Combining unification algorithms for confined regular equational theories

Abstract

This paper presents a method for combining equational unification algorithms to handle terms containing "mixed" sets of function symbols. For example, given one algorithm for unifying associative-commutative operators, and another for unifying commutative operators, our algorithm provides a method for unifying terms containing both kinds of operators. We restrict our attention to a class of equational theories which we call confined regular theories. The algorithms is proven to terminate with a complete and correct set of E-unifiers. An implementation has been done as part of a larger system for reasoning about equational theories.