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Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
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Cited by 457 (20 self)
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Least fixpoints as meanings of recursive definitions.
βηcomplete models for System F
, 2000
"... We show that Friedman's proof of the existence of nontrivial βηcomplete models of λ→ can be extended to system F. We isolate a set of conditions which are sufficient to ensure βηcompleteness for a model of F (and αcompleteness at the level of types), and we discuss which class ..."
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Cited by 3 (2 self)
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We show that Friedman's proof of the existence of nontrivial βηcomplete models of λ→ can be extended to system F. We isolate a set of conditions which are sufficient to ensure βηcompleteness for a model of F (and αcompleteness at the level of types), and we discuss which class of models we get. In particular, the model introduced in [5], having as polymorphic maps exactly all possible Scott continuous maps, is βηcomplete and is hence the first known complete nonsyntactic model of F. In order to have a suitable framework where to express the conditions and develop the proof, we also introduce the very natural notion of "polymax models" of System F.
Building continuous webbed models for System F
, 2000
"... We present here a large family of concrete models for Girard and Reynolds polymorphism (System F ), in a non categorical setting. The family generalizes the construction of the model of Barbanera and Berardi [2], hence it contains complete models for F [5] and we conjecture that it contains models w ..."
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Cited by 1 (0 self)
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We present here a large family of concrete models for Girard and Reynolds polymorphism (System F ), in a non categorical setting. The family generalizes the construction of the model of Barbanera and Berardi [2], hence it contains complete models for F [5] and we conjecture that it contains models which are complete for F . It also contains simpler models, the simplest of them, E 2 ; being a second order variant of the EngelerPlotkin model E . All the models here belong to the continuous semantics and have underlying prime algebraic domains, all have the maximum number of polymorphic maps. The class contains models which can be viewed as two intertwined compatible webbed models of untyped calculus (in the sense of [8]), but it is much larger than this. Finally many of its models might be read as two intertwined strict intersection type systems. Contents 1
βηcomplete models for System F
, 2000
"... We show that Friedman's proof of the existence of nontrivial βηcomplete models of λ→ can be extended to system F. We isolate a set of conditions which are sufficient to ensure βηcompleteness for a model of F (and αcompleteness at the level of types), and we di ..."
Abstract
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We show that Friedman's proof of the existence of nontrivial βηcomplete models of λ→ can be extended to system F. We isolate a set of conditions which are sufficient to ensure βηcompleteness for a model of F (and αcompleteness at the level of types), and we discuss which class of models we get. In particular, the model introduced in [5], having as polymorphic maps exactly all possible Scott continuous maps, is βηcomplete and is hence the first known complete nonsyntactic model of F. In order to have a suitable framework where to express the conditions and develop the proof, we also introduce the very natural notion of "polymax models" of System F. 1