Adventures in Associative-commutative Uniication

We have discovered an eecient algorithm for matching and uniication in associative-commutative (AC) and associative-commutative-idempotent (ACI) equational theories. In most cases of AC uniication and in all cases of ACI uniication our method obviates the need for solving diophantine equations, and thus avoids one of the bottlenecks of other associative-commutative uniication techniques. The algorithm eeciently utilizes powerful constraints to eliminate much of the search involved in generating valid substitutions. Moreover, it is able to generate solutions lazily, enabling its use in an SLD-resolution-based environment like Prolog. We have found the method to run much faster and use less space than other associative-commutative uniication procedures on many commonly encountered AC problems.