Type isomorphisms in a type-assignment framework

摘要

This paper contains a full treatment of isomorphic types for languages equipped with an ML style polymorphic type inference mechanism. Surprisingly enough the results obtained contradict the common-place feeling that (the core of) ML is a subset of second order λ-calculus: we can provide an isomorphism of types that holds in the core ML language, but not in second order λ-calculus. This new isomorphism not only allows to provide a complete (and decidable) axiomatisation of all the type isomorphic in ML style languages, a relevant issue for the type as specifications paradigm in library searches, but also suggest a natural extension that in a sense completes the type-inference mechanism in ML. This extension is easy to implement and allows to get a further insight in the nature of the let polymorphic construct.