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Curry-style type isomorphisms and game semantics

Published online by Cambridge University Press:  01 August 2008

JOACHIM DE LATAILLADE
JOACHIM DE LATAILLADE*
Affiliation:
Laboratory Preuves Programmes Systèmes, CNRS – Paris 7 and 9–90 West Prestland Road – Ottawa, ON K1K 2C3 – Canada Email: delatail@pps.jussieu.fr
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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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Type
Paper
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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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