Rewriting Techniques (PDF)

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.