Formal Parametric Polymorphism

Abstract

A polymorphic function is parametric if its behavior does not depend on the type at which it is instantiated. Starting with Reynolds' work, the study of parametricity is typically semantic. In this paper, we develop a syntactic approach to parametricity, and a formal system that embodies this approach: system ℜ. Girard's system F deals with terms and types; ℜ is an extension of F that deals also with relations between types.