I was surrounded by\nso much happiness, I myself felt as though I had come to the end of\na long journey and was reaching my own place, though I was, in\nreality, bound for Barcelona, and after that up northward through\nthe Cerdagne, and after that to Perigord, and after that to the\nChannel, and so to Sussex, where all journeys end.\n\nThe harbour had about it that Mediterranean-go-as-you-please which\neverywhere in the Mediterranean distinguishes harbours. It was as\nthough the men of that sea had said: \"It never blows for long: let\nus build ourselves a rough refuge and to-morrow sail away.\" We\nneared this harbour, but we flew no flag and made no signal. Beneath\nus the water was so clear that all one need have done to have\nbrought the vessel in if one had not known the channel would have\nbeen to lean over the side and to keep the boy at the helm off the\nvery evident shallows and the crusted rocks by gestures of one's\nhands, for the fairway was like a trench, deep and blue. So we slid\ninto Palma haven, and as we rounded the pier the light wind took us\nfirst abeam and then forward; then we let go and she swung up and\nwas still. They lowered the sails.\n\nThe people who were returning were so full of activity and joy that\nit was like a hive of bees; but I no longer felt this as I had felt\ntheir earlier and more subdued emotion, for the place was no longer\ndistant or mysterious as it had been when first its sons and\ndaughters had come up on deck to welcome it and had given me part of\ntheir delight. It was now an evident and noisy town; hot, violent,\nand strong. The houses had about them a certain splendour, the\ncitizens upon the quays a satisfied and prosperous look. Its\nstreets, where they ran down towards the sea, were charmingly clean\nand cared for, and the architecture of its wealthier mansions seemed\nto me at once unusual and beautiful, for I had not yet seen Spain.\nEach house, so far as I could make out from the water, was entered\nby a fine sculptured porch which gave into a cool courtyard with\narcades under it, and most of the larger houses had escutcheons\ncarved in stone upon their walls.\n\nBut what most pleased me and also seemed most strange was to see\nagainst the East a vast cathedral quite Northern in outline, except\nfor a severity and discipline of which the North is incapable save\nwhen it has steeped itself in the terseness of the classics.\n\nThis monument was far larger than anything in the town. It stood out\nseparate from the town and dominated it upon its seaward side,\nsomewhat as might an isolated hill, a shore fortress of rock. It was\nalmost bare of ornament; its stones were very carefully worked and\nclosely fitted, and little waves broke ceaselessly along the base of\nits rampart. Landwards, a mass of low houses which seemed to touch\nthe body of the building did but emphasise its height. When I had\nlanded I made at once for this cathedral, and with every step it\ngrew greater.\n\nWe who are of the North are accustomed to the enormous; we have\nunearthly sunsets and the clouds magnify our hills. The Southern men\nsee nothing but misproportion in what is enormous. They love to have\nthings in order, and violence in art is odious to them. This high\nand dreadful roof had not been raised under the influences of the\nisland; it had surely been designed just after the re-conquest from\nthe Mohammedans, when a turbulent army, not only of Gascons and\nCatalans, but of Normans also and of Frisians, and of Rhenish men,\nhad poured across the water and had stormed the sea-walls. On this\naccount the cathedral had about it in its sky-line and in its\nimmensity, and in the Gothic point of its windows, a Northern air.\nBut in its austerity and in its magnificence it was Spaniard.\n\nAs I passed the little porch of entry in the side wall I saw a man.\nHe was standing silent and alone; he was not blind and perhaps not\npoor, and as I passed he begged the charity not of money but of\nprayers. When I had entered the cool and darkness of the nave, his\nfigure still remained in my mind, and I could not forget it. I\nremembered the straw hat upon his head and the suit of blue canvas\nwhich he wore, and the rough staff of wood in his hand. I was\nespecially haunted by his expression, which was patient and masqued\nas though he were enduring a pain and chose to hide it.\n\nThe nave was empty. It was a great hollow that echoed and re-echoed;\nthere were no shrines and no lamps, and no men or women praying, and\ntherefore the figure at the door filled my mind more and more, until\nI went out and asked him if he was in need of money, of which at\nthat moment I had none. He answered that his need was not for money\nbut only for prayers.\n\n\"Why,\" said I, \"do you need prayers?\"\n\nHe said it was because his fate was upon him.