The genericity theorem and parametricity in the polymorphic A-calculus

Longo, G., K. M&ted and S. Soloviev, The genericity theorem and parametricity in the polymorphic I-calculus, Theoretical Computer Science 121 (1993) 323-349. This paper focuses on how terms of the polymorphic I-calculus, which may take types as inputs, depend on types. These terms are generally understood, in all models, to have an “essentially” constant meaning on input types. We show how the proof theory of polymorphic I.-calculus suggests a clear syntactic description of this phenomenon. Namely, under a reasonable conditon, we show that if two polymorphic functions agree on a single type, then they agree on all types (equivalently, types are generic inputs).