The Genericity Theorem and the Notion of Parametricity in the Polymorphic λ-calculus

This paper focuses on how terms of second order λ-calculus, which may take types as inputs, depend on types. These terms are generally understood to have an “essentially” constant meaning, in all models, on input types. We show how the proof theory of second order λ-calculus suggests a clear syntactic description of this phenomenon. Namely, under a reasonable condition, we show that identity of two polymorphic functions on a single type implies identity of the functions (equivalently, every type is a generic input).