\n\nI think he spoke the truth. He was standing erect and with dignity,\nhis eyes were not disturbed, and he repeatedly refused the alms of\npassers-by.\n\n\"No one\" said I, \"should yield to these moods.\"\n\nHe answered nothing, but looked pensive like a man gazing at a\nlandscape and remembering his life.\n\nBut it was now the hour when the ship was to be sailing again, and I\ncould not linger, though I wished very much to talk more with him. I\nbegged him to name a shrine where a gift might be of especial value\nto him. He said that he was attached to no one shrine more than to\nany other, and then I went away regretfully, remembering how\nearnestly he had asked for prayers.\n\nThis was in Palma of Majorca not two years ago. There are many such\nmen, but few who speak so humbly.\n\nWhen I had got aboard again the ship sailed out and rounded a\nlighthouse point and then made north to Barcelona. The night fell,\nand next morning there rose before us the winged figures that crown\nthe Custom House of that port and are an introduction to the glories\nof Spain.\n\n\n\n\nON A YOUNG MAN AND AN OLDER MAN\n\n\nA Young Man of my acquaintance having passed his twenty-eighth\nbirthday, and wrongly imagining this date to represent the Grand\nClimacteric, went by night in some perturbation to an Older Man and\nspoke to him as follows:\n\n\"Sir! I have intruded upon your leisure in order to ask your advice\nupon certain matters.\"\n\nThe Older Man, whose thoughts were at that moment intently set upon\nmoney, looked up in a startled way and attempted to excuse himself,\nsuffering as he did from the delusion that the Young Man was after a\nloan. But the Young Man, whose mind was miles away from all such\ntrifling things, continued to press him anxiously without so much as\nnoticing that he had perturbed his Senior.\n\n\"I have come, Sir,\" said he, \"to ask your opinion, advice,\nexperience, and guidance upon something very serious which has\nentered into my life, which is, briefly, that I feel myself to be\ngrowing old.\"\n\nUpon hearing this so comforting and so reasonable a statement the\nOlder Man heaved a profound sigh of relief and turning to him a\nmature and smiling visage (as also turning towards him his person\nand in so doing turning his Polished American Hickory Wood Office\nChair), answered with a peculiar refinement, but not without\nsadness, \"I shall be happy to be of any use I can\"; from which order\nand choice of words the reader might imagine that the Older Man was\nhimself a Colonial, like his chair. In this imagination the reader,\nshould he entertain it, would be deceived.\n\nThe Younger Man then proceeded, knotting his forehead and putting\ninto his eyes that troubled look which is proper to virtue and to\nyouth:\n\n\"Oh, Sir! I cannot tell you how things seem to be slipping from me!\nI smell less keenly and taste less keenly, I enjoy less keenly and\nsuffer less keenly than I did. Of many things which I certainly\ndesired I can only say that I now desire them in a more confused\nmanner. Of certain propositions in which I intensely believed I can\nonly say that I now see them interfered with and criticised\nperpetually, not, as was formerly the case, by my enemies, but by\nthe plain observance of life, and what is worse, I find growing in\nme a habit of reflection for reflection's sake, leading nowhere--and\na sort of sedentary attitude in which I watch but neither judge nor\nsupport nor attack any portion of mankind.\"\n\nThe Older Man, hearing this speech, congratulated his visitor upon\nhis terse and accurate methods of expression, detailed to him the\ncareers in which such habits of terminology are valuable, and also\nthose in which they are a fatal fault.\n\n\"Having heard you,\" he said, \"it is my advice to you, drawn from a\nlong experience of men, to enter the legal profession, and, having\nentered it, to supplement your income with writing occasional\narticles for the more dignified organs of the Press. But if this\nprospect does not attract you (and, indeed, there are many whom it\nhas repelled) I would offer you as an alternative that you should\nproduce slowly, at about the rate of one in every two years, short\nbooks compact of irony, yet having running through them like a\ntwisted thread up and down, emerging, hidden, and re-emerging in the\nstuff of your writing, a memory of those early certitudes and even\nof passion for those earlier revelations.\"\n\nWhen the Older Man had said this he sat silent for a few moments and\nthen added gravely, \"But I must warn you that for such a career you\nneed an accumulated capital of at least \u00a330,000.\"\n\nThe Young Man was not comforted by advice of this sort, and was\ndetermined to make a kind of war upon the doctrine which seemed to\nunderlie it. He said in effect that if he could not be restored to\nthe pristine condition which he felt to be slipping from him he\nwould as lief stop living.