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Rewriting, Computation and Proof

Author: Hubert Comon-Lundh

Publisher: Springer Science & Business Media

Published: 2007-06-22

Total Pages: 287

ISBN-13: 3540731466

Jean-Pierre Jouannaud has played a leading role in the field of rewriting and its technology. This Festschrift volume, published to honor him on his 60th Birthday, includes 13 refereed papers by leading researchers, current and former colleagues. The papers are grouped in thematic sections on Rewriting Foundations, Proof and Computation, and a final section entitled Towards Safety and Security.

Canonical Equational Proofs

Author: Bachmair

Publisher: Springer Science & Business Media

Published: 2013-03-08

Total Pages: 142

ISBN-13: 146847118X

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Equations occur in many computer applications, such as symbolic compu tation, functional programming, abstract data type specifications, program verification, program synthesis, and automated theorem proving. Rewrite systems are directed equations used to compute by replacing subterms in a given formula by equal terms until a simplest form possible, called a normal form, is obtained. The theory of rewriting is concerned with the compu tation of normal forms. We shall study the use of rewrite techniques for reasoning about equations. Reasoning about equations may, for instance, involve deciding whether an equation is a logical consequence of a given set of equational axioms. Convergent rewrite systems are those for which the rewriting process de fines unique normal forms. They can be thought of as non-deterministic functional programs and provide reasonably efficient decision procedures for the underlying equational theories. The Knuth-Bendix completion method provides a means of testing for convergence and can often be used to con struct convergent rewrite systems from non-convergent ones. We develop a proof-theoretic framework for studying completion and related rewrite based proof procedures. We shall view theorem provers as proof transformation procedures, so as to express their essential properties as proof normalization theorems.

Term Rewriting Systems

Author: Terese

Publisher: Cambridge University Press

Published: 2003-03-20

Total Pages: 926

ISBN-13: 9780521391153

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Term rewriting systems developed out of mathematical logic and are an important part of theoretical computer science. They consist of sequences of discrete transformation steps where one term is replaced with another and have applications in many areas, from functional programming to automatic theorem proving and computer algebra. This 2003 book starts at an elementary level with the earlier chapters providing a foundation for the rest of the work. Much of the advanced material appeared here for the first time in book form. Subjects treated include orthogonality, termination, completion, lambda calculus, higher-order rewriting, infinitary rewriting and term graph rewriting. Many exercises are included with selected solutions provided on the web. A comprehensive bibliography makes this book ideal both for teaching and research. A chapter is included presenting applications of term rewriting systems, with many pointers to actual implementations.

Proofs and Algorithms

Author: Gilles Dowek

Publisher: Springer Science & Business Media

Published: 2011-01-11

Total Pages: 161

ISBN-13: 0857291211

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Logic is a branch of philosophy, mathematics and computer science. It studies the required methods to determine whether a statement is true, such as reasoning and computation. Proofs and Algorithms: Introduction to Logic and Computability is an introduction to the fundamental concepts of contemporary logic - those of a proof, a computable function, a model and a set. It presents a series of results, both positive and negative, - Church's undecidability theorem, Gödel’s incompleteness theorem, the theorem asserting the semi-decidability of provability - that have profoundly changed our vision of reasoning, computation, and finally truth itself. Designed for undergraduate students, this book presents all that philosophers, mathematicians and computer scientists should know about logic.

Automated Deduction - CADE-19

Author: Franz Baader

Publisher: Springer

Published: 2003-10-31

Total Pages: 512

ISBN-13: 3540450858

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The refereed proceedings of the 19th International Conference on Automated Deduction, CADE 2003, held in Miami Beach, FL, USA in July 2003. The 29 revised full papers and 7 system description papers presented together with an invited paper and 3 abstracts of invited talks were carefully reviewed and selected from 83 submissions. All current aspects of automated deduction are discussed, ranging from theoretical and methodological issues to the presentation of new theorem provers and systems.

Term Rewriting and Applications

Author: Jürgen Giesl

Publisher: Springer Science & Business Media

Published: 2005-04-07

Total Pages: 528

ISBN-13: 3540255966

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This book constitutes the refereed proceedings of the 16th International Conference on Rewriting Techniques and Applications, RTA 2005, held in Nara, Japan in April 2005. The 29 revised full papers and 2 systems description papers presented together with 5 invited articles were carefully reviewed and selected from 79 submissions. All current issues in Rewriting are addressed, ranging from foundational and methodological issues to applications in various contexts; due to the fact that the first RTA conference was held 20 years ago, the conference offered 3 invited historical papers 2 of which are included in this proceedings.

Rewriting, Computation and Proof

Author: Hubert Comon-Lundh

Publisher: Springer Science & Business Media

Published: 2007-08-18

Total Pages: 287

ISBN-13: 3540731474

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How to Prove It

Author: Daniel J. Velleman

Publisher: Cambridge University Press

Published: 2006-01-16

Total Pages: 401

ISBN-13: 0521861241

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Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.

Rewriting Techniques and Applications

Author: Aart Middeldorp

Publisher: Springer

Published: 2003-06-29

Total Pages: 368

ISBN-13: 3540451277

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This book constitutes the refereed proceedings of the 12th International Conference on Rewriting Techniques and Applications, RTA 2001, held in Utrecht, The Netherlands, in May 2001. The 23 revised full papers presented together with two system descriptions were carefully reviewed and selected from 55 submissions. All current aspects of rewriting are addressed.

Term Rewriting and All That

Author: Franz Baader

Publisher: Cambridge University Press

Published: 1998

Total Pages: 318

ISBN-13: 9780521779203

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Unified and self-contained introduction to term-rewriting; suited for students or professionals.