Classical Combinatory Logic

Combinatory logic shows that bound variables can be eliminated without loss of expressiveness. It has applications both in the foundations of mathematics and in the implementation of functional programming languages. The original combinatory calculus corresponds to minimal implicative logic written...

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Bibliographic Details
Published in:	Discrete mathematics and theoretical computer science Vol. DMTCS Proceedings vol. AF,...; no. Proceedings; pp. 87 - 96
Main Author:	Nour, Karim
Format:	Journal Article Conference Proceeding
Language:	English
Published:	DMTCS 01.01.2005 Discrete Mathematics and Theoretical Computer Science Discrete Mathematics & Theoretical Computer Science
Series:	DMTCS Proceedings
Subjects:	[info.info-lo] computer science [cs]/logic in computer science [cs.lo] [info.info-sc] computer science [cs]/symbolic computation [cs.sc] combinatory logic Computer Science lambda-calculus Logic in Computer Science propositional classical logic Symbolic Computation Combinatory logic Propositional classical logic Lambda-calculus
ISSN:	1365-8050, 1462-7264, 1365-8050
Online Access:	Get full text
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Summary:	Combinatory logic shows that bound variables can be eliminated without loss of expressiveness. It has applications both in the foundations of mathematics and in the implementation of functional programming languages. The original combinatory calculus corresponds to minimal implicative logic written in a system "à la Hilbert''. We present in this paper a combinatory logic which corresponds to propositional classical logic. This system is equivalent to the system $λ ^{Sym}_{Prop}$ of Barbanera and Berardi.
ISSN:	1365-8050 1462-7264 1365-8050
DOI:	10.46298/dmtcs.3469