Optimal Representations of Polymorphic

Many type inference and program analysis systems include notions of subtyping and parametric polymorphism. When used together, these two features induce equivalences that allow types to be simpliied by eliminating quantiied variables. Eliminating variables both improves the readability of types and the performance of algorithms whose complexity depends on the number of type variables. We present an algorithm for simplifying quantiied types in the presence of subtyping and prove it is sound and complete for non-recursive and recursive types. We also show that an extension of the algorithm is sound but not complete for a type language with intersection and union types, as well as for a language of constrained types.