\n\nOn hearing this second statement the Older Man became extremely\ngrave.\n\n\"Young Man,\" said he, \"Young Man, consider well what you are saying!\nThe poet Shakespeare in his most remarkable effort, which, I need\nhardly tell you, is the tragedy of _Hamlet, or the Prince of\nDenmark,_ has remarked that the thousand doors of death stand\nopen. I may be misquoting the words, and if I am I do so boldly and\nwithout fear, for any fool with a book at his elbow can get the\nwords right and yet not understand their meaning. Let me assure you\nthat the doors of death are not so simply hinged, and that any\ndetermination to force them involves the destruction of much more\nthan these light though divine memories of which you speak; they\ninvolve, indeed, the destruction of the very soul which conceives\nthem. And let me assure you, not upon my own experience, but upon\nthat of those who have drowned themselves imperfectly, who have\nenlisted in really dangerous wars, or who have fired revolvers at\nthemselves in a twisted fashion with their right hands, that, quite\napart from that evil to the soul of which I speak, the evil to the\nmere body in such experiments is so considerable that a man would\nrather go to the dentist than experience them.... You will forgive\nme,\" he added earnestly, \"for speaking in this gay manner upon an\nimportant philosophical subject, but long hours of work at the\nearning of my living force me to some relaxation towards the end of\nthe day, and I cannot restrain a frivolous spirit even in the\ndiscussion of such fundamental things.... No, do not, as you put it,\n'stop living.' It hurts, and no one has the least conception of\nwhether it is a remedy. What is more, the life in front of you will\nprove, after a few years, as entertaining as the life which you are\nrapidly leaving.\"\n\nThe Young Man caught on to this last phrase, and said, \"What do you\nmean by 'entertaining'?\"\n\n\"I intend,\" said the Older Man, \"to keep my advice to you in the\nnote to which I think such advice should be set. I will not burden\nit with anything awful, nor weight an imperfect diction with\nabsolute verities in which I do indeed believe, but which would be\naltogether out of place at this hour of the evening. I will not deny\nthat from eleven till one, and especially if one be delivering an\nhistorical, or, better still, a theological lecture, one can without\nloss of dignity allude to the permanent truth, the permanent beauty,\nand the permanent security without which human life wreathes up like\nmist and is at the best futile, at the worst tortured. But you must\nremember that you have come to me suddenly with a most important\nquestion, after dinner, that I have but just completed an essay upon\nthe economic effect of the development of the Manchurian coalfields,\nand that (what is more important) all this talk began in a certain\nkey, and that to change one's key is among the most difficult of\ncreative actions.... No, Young Man, I shall not venture upon the\ntrue reply to your question.\"\n\nOn hearing this answer the Young Man began to curse and to swear and\nto say that he had looked everywhere for help and had never found\nit; that he was minded to live his own life and to see what would\ncome of it; that he thought the Older Man knew nothing of what he\nwas talking about, but was wrapping it all up in words; that he had\nclearly recognised in the Older Man's intolerable prolixity several\nclich\u00e9s or ready-made phrases; that he hoped on reaching the Older\nMan's age he would not have been so utterly winnowed of all\nsubstance as to talk so aimlessly; and finally that he prayed God\nfor a personal development more full of justice, of life, and of\nstuff than that which the Older Man appeared to have suffered or\nenjoyed.\n\nOn hearing these words the Older Man leapt to his feet (which was\nnot an easy thing for him to do) and as one overjoyed grasped the\nYounger Man by the hand, though the latter very much resented such\nantics on the part of Age.\n\n\"That is it! That is it!\" cried the Older Man, looking now far too\nold for his years. \"If I have summoned up in you that spirit I have\nnot done ill! Get you forward in that mood and when you come to my\ntime of life you will be as rotund and hopeful a fellow as I am\nmyself.\"\n\nBut having heard these words the Young Man left him in disgust.\n\nThe Older Man, considering all these things as he looked into the\nfire when he was alone, earnestly desired that he could have told\nthe Young Man the exact truth, have printed it, and have produced a\nproper Gospel. But considering the mountains of impossibility that\nlay in the way of such public action, he sighed deeply and took to\nthe more indirect method. He turned to his work and continued to\nperform his own duty before God and for the help of mankind. This,\non that evening, was for him a review upon the interpretation of the\nword _haga_ in the Domesday Inquest. This kept him up till a\nquarter past one, and as he had to take a train to Newcastle at\neight next morning it is probable that much will be forgiven him\nwhen things are cleared.