Proving termination of logic programs by transforming them into equivalent term rewriting systems

Abstract

A method for proving termination of logic programs is defined by transforming a given logic program and goal into a term rewriting system and starting term respectively. It is proved that the transformation applied to an input-driven logic program and goal yields a term rewriting system and starting term whose reduction tree is finite iff the corresponding SLD tree, using the leftmost selection rule, is finite. The transformation is purely syntactical and the termination of logic programs can be studied by analyzing the produced rewrite system using termination orderings proposed in the term rewriting system literature. It possesses all the advantages of analogous methodologies described in [GW92, RKS92] but it does not require any prior information about modings of predicates since these are computed during the transformation according to the given goal. In general, termination proofs can be given for larger classes of programs than those of [RKS92]. Moreover, it allows the computation of any computed answer substitution for the refutation of an input-driven logic program and goal.