A Rewrite-Based Type Discipline for a Subset of Computer Algebra

This paper is concerned with the type structure of a system including polymorphism, type properties and subtypes. This type system originates from computer algebra but it is not intended to be the solution of all type problems in this area. Types (or sets of types) are denoted by terms in some order-sorted algebra.:[: We consider a rewrite relation in this algebra, which is intended to express subtyping. The relations between the semantics and the axiomatization are investigated. It is shown that the problem of type inference is undecidable but a narrowing strategy for semi-decision procedures is described and studied.