\n\n\n\n\nON THE DEPARTURE OF A GUEST\n\n\n _C'est ma Jeunesse qui s'en va.\n Adieu! la tres gente compagne--\n Oncques ne suis moins gai pour \u00e7a\n (C'est ma Jeunesse qui s'en va)\n Et lon-lon-laire, et lon-lon-l\u00e0\n Peut-etre perd's; peut-etre gagne.\n C'est ma Jeunesse qui s'en va._\n\n(From the Author's MSS. In the library of the Abbey of Theleme.)\n\nHost: Well, Youth, I see you are about to leave me, and since it is\nin the terms of your service by no means to exceed a certain period\nin my house, I must make up my mind to bid you farewell.\n\nYouth: Indeed, I would stay if I could; but the matter lies as you\nknow in other hands, and I may not stay.\n\nHost: I trust, dear Youth, that you have found all comfortable while\nyou were my guest, that the air has suited you and the company?\n\nYouth: I thank you, I have never enjoyed a visit more; you may say\nthat I have been most unusually happy.\n\nHost: Then let me ring for the servant who shall bring down your\nthings.\n\nYouth: I thank you civilly! I have brought them down already--see,\nthey are here. I have but two, one very large bag and this other\nsmall one.\n\nHost: Why, you have not locked the small one! See it gapes!\n\nYouth (_somewhat embarrassed_): My dear Host ... to tell the\ntruth ... I usually put it off till the end of my visits ... but the\ntruth ... to tell the truth, my luggage is of two kinds.\n\nHost: I do not see why that need so greatly confuse you.\n\nYouth (_still more embarrassed_): But you see--the fact is--I\nstay with people so long that--well, that very often they forget\nwhich things are mine and which belong to the house ... And--well,\nthe truth is that I have to take away with me a number of things\nwhich ... which, in a word, you may possibly have thought your own.\n\nHost (_coldly_): Oh!\n\nYouth (_eagerly_): Pray do not think the worse of me--you know\nhow strict are my orders.\n\nHost (_sadly_): Yes, I know; you will plead that Master of\nyours, and no doubt you are right.... But tell me, Youth, what are\nthose things?\n\nYouth: They fill this big bag. But I am not so ungracious as you\nthink. See, in this little bag, which I have purposely left open,\nare a number of things properly mine, yet of which I am allowed to\nmake gifts to those with whom I lingered--you shall choose among\nthem, or if you will, you shall have them all.\n\nHost: Well, first tell me what you have packed in the big bag and\nmean to take away.\n\nYouth: I will open it and let you see. (_He unlocks it and pulls\nthe things out_.) I fear they are familiar to you.\n\nHost: Oh! Youth! Youth! Must you take away all of these? Why, you\nare taking away, as it were, my very self! Here is the love of\nwomen, as deep and changeable as an opal; and here is carelessness\nthat looks like a shower of pearls. And here I see--Oh! Youth, for\nshame!--you are taking away that silken stuff which used to wrap up\nthe whole and which you once told me had no name, but which lent to\neverything it held plenitude and satisfaction. Without it surely\npleasures are not all themselves. Leave me that at least.\n\nYouth: No, I must take it, for it is not yours, though from courtesy\nI forbore to tell you so till now. These also go: Facility, the\nointment; Sleep, the drug; Full Laughter, that tolerated all\nfollies. It was the only musical thing in the house. And I must\ntake--yes, I fear I must take Verse.\n\nHOST: Then there is nothing left!\n\nYOUTH: Oh! yes! See this little open bag which you may choose from!\nFeel it!\n\nHOST (_lifting it_): Certainly it is very heavy, but it rattles\nand is uncertain.\n\nYOUTH: That is because it is made up of divers things having no\nsimilarity; and you may take all or leave all, or choose as you\nwill. Here (_holding up a clout_) is Ambition: Will you have\nthat?...\n\nHOST (_doubtfully_): I cannot tell.... It has been mine and yet\n... without those other things....\n\nYOUTH (_cheerfully_): Very well, I will leave it. You shall\ndecide on it a few years hence. Then, here is the perfume Pride.\nWill you have that?\n\nHOST: No; I will have none of it. It is false and corrupt, and only\nyesterday I was for throwing it out of window to sweeten the air in\nmy room.\n\nYOUTH: So far you have chosen well; now pray choose more.