Conditional Term Rewriting Systems

This volume contains the papers preesented at the Third International Workshop on Conditional Term Rewriting Systems, held in Pont- -Mousson, France, July 8-10, 1992. Topics covered include conditional rewriting and its applications to programming languages, specification languages, automated deduction, constrained rewriting, typed rewriting, higher-order rewriting, and graph rewriting. The volume contains 40 papers, including four invited talks: Algebraic semantics of rewriting terms and types, by K. Meinke; Generic induction proofs, by P. Padawitz; Conditional term rewriting and first-order theorem proving, by D. Plaisted; and Decidability of finiteness properties (abstract), by L. Pacholski. The first CTRS workshop was held at the University of Paris in 1987 and the second at Concordia University, Montreal, in 1990. Their proceddings are published as Lecture Notes in Computer Science Volumes 308 and 516 respectively.

Inhalt
Algebraic semantics of rewriting terms and types.- Context rewriting.- Explicit cyclic substitutions.- Simple type inference for term graph rewriting systems.- Consistency and semantics of equational definitions over predefined algebras.- Completeness of combinations of conditional constructor systems.- Collapsed tree rewriting: Completeness, confluence, and modularity.- Combinations of simplifying conditional term rewriting systems.- Sufficient conditions for modular termination of conditional term rewriting systems.- Termination of combined (rewrite and ?-calculus) systems.- Type removal in term rewriting.- Termination of term rewriting by interpretation.- Path orderings for termination of associative-commutative rewriting.- Generic induction proofs.- A constructor-based approach for positive/negative-conditional equational specifications.- Semantics for positive/negative conditional rewrite systems.- Inductive theorem proving by consistency for first-order clauses.- Reduction techniques for first-order reasoning.- Conditional term rewriting and first-order theorem proving.- Decidability of regularity and related properties of ground normal form languages.- Computing linearizations using test sets.- Proving group isomorphism theorems.- Semigroups satisfying x m+n = x n .- Could orders be captured by term rewriting systems?.- A categorical formulation for critical-pair/completion procedures.- Trace rewriting systems.- A calculus for conditional inductive theorem proving.- Implementing contextual rewriting.- Confluence of terminating membership conditional TRS.- Completeness and confluence of order-sorted term rewriting.- Completion for constrained term rewriting systems.- Generalized partial computation using disunification to solve constraints.- Decidability offiniteness properties.- Termination proofs of well-moded logic programs via conditional rewrite systems.- Logic programs with polymorphic types: A condition for static type checking.- Normalization by leftmost innermost rewriting.- A strategy to deal with divergent rewrite systems.- A new approach to general E-unification based on conditional rewriting systems.- An optimal narrowing strategy for general canonical systems.- Set-of-support strategy for higher-order logic.