Reynolds, John C. 1974b. Towards a Theory of Type Structure. Pages 408--423 of: Colloq. sur la Programmation. Lecture Notes in Computer Science, vol. 19. Springer-Verlag.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of Pure Type Systems is a generalization of the theory of the cube. Because the cube is easier to understand than the theory of PTSs we start with introducing the cube. The cube The cube is a generalization of a set of eight type systems including the well known systems [5] 6] 2 [7][18], 7] and C [19] We give a short description of these four systems below. The system is the basis of all type systems for functional programming. In this system it is possible to define terms that depend on other terms, for instance M j n : n with M : We call M a term depending on ....

J. C. Reynolds. Towards a theory of type structure. Lecture Notes in Computer Science, 19:157--168, 1974. In Paris Programming Symposium.

.... predicative universes Type i can be viewed as set universes; the non propositional types in predicative universes represent sets (or data types) This is in contrast with the view of coding of data types [BB85] in an impredicative type system like Girard Reynold s polymorphic calculus [Gir72, Rey74] or the calculus of constructions [CH88] These predicative universes are supposed to be open in the sense as Martin Lof explains for his type theory [ML75, ML84] For example, the type of natural numbers can be introduced by adding constants N : Type 0 , 0 : N and succ : N N , and a recursion ....

J.C. Reynolds. Towards a theory of type structure. Lecture Notes in Computer Science, 19, 1974.

....the semantics of Quest s progenitor system, Bounded Fun (with coercions) was first given. 3. 1 Semantics of kinds and types The key idea in the underlying mathematical construction is to use a set theoretic approach where the addition of some effectiveness prevents the difficulties discussed in [Reynolds 84] In this regard, the blend of set theoretic intuition and elementary computability provides a simple but robust guideline for the interpretation of programming constructs. The construction is based on Kleene s applicative structure (w, where w is the set of natural numbers, together with a ....

J C.Reynolds: Polymorphism is not set-theoretic, Symposium on Semantics of Data Types (Kahn, MacQueen, and Plotkin eds.) Lecture Notes in Computer Science 173, Springer-Verlag, 1984, pp. 145-156.

....the semantics of Quest s progenitor system, Bounded Fun (with coercions) was first given. 3. 1 Semantics of kinds and types The key idea in the underlying mathematical construction is to use a set theoretic approach where the addition of some effectiveness prevents the difficulties discussed in [Reynolds 84] In this regard, the blend of set theoretic intuition and elementary computability provides a simple but robust guideline for the interpretation of programming constructs. The construction is based on Kleene s applicative structure (w, where w is the set of natural numbers, together with a ....

J C.Reynolds: Polymorphism is not set-theoretic, Symposium on Semantics of Data Types (Kahn, MacQueen, and Plotkin eds.) Lecture Notes in Computer Science 173, SpringerVerlag, 1984, pp. 145-156. Page 50

....is explicit rather than implicit . In other words, type variables, instead of being implicitly quantified (by an external, metalinguistic universal quantifier) are explicitly quantified by a linguistic, second order quantifier, as in second order calculus of Girard and Reynolds [Gir72, Rey74] moreover bounds can be imposed on the quantified type variables obtaining in this way the so called Bounded Quantification. The approach of bounded quantification, which originated in [CW85] by the definition of the language Fun, explicitly blends polymorphism and subtyping by allowing bounds ....

J.C. Reynolds. Towards a theory of type structures. Lecture Notes in Computer Science, 19:408--425, 1974.

....is explicit rather than implicit . In other words, type variables, instead of being implicitly quantified (by an external, metalinguistic universal quantifier) are explicitly quantified by a linguistic, second order quantifier, as in second order calculus of Girard and Reynolds [Gir72, Rey74] moreover bounds can be imposed on the quantified type variables obtaining in this way the so called Bounded Quantification. The approach of bounded quantification, which originated in [CW85] by the definition of the language Fun, explicitly blends polymorphism and subtyping by allowing bounds ....

J.C. Reynolds. Towards a theory of type structures. Lecture Notes in Computer Science, 19:408--425, 1974.

....the above analysis. We can generalise from set theoretic models of a language to models in an arbitrary cartesian closed category. We can then take our relations in an arbitrary category too, with a little extra data and conditions, this category generalising the category of binary relations, cf [8]. Also, we can extend from the simply typed calculus to other languages, for instance incorporating coproducts. In general, our notion of lax logical relation extends to any language extending the simply typed calculus and given by algebraic structure, in a sense we shall make precise. In the ....

....size) We generalise Rel and (ffi 0 ; ffi 1 ) Rel Gamma Set Theta Set to a small category E with finite products together with a strict finite product preserving functor (ffi 0 ; ffi 1 ) E Gamma C Theta C. This is in the same spirit as Ma and Reynolds account of logical relations in [8]. To generalise the notion of composition of relations, we have a functor comp : E Theta C E Gamma E strictly preserving finite products, where E Theta C E is the pullback E Theta C E fl 1 E E fl 0 ffi 1 C ffi 0 in the category Cat and ffi 0 comp = ffi 0 fl 0 ffi 1 comp = ffi 1 ....

Q. Ma and J.C. Reynolds, Types, abstraction and parametric polymorphism 2, Math. Found. of Prog. Lang. Sem. Lecture Notes in Computer Science, Springer (1991).

....2 : int hd [ aa , bb ] val it = aa : string tl [2,3,4,5] val it = 3,4,5] int list tl [ aa , bb ] val it = bb ] string list hd [ 2,3,4] 3] val it = 2,3,4] int list tl [ 2,3,4] 3] val it = 3] int list list 2.2. 1 Second order Lambda Calculus System F [Gir72, GLT89, Rey74] enables us to treat parametric polymorphic functions as firstorder objects. A parametric polymorphic function is also characterized in a model as a function which preserves all the relations between all the types. To explain it in more detail, suppose that F (t) G(t) is a type of a polymorphic ....

Reynolds, J. C., Towards a theory of type structures. Lecture Notes in Computer Science, 19, pp. 408--425, 1974.

....the semantics of Quest s progenitor system, Bounded Fun (with coercions) was first given. 3. 1 Semantics of kinds and types The key idea in the underlying mathematical construction is to use a settheoretic approach where the addition of some effectiveness prevents the difficulties discussed in [Reynolds 84] In this regard, the blend of set theoretic intuition and elementary computability provides a simple but robust guideline for the interpretation of programming constructs. The construction is based on Kleene s applicative structure (w, where w is the set of natural numbers, together with a ....

J C.Reynolds: Polymorphism is not set-theoretic, Symposium on Semantics of Data Types (Kahn, MacQueen, and Plotkin eds.) Lecture Notes in Computer Science 173, Springer-Verlag, 1984, pp. 145-156.

No context found.

Reynolds, John C. 1974b. Towards a Theory of Type Structure. Pages 408--423 of: Colloq. sur la Programmation. Lecture Notes in Computer Science, vol. 19. Springer-Verlag.

No context found.

Reynolds, John C. 1974b. Towards a Theory of Type Structure. Pages 408--423 of: Colloq. sur la Programmation. Lecture Notes in Computer Science, vol. 19. Springer-Verlag.

No context found.

J.C.Reynolds, Towards a theory of type structure, Lecture Notes in Computer Science 19, 408--423, 1972.

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