A Semantic Matching Algorithm : Analysis

A decision procedure for a class of semantic matching problems was proposed in 3], but it yielded eeciency problems, principally because of redundancies. We present in this paper a new semantic matching algorithm for a restricted class of convergent rewrite systems, its theoretical properties, and an eecient implementation. This class of rewrite systems is particularly interesting for functional programming and for program manipulations. To make the algorithm eecient, two techniques are introduced: dependency analysis and sharing analysis. The possibility to divide the semantic matching problems into three complexity classes linear, polynomial, and decidable is also an advantage of our approach. A number of test results shed some light on the eeciency of an ML implementation in the theorem prover Isabelle.