Results 241 to 250 of about 697,012 (268)

A basis result in combinatory logic

The Journal of Symbolic Logic, 1988
The aim of this article is to show that a basis for combinatory logic [2] must contain at least one combinator with rank strictly greater than two. We use notation of [1]. Let Q be a primitive combinator given by its reduction rule Qx ...
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Combinatory Logic

2011
Preface Elements of combinatory logic Objects, combinators and terms Various kinds of combinators Reductions and combinatory bases Main theorems Church-Rosser property Normal forms and consistency Fixed points Second fixed point theorem and undecidability Recursive functions and arithmetic Primitive and partial recursive functions First modeling of ...
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The combinatory foundations of mathematical logic

Journal of Symbolic Logic, 1942
In investigations of the foundations of mathematics we can distinguish two separate tendencies. On the one hand, one may seek to define his subject with greatest possible explicitness: to obtain a formulation which satisfies the most exacting demands for precision, and which is at the same time free from paradoxes and adequate for the purpose.
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On subrecursiveness in weak combinatory logic

1975
In this paper weak combinatory logic as an algorithmic language is considered and various notions of structural and computational complexity are introduced. Particular attention is devoted to the definitional power of a system of combinators,that is to the concept of “subbase”.
Carlo Batini, Alberto Pettorossi
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Logical Aspects of Combinatorial Duality

Canadian Mathematical Bulletin, 1984
AbstractD. R. Woodall has introduced closely-related notions of Menger and König duals which can be applied to a broad range of combinatorial contexts. The present paper considers these two notions for finite ground sets in terms of syntactic duality principles. Specific graph-theoretic interpretations are cited.
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An abstraction algorithm for combinatory logic

The Journal of Symbolic Logic, 1976
This note presents a practical algorithm for carrying out abstraction on combinatory terms. The well-known abstraction algorithms [1, pp. 188ff.] defining abstracts in terms of the combinator sets { S, K }, {
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The Existence of Combinatory Algebras: Combinatory Logic

1993
If the reader has tried to manufacture a useful example of a combinatory algebra for himself, at some stage he will blame me for doing away, along with type differences with a great deal of mathematical intuition. Indeed in this connection the step from the possible to the contradictory has been made by various mathematicians. From the point of view of
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The search for a reduction in combinatory logic equivalent to λβ-reduction

Theoretical Computer Science, 2011
Jonathan P Seldin
exaly  

OTTER experiments in a system of combinatory logic

Journal of Automated Reasoning, 1995
Thomas Jech
exaly  

Equivalences between Pure Type Systems and Systems of Illative Combinatory Logic

Notre Dame Journal of Formal Logic, 2005
M W Bunder
exaly