Solving goals in equational languages

Abstract

Solving equations in equational Horn-clause theories is a programming paradigm that combines logic programming and functional programming in a clean manner. Languages like Eqlog, Slog and Rite, express programs as conditional rewrite rules and goals as equations to be solved. Procedures for completion of conditional equational theories, in a manner akin to that of Knuth and Bendix for unconditional theories, also require methods for solving equations appearing in conditions. Rewrite-based logic-programming uses (conditional) narrowing to solve equational goals. Recently a different, topdown equation solving procedure was proposed for unconditional rewrite systems. In this paper, we express equational goal solving using conditional rules. Some refinements are described: the notion of operator derivability is used to prune useless paths in the search tree and our use of oriented goals eliminates some redundant paths leading to non-normalized solutions. Our goal-directed method can also be extended to handle conditional systems.