A. Simpson, Categorical completeness results for the simply-typed - calculus, in : M. Dezani-Ciancaglini and G. Plotkin eds., Lecture Notes in Computer Science vol. 902, TLCA'95, p.414-427, Springer Verlag, Berlin, 1995. Home/Search Document Not in Database Summary Related Articles Check |
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Building continuous webbed models for System F - Berardi, Berline (1998) (1 citation) (Correct)
....but is not extensional. The interest of trying to answer this latter conjecture is that, whatever the answer will be, it will force us to better understand completeness, and hopefully to nd less technical conditions than the ones which are proposed in [5] in the same sense that Simpson s paper [33] is a progress w.r.t. Friedman s one [13] 5.1 The square models. Denition 6 A square model is a webbed model of the form( Omega ; m; m; j; j) where M : Omega ; m; j) is a reAEexive prime web. A necessary and suOEcient condition for a reAEexive prime web M to give rise to a ....
A. Simpson, Categorical completeness results for the simply-typed - calculus, in : M. Dezani-Ciancaglini and G. Plotkin eds., Lecture Notes in Computer Science vol. 902, TLCA'95, p.414-427, Springer Verlag, Berlin, 1995.
βη-complete models for system F - Berardi, Berline (1999) (Correct)
....if and only if it equates only fij convertible terms. The trivial examples of fij complete models are the fij term models. The term model of System F was the only complete model of F known up to now. For typed calculus, the problem has been tackled by H. Friedman [14] and then A. Simpson [27]) for the simply typed calculus (see below) Concerning untyped calculus, the problem of nding a non syntactical complete model has only been solved recently, by Di Gianantonio, Honsell, Plotkin [12] several interesting related questions being however left open by their result and proof (see ....
....variables are in fact a (trivial) example of ivery genericj maps. In Friedman s proof, full models distinguish between non convertible terms by applying them to ivery genericj maps, built by the Axiom of Choice (of Set Theory) Another possibility for having completeness was discovered by Simpson [27], by building over a syntactic result of Statman [30] Simpson proved that all models of simply typed calculus, which include integers in the base type, and sum and product over such integers, are complete. In this case, the completeness uses as starting point a strong property of sum and ....
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A. Simpson, Categorical completeness results for the simply-typed - calculus, in : M. Dezani-Ciancaglini and G. Plotkin eds., Lecture Notes in Computer Science vol. 902, TLCA'95, p.414-427, Springer Verlag, Berlin, 1995.
βη-complete models for system F - Berardi, Berline (1998) (Correct)
....And variables are in fact a (trivial) example of very generic maps. In Friedman s proof, full models distinguish between non convertible terms by applying them to very generic maps, built by the Choice Axiom of Set Theory. Another possibility for having completeness was discovered by Simpson [27], by building over a syntactic result of Statman [30] Simpson proved that all models including integers in the base type, and sum and product over such integers, are complete. In this case, the completeness uses as starting point a strong property of sum and product: using them, one can encode ....
....since our proof relies on some kinds of logical relations, which, as usual logical relations, do not allow to distinguish elements with the same applicative behavior. The question of finding a fi complete model for F is hence still open, and we propose in [7] a simple candidate. ffl Simpson [27] proved completeness for all models of simply typed calculus including integers, sum and product, by proving they are complete for terms of type T (where T is the type of binary trees) Then he used a result of Statman [30] for deducing completeness at every type. We do not know if this may ....
A. Simpson, Categorical completeness results for the simply-typed - calculus, in : M. Dezani-Ciancaglini and G. Plotkin eds., Lecture Notes in Computer Science vol. 902, TLCA'95, p.414-427, Springer Verlag, Berlin, 1995.
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