Conditional and Typed Rewriting Systems de Stephane Kaplan

Conditional and Typed Rewriting Systems

Stephane Kaplan

Mitsuhiro Okada

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.

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Cuprins

Conditional rewriting in focus.- A maximal-literal unit strategy for horn clauses.- Extended term rewriting systems.- A proof system for conditional algebraic specifications.- Conditional rewriting logic: Deduction, models and concurrency.- Equivalences of rewrite programs.- On finite representations of infinite sequences of terms.- Infinite terms and infinite rewritings.- Testing confluence of nonterminating rewriting systems.- A survey of ordinal interpretations of type ?0 for termination of rewriting systems.- Meta-rule synthesis from crossed rewrite systems.- An application of automated equational reasoning to many-valued logic.- Completion of first-order clauses with equality by strict superposition.- Knuth-bendix completion of horn clause programs for restricted linear resolution and paramodulation.- Proof by consistency in conditional equational theories.- Completion procedures as semidecision procedures.- Errata corrige.- Linear completion.- Clausal rewriting.- Adding algebraic rewriting to the calculus of constructions : Strong normalization preserved.- On sufficient completeness of conditional specifications.- FPL : Functional plus logic programming an integration of the FP and Prolog languages.- Confluence of the disjoint union of conditional term rewriting systems.- Implementing term rewriting by graph reduction: Termination of combined systems.- Compiling concurrent rewriting onto the Rewrite Rule Machine.- Design strategies for rewrite rules.- A simplifier for untyped lambda expressions.- Parallel graph rewriting on loosely coupled machine architectures.- Typed equivalence, type assignment, and type containment.- A fixed-point semantics for feature type systems.- Unique-sort order-sorted theories : A description as monad morphisms.- Equational logics(birkhoff's method revisited).- Compatibility of order-sorted rewrite rules.- An universal termination condition for solving goals in equational languages.- Constrained equational deduction.- Higher-order unification, polymorphism, and subsorts.- Second-order unification in the presence of linear shallow algebraic equations.- An inference system for horn clause logic with equality.