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Curry-style type isomorphisms and game semantics
Published online by Cambridge University Press: 01 August 2008
Abstract
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.
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- Paper
- Information
- Mathematical Structures in Computer Science , Volume 18 , Special Issue 4: Isomorphisms of types and invertibility of lambda terms , August 2008 , pp. 647 - 692
- Copyright
- Copyright © Cambridge University Press 2008
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