Semantic Matching in Rewrite Theories

\Semantic matching" is the process of generating a basis set of substitutions (of terms for variables) that makes one term equal to another in a speci ed theory. We restrict ourselves here to matching problems in equational theories that can be presented as programs in the form of convergent rewrite systems, that is, nite sets of equations that compute unique output values when applied (from left-toright) to input values (a generalization of functional programs). Decidable matching can help in program veri cation and synthesis. We describe a new class of programs for which matching is decidable, which|with some negative results|provide a ner characterization of decidability than was available before.