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.

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.

This book presents the refereed proceedings of the 14th International Symposium on Formal Methods, FM 2006, held in Hamilton, Canada in August 2006.

The 36 revised full papers presented together with 2 invited contributions and extended abstracts of 7 invited industrial presentations were carefully reviewed and selected from 145 submissions. The papers are organized in topical sections on interactive verification, formal modelling of systems, real time, industrial experience, specification and refinement, programming languages, algebra, education, formal modelling of systems, formal aspects of java, model checking, and abstracts of invited talks from the industry day.

This textbook offers a unified, self-contained introduction to the field of term rewriting. Baader and Nipkow cover all the basic material--abstract reduction systems, termination, confluence, completion, and combination problems--but also some important and closely connected subjects: universal algebra, unification theory, Gröbner bases, and Buchberger's algorithm. They present the main algorithms both informally and as programs in the functional language Standard ML (An appendix contains a quick and easy introduction to ML). Key chapters cover crucial algorithms such as unification and congruence closure in more depth and develop efficient Pascal programs. The book contains many examples and over 170 exercises. This is also an ideal reference book for professional researchers: results spread over many conference and journal articles are collected here in a unified notation, detailed proofs of almost all theorems are provided, and each chapter closes with a guide to the literature.

This textbook-like tutorial is a self-contained introduction to interactive proof, specification, and verification in higher-order logic, using the proof assistant Isabelle 2002. In contrast to existing Isabelle documentation, this book provides a direct route into higher-order logic by bypassing first-order logic and minimizing discussion of meta-theory.Isabelle is a generic system for implementing logical formalisms, and Isabelle/HOL is the specialization of Isabelle for higher-order logic; this theorem prover is well suited as a specification and verification system.

The last ten years have seen a gradual fragmentation of the Automated Reas- ing community into various disparate groups, each with its own conference: the Conference on Automated Reasoning (CADE), the International Workshop on First-Order Theorem Proving (FTP), and the International Conference on - tomated Reasoning with Analytic Tableau and Related Methods (TABLEAUX) to name three. During 1999, various members of these three communities d- cussed the idea of holding a joint conference in 2001 to bring our communities togetheragain.Theplanwastoholdaone-o?conferencefor2001, toberepeated ifitprovedasuccess.Thisvolumecontainsthepaperspresentedattheresulting event: the?rstInternationalJointConferenceonAutomatedReasoning(IJCAR 2001), held in Siena, Italy, from June 18 23, 2001. We received 88 research papers and 24 systems descriptions as submissions. Each submission was fully refereed by at least three peers who were asked to writeareportonthequalityofthesubmissions.Thesereportswereaccessibleto membersoftheprogrammecommitteeviaaweb-basedsystemspeciallydesigned for electronic discussions. As a result we accepted 37 research papers and 19 system descriptions, which make up these proceedings. In addition, this volume contains full papers or extended abstracts from the ?ve invited speakers. Tenone-dayworkshopsandfourtutorialswereheldduringIJCAR2001.The automatedtheoremprovingsystemcompetition(CASC)wasorganizedbyGeo? Sutcli?e to evaluate the performance of sound, fully automatic, classical, ?r- order automated theorem proving systems. The third Workshop on Inference in Computational Semantics (ICoS-3) and the 9th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning (CALCULEMUS-2001) were co-located with IJCAR 2001, and held their own associated workshops and produced their own separate proceedings."

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.

This volume contains the final revised versions of the best papers presented at the First International Workshop on Higher-Order Algebra, Logic, and Term Rewriting (HOA '93), held in Amsterdam in September 1993. Higher-Order methods are increasingly applied in functional and logic programming languages, as well as in specification and verification of programs and hardware. The 15 full papers in this volume are devoted to the algebra and model theory of higher-order languages, computational logic techniques including resolution and term rewriting, and specification and verification case studies; in total they provide a competently written overview of current research and suggest new research directions in this vigourous area.

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.

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.