Adventures in associative-commutative unification
Patrick D. Lincoln, Jim Christian · Journal of Symbolic Computation · 1989
We have discovered an efficient algorithm for matching and unification in associative-commutative (AC) equational theories. In most cases of AC unification our method obviates the need for solving diophantine equations, and thus avoids one of the bottlenecks of other associative-commutative unification techniques. The algorithm efficiently 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 unification procedures on many commonly encountered AC problems.