Lecture Notes in Computer Science

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 of finiteness 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.