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Mathematical Structures in Computer Science 12 (2002) 823-874

Beta-eta-complete models for System F

Stefano Berardi 1, Chantal Berline 2

(2002)

We show that Friedman's proof of the existence of non-trivial beta-eta-complete models of the simply typed lambda-calculus can be extended to System F. We isolate a set of conditions which are sufficient to ensure beta-eta-completeness for a model of F (and alpha-completeness at the level of types), and we discuss which class of models we get. In particular, the model introduced by Barbanera and Berardi, having as polymorphic maps exactly all possible Scott continuous maps, is beta-eta-complete and hence is the first known complete nonsyntactical model of F. In order to have a suitable framework in which to express the conditions and develop the proof, we also introduce the very natural notion of "polymax models" of System F.

1 :	Dipartimento di Informatica [Torino]
	Università di Torino
2 :	Preuves, Programmes et Systèmes (PPS)
	CNRS : UMR7126 – Université Paris VII - Paris Diderot

Domaine

:

Mathématiques/Logique

Mots Clés : polymorphism – lambda-calculus – completeness – polymax models

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Contributeur : Chantal Berline <>

Soumis le : Lundi 3 Janvier 2005, 13:22:02

Dernière modification le : Lundi 3 Janvier 2005, 14:19:46