This paper focuses on how terms of the polymorphic λ-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 the proof theory of polymorphic λ-calculus suggests a clear syntactic description of this phenomenon. Namely, under a reasonable condition, we show that if two polymorphic functions agree on a single type, then they agree on all types (equivalently, types are generic inputs).