Unification in combinations of collapse-free theories with disjoint sets of function symbols

Abstract

A unification algorithm for combinations of collapse-free equational theories with disjoint sets of function symbols is presented. The algorithm uses complete unification algorithms for the theories in the combination to compute complete sets of unifiers in the combined theory. It terminates if the algorithms for the theories in the combination terminate. The only restriction on the theories in the combination — apart from disjointness of function symbol sets — is that they must be collapse-free (i.e., they must not have axioms of the form t = x, where t is a non-variable term and x is a variable). This extends the class of equational theories for which the unification problem in combinations can be solved to collapse-free theories. The algorithm is based on a study of the properties of unifiers in combinations of non-regular collapse-free theories.