Tobias Nipkow

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

Stefan Berghofer

Christian Urban

Makarius Wenzel

This book constitutes the refereed proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics, TPHOLs 200, held in Munich, Germany, in August 2009. The 26 revised full papers presented together with 1 proof pearl, 4 tool presentations, and 3 invited papers were carefully reviewed and selected from 55 submissions. The papers cover all aspects of theorem proving in higher order logics as well as related topics in theorem proving and verification such as formal semantics of specification, modeling, and programming languages, specification and verification of hardware and software, formalization of mathematical theories, advances in theorem prover technology, as well as industrial application of theorem provers.

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

Theorem Proving in Higher Order Logics

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

This book constitutes the refereed proceedings of the 9th International Conference on Rewriting Techniques and Applications, RTA-98, held in Tsukuba, Japan, in March/April 1998. The 22 revised full papers presented were carefully selected from a total of 61 submissions by the program committee with the assistance of 113 additional referees. The book covers all current aspects of rewriting including rewriting systems, term rewriting, string rewriting, theorem proving, resolution, normalization, unification, equational logics, lambda calculus, constraint solving, and functional programming.

9th International Conference, RTA-98, Tsukuba, Japan, March 30 - April 1, 1998, Proceedings

Rewriting Techniques and Applications

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

Abstract: "This manual describes how to use the theorem prover Isabelle. For beginners, it explains how to perform simple single-step proofs in the built-in logics. These include first-order logic, a classical sequent calculus, ZF set theory, Constructive Type Theory, and higher-order logic. Each of these logics is described. The manual then explains how to develop advanced tactics and tacticals and how to derive rules. Finally, it describes how to define new logics within Isabelle."

Tobias Nipkow

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