\n\nHOST: I will have this--and this--and this. I will take Health\n(_takes it out of the bag_), not that it is of much use to me\nwithout those other things, but I have grown used to it. Then I will\ntake this (_takes out a plain steel purse and chain_), which is\nthe tradition of my family, and which I desire to leave to my son. I\nmust have it cleaned. Then I will take this (_pulls out a trinket_),\nwhich is the Sense of Form and Colour. I am told it is of less value\nlater on, but it is a pleasant ornament ... And so, Youth, goodbye.\n\nYouth (_with a mysterious smile_): Wait--I have something else\nfor you (_he feels in his ticket pocket_); no less a thing\n(_he feels again in his watch pocket_) than (_he looks a trifle anxious\nand feels in his waistcoat pockets_) a promise from my Master, signed\nand sealed, to give you back all I take and more in Immortality! (_He\nfeels in his handkerchief pocket._)\n\nHost: Oh! Youth!\n\nYouth (_still feeling_): Do not thank me! It is my Master you\nshould thank. (_Frowns_.) Dear me! I hope I have not lost it!\n(_Feels in his trousers pockets._)\n\nHost (_loudly_): Lost it?\n\nYouth (_pettishly_): I did not say I had lost it! I said I\nhoped I had not ... (_feels in his great-coat pocket, and pulls\nout an envelope_). Ah! Here it is! (_His face clouds over_.)\nNo, that is the message to Mrs. George, telling her the time has\ncome to get a wig ... (_Hopelessly_): Do you know I am afraid I\nhave lost it! I am really very sorry--I cannot wait. (_He goes\noff_.)\n\n\n\n\nON DEATH\n\n\nI knew a man once who made a great case of Death, saying that he\nesteemed a country according to its regard for the conception of\nDeath, and according to the respect which it paid to that\nconception. He also said that he considered individuals by much the\nsame standard, but that he did not judge them so strictly in the\nmatter, because (said he) great masses of men are more permanently\nconcerned with great issues; whereas private citizens are disturbed\nby little particular things which interfere with their little\nparticular lives, and so distract them from the general end.\n\nThis was upon a river called Boutonne, in Vend\u00e9e, and at the time I\ndid not understand what he meant because as yet I had had no\nexperience of these things. But this man to whom I spoke had had\nthree kinds of experience; first, he had himself been very probably\nthe occasion of Death in others, for he had been a soldier in a war\nof conquest where the Europeans were few and the Barbarians many!\nsecondly, he had been himself very often wounded, and more than once\nall but killed; thirdly, he was at the time he told me this thing an\nold man who must in any case soon come to that experience or\ncatastrophe of which he spoke.\n\nHe was an innkeeper, the father of two daughters, and his inn was by\nthe side of the river, but the road ran between. His face was more\nanxiously earnest than is commonly the face of a French peasant, as\nthough he had suffered more than do ordinarily that very prosperous,\nvery virile, and very self-governing race of men. He had also about\nhim what many men show who have come sharply against the great\nrealities, that is, a sort of diffidence in talking of ordinary\nthings. I could see that in the matters of his household he allowed\nhimself to be led by women. Meanwhile he continued to talk to me\nover the table upon this business of Death, and as he talked he\nshowed that desire to persuade which is in itself the strongest\nmotive of interest in any human discourse.\n\nHe said to me that those who affected to despise the consideration\nof Death knew nothing of it; that they had never seen it close and\nmight be compared to men who spoke of battles when they had only\nread books about battles, or who spoke of sea-sickness though they\nhad never seen the sea. This last metaphor he used with some pride,\nfor he had crossed the Mediterranean from Provence to Africa some\nfive or six times, and had upon each occasion suffered horribly;\nfor, of course, his garrison had been upon the edge of the desert,\nand he had been a soldier beyond the Atlas. He told me that those\nwho affected to neglect or to despise Death were worse than children\ntalking of grown-up things, and were more like prigs talking of\nphysical things of which they knew nothing.\n\nI told him then that there were many such men, especially in the\ntown of Geneva. This, he said, he could well believe, though he had\nnever travelled there, and had hardly heard the name of the place.\nBut he knew it for some foreign town. He told me, also, that there\nwere men about in his own part of the world who pretended that since\nDeath was an accident like any other, and, moreover, one as certain\nas hunger or as sleep, it was not to be considered. These, he said,\nwere the worst debaters upon his favourite subject.