J-Y.Girard: Une extension de l'interprtation de Gdel l'analyse, et son application l'limination des coupures dans l'analyse et la thorie des types, Proceedings of the second Scandinavian logic symposium, J.E.Fenstad Ed. pp. 63-92, North-Holland, 1971.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... operators, such as function spaces and cartesian products, but very few languages allow new operators to be defined, or restrict them to first order (types to types) Higher order operators embody a surprising expressive power; they define one of the largest known classes of total functions [Girard 71] and every free algebra with total operations (booleans, integers, lists, trees, etc. is uniformly representable in them [Bhm Berarducci 85] see the example below for booleans) Because of this, we believe they will turn out to be very useful for parametrization and for carrying out ....

....of List(A) with head tail end; The other basic list operations are left as an exercise. Go look at the List library interface; it is an existential type containing an operator. 7. Power kinds Most of the quantifier and operator structure described so far derives from Girard s system Fw [Girard 71] The main new fundamental notion in Quest is the integration of subtyping with type quantification. This allows us to express more directly a wider range of programming situations and programming language features, as well as to introduce new ones. In this section we define a subtyping relation ....

J-Y.Girard: Une extension de l'interprtation de Gdel l'analyse, et son application l'limination des coupures dans l'analyse et la thorie des types, Proceedings of the second Scandinavian logic symposium, J.E.Fenstad Ed. pp. 63-92, North-Holland, 1971.

....lc: x:A. B(x) let x,y = c in y : A. B: AType. c: x:A. B(x) B(lft(A) B) c) 6. 11 Data abstraction Following Mitchell and Plotkin [Mitchell 85] it is possible to treat abstract types as existential types, given operators for building and examining objects of existential types [Girard 71] We consider here a pack operator, which packages an object so that it has an existential type (and hides some type information which is usually interpreted as the representation of the abstract type) and an open operator, which allows one to open and use a package without getting access to the ....

J-Y.Girard: Une extension de l'interprtation de Gdel l'analyse, et son application l'limination des coupures dans l'analyse et la thorie des types, Proceedings of the second Scandinavian logic symposium, J.E.Fenstad Ed. pp. 63-92, North-Holland, 1971.

....coproducts; well pointedness 4.2.1 Terminal objects 4.2.2 Binary products 4.2.3 Initial objects 4.2.4 Binary coproducts 4.2.5 Well pointedness 4.3 CL isomorphisms 4.3.1 Double negation 4.3.2 Existentials 4.3.3 Other cl isomorphisms Acknowledgments References Page 3 1. Introduction System F [Gir 71] Rey 74] is a well known typed l calculus with polymorphic types that provides a basis for polymorphic programming languages. We study an extension of F that combines parametric polymorphism [Str 67] with subtyping. We call this language F : where : is our symbol for the subtype relation. F ....

....typing over F, a set of examples in section 3 demonstrating the expressiveness of F : some reported earlier in [CL 90] and in [Ghe 90] with attribution) and in section 4 some categorical properties of the theory when restricted to closed terms. 2. System F : F : is obtained by extending F [Gir 71] Rey 74] see Appendix) with a notion of subtyping ( This extension allows us to remain within a pure calculus. That is, we introduce neither the basic types, nor the structured types, normally associated with subtyping in programming languages. Instead, we show that these programming types ....

J-Y.Girard: Une extension de l'interprtation de Gdel l'analyse, et son application l'limination des coupures dans l'analyse et la thorie des types, Proceedings of the second Scandinavian logic symposium, J.E.Fenstad Ed. pp. 63-92, North-Holland, 1971.

....coproducts; well pointedness 4.2.1 Terminal objects 4.2.2 Binary products 4.2.3 Initial objects 4.2.4 Binary coproducts 4.2.5 Well pointedness 4.3 CL isomorphisms 4.3.1 Double negation 4.3.2 Existentials 4.3.3 Other cl isomorphisms Acknowledgments References Page 3 1. Introduction System F [Gir 71] Rey 74] is a well known typed l calculus with polymorphic types that provides a basis for polymorphic programming languages. We study an extension of F that combines parametric polymorphism [Str 67] with subtyping. We call this language F : where : is our symbol for the subtype ....

....over F, a set of examples in section 3 demonstrating the expressiveness of F : some reported earlier in [CL 90] and in [Ghe 90] with attribution) and in section 4 some categorical properties of the theory when restricted to closed terms. 2. System F : F : is obtained by extending F [Gir 71] Rey 74] see Appendix) with a notion of subtyping ( This extension allows us to remain within a pure calculus. That is, we introduce neither the basic types, nor the structured types, normally associated with subtyping in programming languages. Instead, we show that these programming types ....

J-Y.Girard: Une extension de l'interprtation de Gdel l'analyse, et son application l'limination des coupures dans l'analyse et la thorie des types, Proceedings of the second Scandinavian logic symposium, J.E.Fenstad Ed. pp. 63-92, North-Holland, 1971.

....identifiers, except other interfaces) they can be used as units of compilation. 2.2. Theory and practice The conceptual framework for typeful programming is to be found in various theories of typed l calculi [Reynolds 74] Martin Lf 80] in particular, we were inspired by Girard s system Fw [Girard 71] and by the theory of Constructions [Coquand Huet 85] Hyland Pitts 87] This collection of theories, generically referred to as type theory, studies very expressive type structures in the framework of constructive logic. More often than not, these theoretical structures have direct ....

.... operators, such as function spaces and cartesian products, but very few languages allow new operators to be defined, or restrict them to first order (types to types) Higher order operators embody a surprising expressive power; they define one of the largest known classes of total functions [Girard 71] and every free algebra with total operations (booleans, integers, lists, trees, etc. is uniformly representable in them [Bhm Berarducci 85] see the example below for booleans) Because of this, we believe they will turn out to be very useful for parametrization and for carrying out ....

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J-Y.Girard: Une extension de l'interprtation de Gdel l'analyse, et son application l'limination des coupures dans l'analyse et la thorie des types, Proceedings of the second Scandinavian logic symposium, J.E.Fenstad Ed. pp. 63-92, North-Holland, 1971.

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J-Y.Girard: Une extension de l'interprtation de Gdel l'analyse, et son application l'limination des coupures dans l'analyse et la thorie des types, Proceedings of the second Scandinavian logic symposium, J.E.Fenstad Ed. pp. 63-92, North-Holland, 1971.

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J-Y.Girard: Une extension de l'interprtation de Gdel l'analyse, et son application l'limination des coupures dans l'analyse et la thorie des types, Proceedings of the second Scandinavian logic symposium, J.E.Fenstad Ed. pp. 63-92, North-Holland, 1971.

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J.-Y.Girard: Une extension de l'interprtation de Gdel l'analyse, et son application l'limination des coupures dans l'analyse et la thorie des types, Proceedings of the second Scandinavian logic symposium, J.E.Fenstad Ed. pp. 63-92, North-Holland, 1971.

No context found.

J-Y.Girard: Une extension de l'interprtation de Gdel a l'analyse, et son application l'limination des coupures dans l'analyse et la thorie des types, Proceedings of the second Scandinavian logic symposium, J.E.Fenstad Ed. pp. 63-92, North-Holland, 1971.

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