Computing with rewrite systems

Term-rewriting systems, that is, sets of directed equations, provide a paradigm of computation with particularly simple syntax and semantics. Rewrite systems may be used for straightforward computation by simplifying terms. We show how, in addition, restricted forms of the Knuth—Bendix “completion” procedure may be used to interpret logic programs written as a set of equivalence-preserving rewrite rules. We discuss verification issues and also illustrate the use of the full completion procedure to synthesize rewrite programs from specifications.