N. McCracken, A Finitary Retract Model for the Polymorphic -calculus, unpublished, 1984. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Building continuous webbed models for System F - Berardi, Berline (1998) (1 citation) (Correct)
....By contrast many of our models are complete for Fj (cf. Section 6.1) Comparing webbed models with u.r. models. Another interesting connection is the one with universal retraction models or u:r: models, which were introduced, for the continuous semantics, by D. Scott and McCracken in [30] 31] [23] and continued by Amadio Bruce Longo [1] In these models terms are interpreted as elements of a model of the untyped calculus, and types are interpreted by retractions ranging over a suitable class. The word iuniversalj refers to the fact that in these models there is a type of all types. Then ....
....the u:r: models. Univ is the category of Scott domains, or complete lattices in some cases, and continuous functions. First one xes a reAEexive object (M; q; ap) of Univ; namely a model of untyped calculus in this category. Then, we let c 2 M be the code in M of a universal nitary retraction [23], 31] or a universal nitary projection [1] or a universal closure [30] In the stable semantics all retractions are nitary and c can be taken as the code of any 27 universal (stable) retraction [4] The necessary background and the missing proofs below can be found in [6] which surveys the ....
N. McCracken, A Finitary Retract Model for the Polymorphic -calculus, unpublished, 1984.
βη-complete models for system F - Berardi, Berline (1999) (Correct)
....having as polymorphic maps exactly all possible Scott continuous maps, is fij complete. 1 Introduction. In this paper we will progress in the study of non trivial models of the notion of polymorphic maps of System F ( 15] 25] This study was started in Girard [15] Scott [29] and McCracken [19], Reynolds [26] Girard [16] and continued by Amadio Bruce Longo [2] Coquand Gunter Winskel [11] and Berardi [6] Our contribution is to prove that there exists a large class of non trivial fij complete models of F . Essentially, this class consists of models having primitive types for basic ....
....it should be clear that we will not be concerned here with these kinds of models. The rst models with non constant polymorphic maps, that we will call here universal retraction models or u:r: models, were introduced, for the continuous semantics, by D. Scott and McCracken in [28] 2 , 29] [19] and continued by Amadio Bruce Longo [2] In these models, terms are interpreted as elements of a model of the untyped calculus, and types are ranges of (suitable) retractions of the model, and are identied with such retractions. The word iuniversalj refers to the fact that, in these models, ....
N. McCracken, A Finitary Retract Model for the Polymorphic -calculus, unpublished, 1984.
βη-complete models for system F - Berardi, Berline (1998) (Correct)
....It should hence be clear that we will not be concerned here with this kind of models. The first models with non constant polymorphic maps, that we will call here universal retraction models or u:r: models, were introduced, for the continuous semantics, by D. Scott and McCracken in [28] 29] [20] and continued by Amadio Bruce Longo [2] In these models terms are interpreted as elements of a model of the untyped calculus, and types are ranges of a (suitable subclass of) retractions of the model, and identified with such retractions. The word universal refers to the fact that in these ....
N. McCracken, A Finitary Retract Model for the Polymorphic -calculus, unpublished, 1984.
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