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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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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
A presentation of the CurryHoward Correspondance.
, 1997
"... These notes are extracted from the rst version of the paper iFrom Computation to Foundations: the calculus and its webbed modelsj. They nearly disappeared in the revised version of that paper, and we make them available separately. 0.1 calculus as a foundation for Programming Theory. calculu ..."
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These notes are extracted from the rst version of the paper iFrom Computation to Foundations: the calculus and its webbed modelsj. They nearly disappeared in the revised version of that paper, and we make them available separately. 0.1 calculus as a foundation for Programming Theory. calculus came back to the front of the scene in the sixties with the development of Computer Science, under the impulse of Landin [21] and Backus (cf. [1]) and generated the family of functional languages (Lisp [McCarthy 1960], Haskell, Miranda, ML, Caml, ...). In functional languages functions and functionals may be passed as arguments to a program as easily as concrete datas, which is not the case with imperative languages (Fortran, Pascal, C ) (the other conceptual dioeerences between imperative programming (founded by Von Neumann) and functional programming are clearly explained e.g. in the rst pages of [1]). See barendregt's survey [2]: The other main conceptual contribution of calculus to P...