A Method for Implementing Equational Theories as Logic Programs

Equational theories underly many elds of computing, including functional programming, symbolic algebra, theorem proving, term rewriting and constraint solving. In this paper we show a method for implementing many equational theories with a limited class of logic programs. We de ne regular equational theories, a useful class of theories, and illustrate with a number of examples how our method can be used in obtaining e cient implementations for them. The signi cance of our method is that: It is simple and easy to apply. Although executable, it supports separation of concerns between speci cation and implementation. Its class of logic programs execute with impressive e ciency using Prolog. It permits interesting compilation and optimization techniques that can improve execution e ciency still further. It o ers perspectives on term rewriting and functional programming evaluation strategies, how they can be compiled, and how they can be integrated with logic programming e ectively.