\n\nNow as he talked in this fashion I confess that I was very bored. I\nhad desired to go on to Angoul\u00e9me upon my bicycle, and I was at that\nage when all human beings think themselves immortal. I had desired\nto get off the main high road into the hills upon the left, to the\neast of it, and I was at an age when the cessation of mundane\nexperience is not a conceivable thing. Moreover, this innkeeper had\nbeen pointed out to me as a man who could give very useful\ninformation upon the nature of the roads I had to travel, and it had\nnever occurred to me that he would switch me off after dinner upon a\nhobby of his own. To-day, after a wider travel, I know well that all\ninnkeepers have hobbies, and that an abstract or mystical hobby of\nthis sort is amongst the best with which to pass an evening. But no\nmatter, I am talking of then and not now. He kept me, therefore,\nuninterested as I was, and continued:\n\n\"People who put Death away from them, who do not neglect or despise\nit but who stop thinking about it, annoy me very much. We have in\nthis village a chemist of such a kind. He will have it that, five\nminutes afterwards, a man thinks no more about it.\" Having gone so\nfar, the innkeeper, clenching his hands and fixing me with a\nbrilliant glance from his old eyes, said:\n\n\"With such men I will have nothing to do!\"\n\nIndeed, that his chief subject should be treated in such a fashion\nwas odious to him, and rightly, for of the half-dozen things worth\nstrict consideration, there is no doubt that his hobby was the\nchief, and to have one's hobby vulgarly despised is intolerable.\n\nThe innkeeper then went on to tell me that so far as he could make\nout it was a man's business to consider this subject of Death\ncontinually, to wonder upon it, and, if he could, to extract its\nmeaning. Of the men I had met so far in life, only the Scotch and\ncertain of the Western French went on in this metaphysical manner:\nthus a Breton, a Basque, and a man in Ecclefechan (I hope I spell it\nright) and another in Jedburgh had already each of them sent me to\nmy bed confused upon the matter of free will. So this Western\ninnkeeper refused to leave his thesis. It was incredible to him that\na Sentient Being who perpetually accumulated experience, who grew\nriper and riper, more and more full of such knowledge as was native\nto himself and complementary to his nature, should at the very\ncrisis of his success in all things intellectual and emotional,\ncease suddenly. It was further an object to him of vast curiosity\nwhy such a being, since a future was essential to it, should find\nthat future veiled.\n\nHe presented to me a picture of men perpetually passing through a\nfield of vision out of the dark and into the dark. He showed me\nthese men, not growing and falling as fruits do (so the modern\nvulgar conception goes) but alive throughout their transit: pouring\nlike an unbroken river from one sharp limit of the horizon whence\nthey entered into life to that other sharp limit where they poured\nout from life, not through decay, but through a sudden catastrophe.\n\n\"I,\" said he, \"shall die, I do suppose, with a full consciousness of\nmy being and with a great fear in my eyes. And though many die\ndecrepit and senile, that is not the normal death of men, for men\nhave in them something of a self-creative power, which pushes them\non to the further realisation of themselves, right up to the edge of\ntheir doom.\"\n\nI put his words in English after a great many years, but they were\nsomething of this kind, for he was a metaphysical sort of man.\n\nIt was now near midnight, and I could bear with such discussions no\nlonger; my fatigue was great and the hour at which I had to rise\nnext day was early. It was, therefore, in but a drowsy state that I\nheard him continue his discourse. He told me a long story of how he\nhad seen one day a company of young men of the New Army, the\nconscripts, go marching past his house along the river through a\ndriving snow. He said that first he heard them singing long before\nhe saw them, that then they came out like ghosts for a moment\nthrough the drift, that then in the half light of the winter dawn\nthey clearly appeared, all in step for once, swinging forward,\nmuffled in their dark blue coats, and still singing to the lift of\ntheir feet; that then on their way to the seaport, they passed again\ninto the blinding scurry of the snow, that they seemed like ghosts\nagain for a moment behind the veil of it, and that long after they\nhad disappeared their singing could still be heard.