Towards A Proof Theory Of Rewriting
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Author |
: Barnaby P. Hilken |
Publisher |
: |
Total Pages |
: 34 |
Release |
: 1994 |
ISBN-10 |
: UCSC:32106012164288 |
ISBN-13 |
: |
Rating |
: 4/5 (88 Downloads) |
Synopsis Towards a Proof Theory of Rewriting by : Barnaby P. Hilken
Abstract: "This paper describes the simply-typed 2-[lambda]- calculus, a language with three levels: types, terms and rewrites. The types and terms are those of the simply-typed [lambda]-calculus, and the rewrites are expressions denoting sequences of [beta]-reductions and [eta]- expansions. An equational theory is imposed on the rewrites, based on 2- categorical justifications, and the word problem for this theory is solved by finding a canonical expression in each equivalence class. The canonical form of rewrites allows us to prove several properties of the calculus, including a strong form of confluence and a classification of the long-[beta]-[eta]-normal forms in terms of their rewrites. Finally we use these properties as the basic definitions of a theory of categorical rewriting, and find that the expected relationships between confluence, strong normalisation and normal forms hold."
Author |
: Terese |
Publisher |
: Cambridge University Press |
Total Pages |
: 926 |
Release |
: 2003-03-20 |
ISBN-10 |
: 0521391156 |
ISBN-13 |
: 9780521391153 |
Rating |
: 4/5 (56 Downloads) |
Synopsis Term Rewriting Systems by : Terese
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.
Author |
: Franz Baader |
Publisher |
: Cambridge University Press |
Total Pages |
: 318 |
Release |
: 1998 |
ISBN-10 |
: 0521779200 |
ISBN-13 |
: 9780521779203 |
Rating |
: 4/5 (00 Downloads) |
Synopsis Term Rewriting and All That by : Franz Baader
Unified and self-contained introduction to term-rewriting; suited for students or professionals.
Author |
: Hubert Comon-Lundh |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 287 |
Release |
: 2007-06-22 |
ISBN-10 |
: 9783540731467 |
ISBN-13 |
: 3540731466 |
Rating |
: 4/5 (67 Downloads) |
Synopsis Rewriting, Computation and Proof by : Hubert Comon-Lundh
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.
Author |
: Juliette Kennedy |
Publisher |
: Springer |
Total Pages |
: 411 |
Release |
: 2017-07-10 |
ISBN-10 |
: 9783662553862 |
ISBN-13 |
: 3662553864 |
Rating |
: 4/5 (62 Downloads) |
Synopsis Logic, Language, Information, and Computation by : Juliette Kennedy
Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 24th Workshop on Logic, Language, Information and Communication, WoLLIC 2017, held in London, UK, in August 2017. The 28 contributed papers were carefully reviewed and selected from 61 submissions. They cover interdisciplinary research in pure and applied logic, aiming at interactions between logic and the sciences related to information and computation.
Author |
: Andrei Voronkov |
Publisher |
: Springer |
Total Pages |
: 467 |
Release |
: 2008-07-11 |
ISBN-10 |
: 9783540705901 |
ISBN-13 |
: 3540705902 |
Rating |
: 4/5 (01 Downloads) |
Synopsis Rewriting Techniques and Applications by : Andrei Voronkov
This book constitutes the refereed proceedings of the 19th International Conference on Rewriting Techniques and Applications, RTA 2008, held in Hagenberg, Austria, July 15-17, in June 2008 as part of the RISC Summer 2008. The 30 revised full papers presented were carefully reviewed and selected from 57 initial submissions. The papers cover current research on all aspects of rewriting including typical areas of interest such as applications, foundational issues, frameworks, implementations, and semantics.
