Parametricity as Subtyping (preliminary Report)

A polymorphic function is parametric if it has uniform behavior for all type parameters. This property is useful when writing, reasoning about, and compiling functional programs. We show how to syntactically deene and reason about parametricity in a language with intersection types and bounded polymorphism. Within this framework, parametricity is subtyping, and reasoning about para-metricity becomes reasoning about the well-typedness of terms. This work also demonstrates the expressive-ness of languages that combine intersection types and bounded polymorphism.