Towards A Proof Theory Of Rewriting
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Author | : Barnaby P. Hilken |
Publisher | : |
Total Pages | : 34 |
Release | : 1994 |
Genre | : Proof theory |
ISBN | : |
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 | : Gilbert Baumslag |
Publisher | : Springer Science & Business Media |
Total Pages | : 235 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461397308 |
The papers in this volume are the result of a workshop held in January 1989 at the Mathematical Sciences Research Institute. Topics covered include decision problems, finitely presented simple groups, combinatorial geometry and homology, and automatic groups and related topics.
Author | : Sophie Tison |
Publisher | : Springer |
Total Pages | : 397 |
Release | : 2003-08-02 |
Genre | : Computers |
ISBN | : 3540456104 |
This book constitutes the refereed proceedings of the 13th International Conference on Rewriting Techniques and Applications, RTA 2002, held in Copenhagen, Denmark, in July 2002. The 20 regular papers, two application papers, and four system descriptions presented together with three invited contributions were carefully reviewed and selected from 49 submissions. All current aspects of rewriting are addressed.
Author | : Vincent van Oostrom |
Publisher | : Springer Science & Business Media |
Total Pages | : 322 |
Release | : 2004-05-24 |
Genre | : Mathematics |
ISBN | : 3540221530 |
This book constitutes the refereed proceedings of the 15th International Conference on Rewriting Techniques and Applications, RTA 2004, held in Aachen, Germany in June 2004.
Author | : Terese |
Publisher | : Cambridge University Press |
Total Pages | : 926 |
Release | : 2003-03-20 |
Genre | : Computers |
ISBN | : 9780521391153 |
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 | : Hubert Comon-Lundh |
Publisher | : Springer Science & Business Media |
Total Pages | : 287 |
Release | : 2007-06-22 |
Genre | : Computers |
ISBN | : 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.
Author | : Vlad Rusu |
Publisher | : Springer |
Total Pages | : 273 |
Release | : 2018-09-07 |
Genre | : Computers |
ISBN | : 3319998404 |
This book constitutes revised selected papers from the 12th International Workshop on Rewriting Logic and Its Applications, WRLA 2018, held in Thessaloniki, Greece, in June 2018. The 12 full papers presented in this volume were carefully reviewed and selected from 21 submissions. They deal with rewriting, a natural model of computation and an expressive semantic framework for concurrency, parallelism, communication, and interaction, and its applications.
Author | : Stephane Kaplan |
Publisher | : Springer Science & Business Media |
Total Pages | : 500 |
Release | : 1991-08-07 |
Genre | : Computers |
ISBN | : 9783540543176 |
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 |
Genre | : Mathematics |
ISBN | : 1483259676 |
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 | : Harald Ganzinger |
Publisher | : Springer Science & Business Media |
Total Pages | : 456 |
Release | : 1996-07 |
Genre | : Computers |
ISBN | : 9783540614647 |
This book constitutes the refereed proceedings of the 7th International Conference on Rewriting Techniques and Applications, RTA-96, held in New Brunswick, NJ, USA, in July 1996. The 27 revised full papers presented in this volume were selected from a total of 84 submissions, also included are six system descriptions and abstracts of three invited papers. The topics covered include analysis of term rewriting systems, string and graph rewriting, rewrite-based theorem proving, conditional term rewriting, higher-order rewriting, unification, symbolic and algebraic computation, and efficient implementation of rewriting on sequential and parallel machines.