J. Lambek. From lambda calculus to Cartesian closed categories. In J. P. Seldin and J. Hindley, editors, To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, pages 376--402. Academic Press, 1980. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Retrieving Library Functions By Unifying Types Modulo Linear.. - Rittri (1992) (13 citations) (Correct)
....(or arrows) between types, and a notion of type isomorphism. Some categories can be seen as models for various versions of calculus; the most well known are the Cartesian closed categories, or CCCs. We do not have to define the CCCisomorphism in a categorical way; we can use a result by Lambek [11] instead: two types A and B are isomorphic in all Cartesian closed categories if, and only if, there are expressions f : A B and g : B A such that the equalities g ffi f = id A and f ffi g = id B hold in simply typed fij calculus with surjective pairing. I write this as A AE B or f A AE B: ....
J. Lambek. From lambda calculus to Cartesian closed categories. In J. P. Seldin and J. Hindley, editors, To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, pages 376--402. Academic Press, 1980.
Kripke-Style Models for Typed Lambda Calculus - Mitchell, Moggi (1996) (39 citations) (Correct)
....to provide a completeness theorem. Since categorical logic is essentially intuitionistic, the equivalence between typed lambda theories (de ned using the traditional axiom system) and arbitrary cartesian closed categories could be considered an intuitionistic completeness theorem (see, e.g. [Fou77, Lam80, LS86]) However, we prefer the completeness theorem using only Kripke models for several reasons. For one, Kripke models are relatively easy to picture, and they seem to support a set like intuition about the lambda terms better than arbitrary cartesian closed categories. In addition, predicate logic ....
J. Lambek. From lambda calculus to cartesian closed categories. In To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, pages 375-402, Academic Press, 1980.
On The Equivalence between CM-C and TIM - Lins, Thompson (1992) (4 citations) (Correct)
....a rewriting law. In rewriting a combinator expression, Turner rewrites the leftmost outermost reducible subexpression (or redex) at each stage. When no further rewriting can take place the expression is said to be in normal form. Another theory of functions is provided by Category Theory [4], and we can see the notation used herein as providing an alternative set of combinators. The original system of Categorical Combinators was developed by Curien [1] This work was inspired by the equivalence of the theories of typed calculus and Cartesian Closed Categories as shown by Lambek ....
....[4] and we can see the notation used herein as providing an alternative set of combinators. The original system of Categorical Combinators was developed by Curien [1] This work was inspired by the equivalence of the theories of typed calculus and Cartesian Closed Categories as shown by Lambek [4] and Scott [15] Aiming to implement lazy functional languages in an efficient way using rewriting of Categorical Combinators we developed a number of optimisations [5, 7] of the naive system, the most refined of which was the system of Linear Categorical Combinators [7] The modifications ....
J.Lambek. From lambda-calculus to cartesian closed categories. In J.P.Seldin and J.R.Hindley, editors, in To H.B.Curry: Essays on Combinatory Logic, Lambda-Calculus and Formalism. Academic Press, 1980.
Implementing SASL using Categorical Multi-Combinators - Lins, Thompson (1990) (Correct)
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J.Lambek, `From lambda-calculus to cartesian closed categories', in J.P.Seldin and J.R.Hindley (eds), To H.B.Curry: Essays on Combinatory Logic, Lambda-Calculus and Formalism, Academic Press, 1980.
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