Set-theoretic foundation of parametric polymorphism and subtyping

Abstract

We define and study parametric polymorphism for a type system with recursive, product, union, intersection, negation, and function types. We first recall why the definition of such a system was considered hard "when not impossible" and then present the main ideas at the basis of our solution. In particular, we introduce the notion of "convexity" on which our solution is built up and discuss its connections with parametricity as defined by Reynolds to whose study our work sheds new light.