Tobias Nipkow

This volume contains thoroughly refereed and revised full papers selected from the presentations at the first workshop held under the auspices of the ESPRIT Basic Research Action 6453 Types for Proofs and Programs in Nijmegen, The Netherlands, in May 1993. As the whole ESPRIT BRA 6453, this volume is devoted to the theoretical foundations, design and applications of systems for theory development. Such systems help in designing mathematical axiomatisation, performing computer-aided logical reasoning, and managing databases of mathematical facts; they are also known as proof assistants or proof checkers.

International Workshop TYPES '93, Nijmegen, The Netherlands, May 24 - 28, 1993. Selected Papers

Types for Proofs and Programs

Jayadev Misra

Emil Sekerinski

This book presents the refereed proceedings of the 14th International Symposium on Formal Methods, FM 2006, held in Hamilton, Canada, August 2006. The book presents 36 revised full papers together with 2 invited contributions and extended abstracts of 7 invited industrial presentations, organized in topical sections on interactive verification, formal modelling of systems, real time, industrial experience, specification and refinement, programming languages, algebra, formal modelling of systems, and more.

14th International Symposium on Formal Methods, Hamilton, Canada, August 21-27, 2006, Proceedings

FM 2006: Formal Methods

Rajeev Gore

Alexander Leitsch

This book constitutes the refereed proceedings of the First International Joint Conference on Automated Reasoning, IJCAR 2001, held in Siena, Italy, in June 2001. The 37 research papers and 19 system descriptions presented together with three invited contributions were carefully reviewed and selected from a total of 112 submissions. The book offers topical sections on description, modal, and temporal logics; saturation based theorem proving, applications, and data structures; logic programming and nonmonotonic reasoning; propositional satisfiability and quantified Boolean logic; logical frameworks, higher-order logic, and interactive theorem proving; equational theorem proving and term rewriting; tableau, sequent, and natural deduction calculi and proof theory; automata, specification, verification, and logics of programs; and nonclassical logics.

First International Joint Conference, IJCAR 2001 Siena, Italy, June 18-23, 2001 Proceedings

Automated Reasoning

Lawrence C. Paulson

Markus Wenzel

This volume is a self-contained introduction to interactive proof in high- order logic (HOL), using the proof assistant Isabelle 2002. Compared with existing Isabelle documentation, it provides a direct route into higher-order logic, which most people prefer these days. It bypasses ?rst-order logic and minimizes discussion of meta-theory. It is written for potential users rather than for our colleagues in the research world. Another departure from previous documentation is that we describe Markus Wenzel’s proof script notation instead of ML tactic scripts. The l- ter make it easier to introduce new tactics on the ?y, but hardly anybody does that. Wenzel’s dedicated syntax is elegant, replacing for example eight simpli?cation tactics with a single method, namely simp, with associated - tions. The book has three parts. – The ?rst part, Elementary Techniques, shows how to model functional programs in higher-order logic. Early examples involve lists and the natural numbers. Most proofs are two steps long, consisting of induction on a chosen variable followed by the auto tactic. But even this elementary part covers such advanced topics as nested and mutual recursion. – The second part, Logic and Sets, presents a collection of lower-level tactics that you can use to apply rules selectively. It also describes I- belle/HOL’s treatment of sets, functions, and relations and explains how to de?ne sets inductively. One of the examples concerns the theory of model checking, and another is drawn from a classic textbook on formal languages.

A Proof Assistant for Higher-Order Logic

Isabelle/HOL

Orna Grumberg

Benedikt Hauptmann

NATO Emerging Security Challenges Division

Tools for Analysis and Verification

Software Safety and Security

Stefan Berghofer

Christian Urban

Makarius Wenzel

This volume constitutes the proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics (TPHOLs 2009), which was held during August 17-20, 2009 in Munich, Germany. TPHOLs covers all aspects of theorem proving in higher order logics as well as related topics in theorem proving and veri?cation. There were 55 papers submitted to TPHOLs 2009 in the full research c- egory, each of which was refereed by at least three reviewers selected by the ProgramCommittee. Of these submissions, 26 researchpapers and 1 proofpearl were accepted for presentation at the conference and publication in this v- ume. In keeping with longstanding tradition, TPHOLs 2009 also o?ered a venue for the presentation of emerging trends, where researchers invited discussion by means of a brief introductory talk and then discussed their work at a poster session. A supplementary proceedings volume was published as a 2009 technical report of the Technische Universit¨ at Munc ¨ hen. The organizers are grateful to David Basin, John Harrison and Wolfram Schulte for agreeing to give invited talks. We also invited four tool devel- ers to give tutorials about their systems. The following speakers kindly accepted our invitation and we are grateful to them: John Harrison (HOL Light), Adam Naumowicz (Mizar), Ulf Norell (Agda) and Carsten Schur ¨ mann (Twelf).

22nd International Conference, TPHOLs 2009, Munich, Germany, August 17-20, 2009, Proceedings

Theorem Proving in Higher Order Logics

Gerwin Klein

Part I of this book is a practical introduction to working with the Isabelle proof assistant. It teaches you how to write functional programs and inductive definitions and how to prove properties about them in Isabelle’s structured proof language. Part II is an introduction to the semantics of imperative languages with an emphasis on applications like compilers and program analysers. The distinguishing feature is that all the mathematics has been formalised in Isabelle and much of it is executable. Part I focusses on the details of proofs in Isabelle; Part II can be read even without familiarity with Isabelle’s proof language, all proofs are described in detail but informally. The book teaches the reader the art of precise logical reasoning and the practical use of a proof assistant as a surgical tool for formal proofs about computer science artefacts. In this sense it represents a formal approach to computer science, not just semantics. The Isabelle formalisation, including the proofs and accompanying slides, are freely available online, and the book is suitable for graduate students, advanced undergraduate students, and researchers in theoretical computer science and logic.

With Isabelle/HOL

Concrete Semantics

Tobias Nipkow

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