\n\nBy this time I was most confused as to what lesson he would convey,\nand sleep had nearly overcome me, but I remember his telling me that\nsuch a sight stood to him at the moment and did still stand for the\npassage of the French Armies perpetually on into the dark, century\nafter century, destroyed for the most part upon fields of battle. He\ntold me that he felt like one who had seen the retreat from Moscow,\nand he would, I am sure, had I not determined to leave him and to\ntake at least some little sleep, have asked me what fate there was\nfor those single private soldiers, each real, each existent, while\nthe Army which they made up and of whose \"destruction\" men spoke,\nwas but a number, a notion, a name. He would have pestered me, if my\nmind had still been active, as to what their secret destinies were\nwho lay, each man alone, twisted round the guns after the failure to\nhold the Bridge of the Beresina. He might have gone deeper, but I\nwas too tired to listen to him any more.\n\nThis human debate of ours (and very one-sided it was!) is now\nresolved, for in the interval since it was engaged the innkeeper\nhimself has died.\n\n\n\n\nON COMING TO AN END\n\n\nOf all the simple actions in the world! Of all the simple actions in\nthe world!\n\nOne would think it could be done with less effort than the heaving\nof a sigh.... Well--then, one would be wrong.\n\nThere is no case of Coming to an End but has about it something of\nan effort and a jerk, as though Nature abhorred it, and though it be\ntrue that some achieve a quiet and a perfect end to one thing or\nanother (as, for instance, to Life), yet this achievement is not\narrived at save through the utmost toil, and consequent upon the\nmost persevering and exquisite art.\n\nNow you can say that this may be true of sentient things but not of\nthings inanimate. It is true even of things inanimate.\n\nLook down some straight railway line for a vanishing point to the\nperspective: you will never find it. Or try to mark the moment when\na small target becomes invisible. There is no gradation; a moment it\nwas there, and you missed it--possibly because the Authorities were\nnot going in for journalism that day, and had not chosen a dead calm\nwith the light full on the canvas. A moment it was there and then,\nas you steamed on, it was gone. The same is true of a lark in the\nair. You see it and then you do not see it, you only hear its song.\nAnd the same is true of that song: you hear it and then suddenly you\ndo not hear it. It is true of a human voice, which is familiar in\nyour ear, living and inhabiting the rooms of your house. There comes\na day when it ceases altogether--and how positive, how definite and\nhard is that Coming to an End.\n\nIt does not leave an echo behind it, but a sharp edge of emptiness,\nand very often as one sits beside the fire the memory of that voice\nsuddenly returning gives to the silence about one a personal force,\nas it were, of obsession and of control. So much happens when even\none of all our million voices Comes to an End.\n\nIt is necessary, it is august and it is reasonable that the great\nstory of our lives also should be accomplished and should reach a\nterm: and yet there is something in that hidden duality of ours\nwhich makes the prospect of so natural a conclusion terrible, and it\nis the better judgment of mankind and the mature conclusion of\ncivilisations in their age that there is not only a conclusion here\nbut something of an adventure also. It may be so.\n\nThose who solace mankind and are the principal benefactors of it, I\nmean the poets and the musicians, have attempted always to ease the\nprospect of Coming to an End, whether it were the Coming to an End\nof the things we love or of that daily habit and conversation which\nis our life and is the atmosphere wherein we loved them. Indeed this\nis a clear test whereby you may distinguish the great artists from\nthe mean hucksters and charlatans, that the first approach and\nreveal what is dreadful with calm and, as it were, with a purpose to\nuse it for good while the vulgar catchpenny fellows must liven up\ntheir bad dishes as with a cheap sauce of the horrible, caring\nnothing, so that their shrieks sell, whether we are the better for\nthem or no.\n\nThe great poets, I say, bring us easily or grandly to the gate: as\nin that _Ode to a Nightingale_ where it is thought good (in an\nimmortal phrase) to pass painlessly at midnight, or, in the glorious\nline which Ronsard uses, like a salute with the sword, hailing \"la\nprofitable mort.\"\n\nThe noblest or the most perfect of English elegies leaves, as a sort\nof savour after the reading of it, no terror at all nor even too\nmuch regret, but the landscape of England at evening, when the smoke\nof the cottages mixes with autumn vapours among the elms; and even\nthat gloomy modern _Ode to the West Wind_, unfinished and\ntouched with despair, though it will speak of--\n\n ... that outer place forlorn\n Which, like an infinite grey sea, surrounds\n With everlasting calm the land of human sounds;\n\nyet also returns to the sacramental earth of one's childhood where\nit says:\n\n For now the Night completed tells her tale\n Of rest and dissolution: gathering round\n Her mist in such persuasion that the ground\n Of Home consents to falter and grow pale.