Formal parametric polymorphism
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
Full abstraction for idealized Algol with passive expressions
Theoretical Computer Science - Special issue on linear logic, 1
On full abstraction for PCF: I, II, and III
Information and Computation
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A Logic for Parametric Polymorphism
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Towards a theory of type structure
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Full abstraction for functional languages with control
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Parametricity as a notion of uniformity in reflexive graphs
Parametricity as a notion of uniformity in reflexive graphs
Evolving games and essential nets for affine polymorphism
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
A game semantics for generic polymorphism
FOSSACS'03/ETAPS'03 Proceedings of the 6th International conference on Foundations of Software Science and Computation Structures and joint European conference on Theory and practice of software
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Curry-style system F, that is, system F with no explicit types in terms, may be viewed as a core presentation of polymorphism from the point of view of programming languages. This paper gives a characterisation of type isomorphisms for this language using a game model, whose intuitions come from both the syntax and the game semantics universe. The model is composed of an untyped part to interpret terms, a notion of arena to interpret types and a typed part to express the fact that an untyped strategy σ plays on an arena A. By analysing isomorphisms in the model, we prove that the equational system corresponding to type isomorphisms for Curry-style system F is the extension of the equational system for Church-style isomorphisms with a new, non-trivial equation: ∀X.AA[∀Y.Y/X] if X appears only positively in A.