Polymorphic Contracts

Manifest contracts track precise properties by refining types with predicates—e.g., {x :Int | x > 0} denotes the positive integers. Contracts and polymorphism make a natural combination: programmers can give strong contracts to abstract types, precisely stating preand post-conditions while hiding implementation details—for example, an abstract type of stacks might specify that the pop operation has input type {x :α Stack | not (empty x )}. We formalize this combination by defining FH, a polymorphic calculus with manifest contracts, and establishing fundamental properties including type soundness and relational parametricity. Our development relies on a significant technical improvement over earlier presentations of contracts: instead of introducing a denotational model to break a problematic circularity between typing, subtyping, and evaluation, we develop the metatheory of contracts in a completely syntactic fashion, omitting subtyping from the core system and recovering it post facto as a derived property.