Unification in a Combination of Equational Theories with Shared Constants and its Application to Primal Algebras

We extend the results on combination of disjoint equational theories to combination of equational theories where the only function symbols shared are constants. This is possible because there exist nitely many proper shared terms (the constants) which can be assumed irreducible in any equa-tional proof of the combined theory. We establish a connection between the equational combination framework and a more algebraic one. A uniication algorithm provides a symbolic constraint solver in the combination of algebraic structures whose nite domains of values are non disjoint and correspond to constants. Primal algebras are particular nite algebras of practical relevance for manipulating hardware descriptions.