\n And the stars are put out and the trees fail.\n Nor anything remains but that which drones\n Enormous through the dark....\n\nAnd again, in another place, where it prays that one may at the last\nbe fed with beauty---\n\n ... as the flowers are fed\n That fill their falling-time with generous breath:\n Let me attain a natural end of death,\n And on the mighty breast, as on a bed,\n Lay decently at last a drowsy head,\n Content to lapse in somnolence and fade\n In dreaming once again the dream of all things made.\n\nThe most careful philosophy, the most heavenly music, the best\nchoice of poetic or prosaic phrase prepare men properly for man's\nperpetual loss of this and of that, and introduce us proudly to the\nsimilar and greater business of departure from them all, from\nwhatever of them all remains at the close.\n\nTo be introduced, to be prepared, to be armoured, all these are\nexcellent things, but there is a question no foresight can answer\nnor any comprehension resolve. It is right to gather upon that\nquestion the varied affections or perceptions of varying men.\n\nI knew a man once in the Tourdenoise, a gloomy man, but very rich,\nwho cared little for the things he knew. This man took no pleasure\nin his fruitful orchards and his carefully ploughed fields and his\nharvests. He took pleasure in pine trees; he was a man of groves and\nof the dark. For him that things should come to an end was but part\nof an universal rhythm; a part pleasing to the general harmony, and\nmaking in the music of the world about him a solemn and, oh, a\nconclusive chord. This man would study the sky at night and take\nfrom it a larger and a larger draught of infinitude, finding in this\nexercise not a mere satisfaction, but an object and goal for the\nmind; when he had so wandered for a while under the night he seemed,\nfor the moment, to have reached the object of his being.\n\nAnd I knew another man in the Weald who worked with his hands, and\nwas always kind, and knew his trade well; he smiled when he talked\nof scythes, and he could thatch. He could fish also, and he knew\nabout grafting, and about the seasons of plants, and birds, and the\nway of seed. He had a face full of weather, he fatigued his body, he\nwatched his land. He would not talk much of mysteries, he would\nrather hum songs. He loved new friends and old. He had lived with\none wife for fifty years, and he had five children, who were a\npoliceman, a schoolmistress, a son at home, and two who were\nsailors. This man said that what a man did and the life in which he\ndid it was like the farmwork upon a summer's day. He said one works\na little and rests, and works a little again, and one drinks, and\nthere is a perpetual talk with those about one. Then (he would say)\nthe shadows lengthen at evening, the wind falls, the birds get back\nhome. And as for ourselves, we are sleepy before it is dark.\n\nThen also I knew a third man who lived in a town and was clerical\nand did no work, for he had money of his own. This man said that all\nwe do and the time in which we do it is rather a night than a day.\nHe said that when we came to an end we vanished, we and our works,\nbut that we vanished into a broadening light.\n\nWhich of these three knew best the nature of man and of his works,\nand which knew best of what nature was the end?\n\n * * * * *\n\nWhy so glum, my Lad, or my Lass (as the case may be), why so heavy\nat heart? Did you not know that you also must Come to an End?\n\nWhy, that woman of Etaples who sold such Southern wine for the\ndissipation of the Picardian Mist, her time is over and gone and the\nwine has been drunk long ago and the singers in her house have\ndeparted, and the wind of the sea moans in and fills their hall. The\nLords who died in Roncesvalles have been dead these thousand years\nand more, and the loud song about them grew very faint and dwindled\nand is silent now: there is nothing at all remains.\n\nIt is certain that the hills decay and that rivers as the dusty\nyears proceed run feebly and lose themselves at last in desert\nsands; and in its aeons the very firmament grows old. But evil also\nis perishable and bad men meet their judge. Be comforted.\n\nNow of all endings, of all Comings to an End none is so hesitating\nas the ending of a book which the Publisher will have so long and\nthe writer so short: and the Public (God Bless the Public) will have\nwhatever it is given.\n\nBooks, however much their lingering, books also must Come to an End.\nIt is abhorrent to their nature as to the life of man. They must be\nsharply cut off. Let it be done at once and fixed as by a spell and\nthe power of a Word; the word\n\nFINIS\n\n\n\n\n\n\n\n\n\n\nEnd of Project Gutenberg's On Nothing & Kindred Subjects, by Hilaire Belloc\n\n*** ","meta":{"redpajama_set_name":"RedPajamaBook"}}