A. Church. A set of postulates for the foundation of logic. Annals of Math. (2), 33:346--366, 1932.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....doctrines of classes is that they are there from the beginning . So, even for Poincar e there should be no evident fallacy in impredicative de nitions. The derami cation has played an important role in the development of type theory. In 1932 and 1933, Church presented his (untyped) calculus [12, 13]. In 1940 he combined this theory with a derami ed version of Russell s theory of types to the system that is known as the simply typed calculus . 5 The Simple Theory of Types 5.1 Constructing the Simple Theory of Types stt from rtt So far, we have seen the development of type theory ....

A. Church. A set of postulates for the foundation of logic (2). Annals of Mathematics, 34:839-864, 1933.

....and that Church had answered that there was no particular reason for choosing , that some letter was needed and happened to have been chosen. Moreover, Curry had told him that Church had a manuscript in which there were many occurrences of already in 1929, so three years before the paper [12] appeared. In modern terminology, we could say that the functions (x) and (x) have the same course of values if they have the same graph. Frege did not provide a satisfying intuition for the formal notion of courseof values of a function. He treated courses of values as ordinary objects. As a ....

....doctrines of classes is that they are there from the beginning . So, even for Poincar e there should be no evident fallacy in impredicative de nitions. The derami cation has played an important role in the development of type theory. In 1932 and 1933, Church presented his (untyped) calculus [12, 13]. In 1940 he combined this theory with a derami ed version of Russell s theory of types to the system that is known as the simply typed calculus . 5 The Simple Theory of Types 5.1 Constructing the Simple Theory of Types stt from rtt So far, we have seen the development of type theory ....

A. Church. A set of postulates for the foundation of logic (1). Annals of Mathematics, 33:346-366, 1932.

....and typing, principal type and typing see sections 4 and 5. 7 3 Simple Types Studies about types in programming languages are usually developed under the background of the simply typed calculus. This calculus was defined from the untyped calculus, both defined by Church, in the 1930s [Chu32, Chu36, Chu41] Untyped calculus provides a very simple model of evaluation. Despite this simplicity, calculus is a universal computability model, in the sense that any recursive function [Kle36] as well as any function computable by a Turing [Tur37] can be expressed as a term of the ....

A. Church. A set of postulates for the foundation of logic. Ann. of Math., 33:346--366, 1932.

....and results concerning the lambda calculus and the theory of lambda abstraction algebras. Our main references will be [15] and [17] for lambda abstraction algebras and Barendregt s book [1] for lambda calculus. 1. 1 Lambda calculus The untyped lambda calculus was introduced by Church (Church [4, 5]) as a foundation for logic. Although the appearance of paradoxes caused the program to fail, a consistent part of the theory turned out to be successful as a theory of functions as rules (formalized as terms of the lambda calculus) that stresses the computational process of going from argument ....

Church, A., "A set of postulates for the foundation of logic", Annals of Math., vol. 2 (1933), pp. 346-366.

....with the lambda theory generated by equating all the unsolvable terms. Key words and phrases. Lambda calculus, lambda abstraction algebras, combinatory algebras, lattice of lambda theories, modularity, commutator. 1 Introduction The untyped lambda calculus was introduced by Church [3, 4] as a foundation for logic. Although the appearance of paradoxes caused the program to fail, a consistent part of the theory turned out to be successful as a theory of functions as rules (formalized as terms of the lambda calculus) that stresses the computational process of going from the ....

A. Church, A set of postulates for the foundation of logic. Annals of Math. 2 (1933) 346--366

....is not congruence modular and that the lattice of lambda theories is not modular. Key words and phrases. Lambda calculus, lambda abstraction algebras, combinatory algebras, lattice of lambda theories, modularity, commutator. 1 Introduction The untyped lambda calculus was introduced by Church [3, 4] as a foundation for logic. Although the appearance of paradoxes caused the program to fail, a consistent part of the theory turned out to be successful as a theory of functions as rules (formalized as terms of the lambda calculus) that stresses the computational process of going from the ....

A. Church, A set of postulates for the foundation of logic. Annals of Math. 2 (1933) 346--366

....results concerning the lambda calculus and the theory of lambda abstraction algebras. Our main references will be [35] and [37] for lambda abstraction algebras and Barendregt s book [3] for lambda calculus. 4 ANTONINO SALIBRA Lambda calculus. The untyped lambda calculus was introduced by Church [9, 10] as a foundation for logic. Although the appearance of paradoxes caused the program to fail, a consistent part of the theory turned out to be successful as a theory of functions as rules (formalized as terms of the lambda calculus) that stresses the computational process of going from argument ....

