The genericity theorem and the notion of parametricity in the polymorphic lambda -calculus

Abstract

The authors focus on how polymorphic functions, which may take types as inputs, depend on types. These functions are generally understood to have an essentially constant meaning, in all models, on input types. It is shown how the proof theory of the polymorphic lambda -calculus suggests a clear syntactic description of this phenomenon. Under a reasonable condition, it is shown that identity of two polymorphic functions on a single type implies identity of the functions (equivalently, every type is a generic input).<>