Author |
: Stephane Kaplan |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 500 |
Release |
: 1991-08-07 |
ISBN-10 |
: 3540543171 |
ISBN-13 |
: 9783540543176 |
Rating |
: 4/5 (71 Downloads) |
Synopsis Conditional and Typed Rewriting Systems by : Stephane Kaplan
In recent years, extensions of rewriting techniques that go beyond the traditional untyped algebraic rewriting framework have been investigated and developed. Among these extensions, conditional and typed systems are particularly important, as are higher-order systems, graph rewriting systems, etc. The international CTRS (Conditional and Typed Rewriting Systems) workshops are intended to offer a forum for researchers on such extensions of rewriting techniques. This volume presents the proceedings of the second CTRS workshop, which contributed to discussion and evaluation of new directions of research. (The proceedings of the first CTRS workshop are in Lecture Notes in Computer Science, Vol. 308.) Several important directions for extensions of rewriting techniques were stressed, which are reflected in the organization of the chapters in this volume: - Theory of conditional and Horn clause systems, - Infinite terms, non-terminating systems, and termination, - Extension of Knuth-Bendix completion, - Combined systems, combined languages and modularity, - Architecture, compilers and parallel computation, - Basic frameworks for typed and order-sorted systems, - Extension of unification and narrowing techniques.
Author |
: Hassan Aït-Kaci |
Publisher |
: Academic Press |
Total Pages |
: 400 |
Release |
: 2014-05-10 |
ISBN-10 |
: 9781483259673 |
ISBN-13 |
: 1483259676 |
Rating |
: 4/5 (73 Downloads) |
Synopsis Rewriting Techniques by : Hassan Aït-Kaci
Resolution of Equations in Algebraic Structures: Volume 2, Rewriting Techniques is a collection of papers dealing with the construction of canonical rewrite systems, constraint handling in logic programming, and completion algorithms for conditional rewriting systems. Papers discuss the Knuth-Bendix completion method which constructs a complete system for a given set of equations, including extensions of the method dealing with termination, unfailing completion, and associative-communicative completion. One paper examines the various practical techniques that can be used to extend Prolog as a constraint solver, particularly on techniques that solve boolean equations, imposing inequality, disequality, and finitary domain constraints on variables. Another paper presents a sufficient condition for confluence of conditional rewriting, and a practical unification algorithm modulo conditional rewriting through the notion of conditional narrowing. One paper analyzes the possibility of using completion for inductive proofs in the initial algebra of an equational variety without explicit induction. Another papers discusses solving systems of word equations in the free monoid and the free group, where a solution is defined as a word homomorphism. Programmers, mathematicians, students, and instructors involved in computer science and computer logic will find this collection valuable.
Author |
: Nachum Dershowitz |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 598 |
Release |
: 1989 |
ISBN-10 |
: 3540510818 |
ISBN-13 |
: 9783540510819 |
Rating |
: 4/5 (18 Downloads) |
Synopsis Rewriting Techniques and Applications by : Nachum Dershowitz
Rewriting has always played an important role in symbolic manipulation and automated deduction systems. The theory of rewriting is an outgrowth of Combinatory Logic and the Lambda Calculus. Applications cover broad areas in automated reasoning, programming language design, semantics, and implementations, and symbolic and algebraic manipulation. The proceedings of the third International Conference on Rewriting Techniques and Applications contain 34 regular papers, covering many diverse aspects of rewriting (including equational logic, decidability questions, term rewriting, congruence-class rewriting, string rewriting, conditional rewriting, graph rewriting, functional and logic programming languages, lazy and parallel implementations, termination issues, compilation techniques, completion procedures, unification and matching algorithms, deductive and inductive theorem proving, Gröbner bases, and program synthesis). It also contains 12 descriptions of implemented equational reasoning systems. Anyone interested in the latest advances in this fast growing area should read this volume.
Author |
: Ralf Treinen |
Publisher |
: Springer |
Total Pages |
: 401 |
Release |
: 2009-06-19 |
ISBN-10 |
: 9783642023484 |
ISBN-13 |
: 3642023487 |
Rating |
: 4/5 (84 Downloads) |
Synopsis Rewriting Techniques and Applications by : Ralf Treinen
This book constitutes the refereed proceedings of the 20th International Conference on Rewriting Techniques and Applications, RTA 2009, held in Brasília, Brazil, during June 29 - July 1, 2009. The 22 revised full papers and four system descriptions presented were carefully reviewed and selected from 59 initial submissions. The papers cover current research on all aspects of rewriting including typical areas of interest such as applications, foundational issues, frameworks, implementations, and semantics.