A. Church, A set of postulates for the foundation of logic, Annals of Math. 2 (1933), 346--366.

....holds. Thus, the first purpose of terms was clearly to represent formulae and predicates. 1 Church thought first it would be possible to avoid Russell s paradox without introducing types, but by staying within an intuitionistic logic that use only some limited form of the law of excluded middle [4]. This system was however shown to be inconsistent by his students Kleene and Rosser [16] 1 . Church formulated then an elegant formulation of higher order logic, using simply typed calculus [5] which can be seen as a simplification of the type system used in Principia Mathematica, but also is ....

....for representing consequent portion of mathematics that have found later to result in paradoxes. As we have seen, the first such example was the system of Frege, where the inconsistency was noticed by Russell. The same kind of paradoxes was found later by Curry in a variation of Church s system [4]. The inconsistency found in Church s untyped system was a variant of Richard s paradox. The paradox of Burali Forti was used by Rosser to get an inconsistency in one version of Quine s new foundation system (the consistency of the current version is open) A variation of this paradox can be done ....

A. Church. A Set of Postulates for the Foundation of Logic. Annals of Mathematics, 33 (1932), p. 346-366.

....the first order predicate logic. In this paper a proof is given that the variety of lambda abstraction algebras is not congruence modular. Some simple applications of this result to lambda calculus are also obtained. 1. Introduction The untyped lambda calculus was introduced by Church [3, 4] as a foundation for logic. Although the appearance of paradoxes caused the program to fail, a consistent part of the theory turned out to be successful as a theory of functions as rules (formalized as terms of the lambda calculus) that stresses the computational process of going from the ....

A. Church, A set of postulates for the foundation of logic, Annals of Math. 2 (1933), 346--366.

....for instance in callby name (x. I) Omega and I are semantically the same, whereas in call by value (x. I) Omega is the same as Omega . No characterisation is known of the equivalence on terms induced by the call by value encoding V . 14 Notes The calculus was introduced by Church [Chu32, Chu41] who was hoping to use it, on the one hand, to produce a foundation for logic and mathematics and, on the other hand, to understand mathematically the notion of function. While the rst goal failed, the second one has been a remarkable success. Church (and Kleene, who proved important ....

A. Church. A set of postulates for the foundations of logic. Ann. of Math., 33:346366, 1932.

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A. Church. A set of postulates for the foundation of logic. Annals of Math. (2), 33:346--366, 1932.

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A. Church. A set of postulates for the foundation of logic. Annals of Math. (2), 33:346--366, 1932.

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Alonzo Church, A set of postulates for the foundation of logic. Annals of Mathematics, II.33:346--366, 1932.

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Alonzo Church. A set of postulates for the foundation of logic (second paper). Annals of Mathematics, 34:839-864, 1933.

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Alonzo Church. A set of postulates for the foundation of logic. Annals of Mathematics, 33:346-366, 1932.

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A. Church. A set of postulates for the foundation of logic. In Annals of Mathematics 2, 1932/33.

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A. Church. A Set of Postulates for the Foundation of Logic. . Annals of MATH. , 33:pages 346-366, 1932.

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Alonzo Church. A set of postulates for the foundation of logic (second paper). Annals of Mathematics, 34:839--864, 1933.

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Alonzo Church. A set of postulates for the foundation of logic. Annals of Mathematics, 33:346--366, 1932.

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A. Church. A set of postulates for the foundation of logic (2). Annals of Mathematics, 34:839-864, 1933.

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A. Church. A set of postulates for the foundation of logic (1). Annals of Mathematics, 33:346-366, 1932.

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A. Church, A set of postulates for the foundation of logic (1), Annals of Mathematics, vol. 33 (1932), pp. 346--366.

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A. Church, A set of postulates for the foundation of logic, Annals of Mathematics 33 (1932) 346--366.

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Alonzo Church, 1932. A Set of Postulates for the Foundation of Logic. Annals of Mathematics, Vol. 33, pp. 346--366.

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Church, A., A Set of Postulates for the Foundation of Logic. Annals of Math. 33, 2nd series (1932), pp. 346-366.

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