Properties of a Rewrite System for Unification with Expansion Variables⋆

A study of properties of a rewrite system for solving constraint sets that are instances of the unification with expansion variables problem. The terms in the constraints are built from the intersection type constructors plus type variables and applied expansion variables. We show that: • Constraint set rewriting is confluent (modulo isomorphism). • There is a set of well-named constraint sets which is closed under reduction and normalisation of well-named sets always produces a unifier. • The rewrite system partitions naturally such that all reductions of wellnamed constraint sets are finite (terminating) with each part. • The subset of acyclic well-named constraint sets is preserved by reduction the occur check may be omitted for reduction of such sets. • The acyclic well-named constraint sets include those necessary for intersection typing inference, therefore the above properties hold for its application in the intersection type framework of System E.