Proofs and types
A framework for defining logics
Journal of the ACM (JACM)
Handbook of logic in computer science (vol. 2)
Formal parametric polymorphism
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
TACS '91 Proceedings of the International Conference on Theoretical Aspects of Computer Software
A Logic for Parametric Polymorphism
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
A Model for Formal Parametric Polymorphism: A PER Interpretation for System R
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Axiomatic criteria for quotients and subobjects for higher-order data types
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
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Plotkin and Abadi have proposed a syntactic system for parametricity based on a second order predicate logic. This paper shows three theorems about that system. The first is consistency of the system, which is proved by the method of relativization. The second is that polyadic parametricities of recursive types are equivalent to each other. The third is that the theory of parametricity for recursive types is self-realizable. As a corollary of the third theorem, the theory of parametricity for recursive types satisfies the term extraction property.