Sorted Unification Using Set Constraints

This paper describes a new representation for sortal constraints and a uniication algorithm for the corresponding constrained terms. Variables range over sets of terms described by systems of set constraints that can express limited inter-variable dependencies. These sets of terms are more general than regular tree languages, but are still closed under intersection. The new uniication algorithm shows sorted uniication to be decidable for a broad class of sorted signatures, which we call semi-linear, and, more generally , for sort theories with a least Herbrand model that can be represented using the new constraints. A nite representation of a complete set of well-sorted uniiers can always be found, even in those cases where this set is innnite.