K. B. Bruce, A. R. Meyer: The Semantics of Second Order Polymorphic Lambda Calculus, in G. Kahn, D. B. MacQueen, G. Plotkin (Eds.): Semantics of Data Types, Springer LNCS 173, 1984, 131-144  Home/Search   Document Not in Database   Summary   Related Articles   Check

....that can be de ned and used in schema de nitions. In this paper, we consider three di erent type systems which are a simple type system with set semantics, 3 the typed calculus with a semantics given by cartesian closed categories, and a slightly extended version of Girard Reynolds polymorphism [17, 43, 51]. For the third case it is well known that there is no set theoretic semantics, but suitable semantics can be obtained in the e ective topos [35, 33, 53] or even in Grothendieck topoi [50] Moreover, we may always ask how good a model is with respect to computational aspects. Here again it may be ....

K. B. Bruce, A. R. Meyer: The Semantics of Second Order Polymorphic Lambda Calculus, in G. Kahn, D. B. MacQueen, G. Plotkin (Eds.): Semantics of Data Types, Springer LNCS 173, 1984, 131-144

....many sorted in nitary logic, but in this case a type would be just a sort in L interpreted by a set. This is not in accordance with any established approach to type theory in computer science [7, 9, 15, 23] In particular, it can be hardly combined with approaches to type theory based on calculi [4, 15, 17]. Fortunately, L 1 is not the only logic that assures the existence of predicate transformers as a basis for axiomatic semantics. An alternative is higher order intuitionistic logic [8] or in nitary coherent logic [12] The existence proof for predicate transformers in these logics is ....

K. B. Bruce, A. R. Meyer: The Semantics of Second Order Polymorphic Lambda Calculus, in G. Kahn, D. B. MacQueen, G. Plotkin (Eds.): Semantics of Data Types, Springer LNCS 173, 1984, pp. 131-144

....concerns the semantics of the type system, i.e. the variety of types that can be de ned and used in schema de nitions. We consider three di erent approaches based on a simple type system with set semantics, the typed calculus and a slightly extended version of Girard Reynolds polymorphism [17, 42, 48]. For the third case it is well known that there is no set theoretic model. In this case, however, suitable models can be obtained in the e ective topos [34, 32, 50] or even in Grothendieck topoi [47] Moreover, we may always ask how good a model is with respect to computational aspects. Here ....

K. B. Bruce, A. R. Meyer: The Semantics of Second Order Polymorphic Lambda Calculus , in G. Kahn, D. B. MacQueen, G. Plotkin (Eds.): Semantics of Data Types , Springer LNCS 173, 1984, 131-144

.... [Rezus 85] Relevant languages have been proposed such as Russell [Boehm 80] and Pebble [Burstall 84] Relevant formal systems have been widely studied; they include intuitionistic logic and type theory [Scott 70] Martin Lf 80] second order lambda calculus [Girard 72] Reynolds 74] Fortune 83] Bruce 84] Automath [de Bruijn 80] Barendregt 83] the theory of constructions [Coquand 85a, 85b] the foundations of Russell [Hook 84] Donahue 85] and a calculus with Type:Type [Meyer 86] Somehow, a clear connection between these ideas, from the programming language point of view, was missing. For ....

K.B.Bruce, R.Meyer: The semantics of second order polymorphic lambda calculus, in Semantics of Data Types, Lecture Notes in Computer Science 173, Springer-Verlag, 1984.

....than ML s [Coppo 80] although the type system is undecidable. The ideal model of types [MacQueen 84] is the model which more directly embodies the idea of implicit polymorphic types, and has its roots in Scott, and in Milner s original paper. Explicit polymorphism has also its own story, see [Bruce 84] for an extensive treatment and references, and [Cardelli 86] for examples. The relations between implicit and explicit polymorphism are actively being investigated, see for example [McCracken 84] Page 4 Pragmatic motivation Parametric polymorphic type systems share with Algol 68 properties ....

K.B.Bruce, R.Meyer: The semantics of second order polymorphic lambda calculus, in Semantics of Data Types, Lecture Notes in Computer Science 173, SpringerVerlag, 1984. Also to appear under the same title together with J.C.Mitchell.

....In view of this intuitive appeal, we have chosen the ideal model as our underlying view of types, but much of our discussion could be carried over, and sometimes even improved, if we chose to refer to other models. The idea of types as parameters is fully developed in the second order l calculus [Bruce 84] The (only known) denotational models the second order l calculus are retract models [Scott 76] Here, types are not sets of objects but special functions (called retracts) these can be interpreted as identifying sets of objects, but are objects themselves. Because of the property that types ....

K.B.Bruce, R.Meyer: The semantics of second order polymorphic lambda calculus, in Sematics of Data Types, G.Kahn, D.B.MacQueen and G.Plotkin Ed. Lecture Notes in Computer Science 173, Springer-Verlag, 1984.

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K.B.Bruce, R.Meyer: The semantics of second order polymorphic lambda calculus, in Semantics of Data Types, Lecture Notes in Computer Science 173, Springer-Verlag, 1984.

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