Parametric polymorphism and operational equivalence

Abstract Studies of the mathematical properties of impredicatively polymorphic types have for the most part focused on the polymorphic lambda calculus of Girard-Reynolds, which is a calculus of total polymorphic functions. This paper considers polymorphic types from a functional programming perspective, where the partialness arising from the presence of fixpoint recursion complicates the nature of potentially infinite (‘lazy’) datatypes. An operationally-based approach to Reynolds' notion of relational parametricity is developed for an extension of Plotkin's PCF with ∀types and lazy lists. The resulting logical relation is shown to be a useful tool for proving properties of polymorphic types up to a notion of operational equivalence based on Morris-style contextual equivalence.

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