Polymorphic types and widening operators

Abstract

Because of the ease of use and the versatility of widening operators, there seem to be good candidates for defining new type inference strategy wherever the type inference problem is not decidable.

More precisely, in this paper, we exhibit some widening operators that either mimic some type inference strategy that are already implemented in some languages, or extend the ML-type system. In fact, those widening operators are only selected operators from a much larger family of widening operators listed on figure 3 that works very well on the ML-type algebra.

But widening operators can be used to solve other problems than the termination of the ML+type inference problem. For example, in [7] we have introduced a new type algebra called Fractional Types. Since the intersection of two fractional types is not computable in some cases, we have to use a widening operator to compute a lower approximation of the intersection of two fractional types, and to ensure algorithm termination.

We intend to develop the widening techniques presented in this paper:

• to search for sharper widening than those realized de facto by specific known algorithms, not only in ML, but wherever type inference is possible;

• to bridge the gap between type inference and abstract interpretation techniques.