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June 2011 A proof-theoretic treatment of λ-reduction with cut-elimination: λ-calculus as a logic programming language
Michael Gabbay
J. Symbolic Logic 76(2): 673-699 (June 2011). DOI: 10.2178/jsl/1305810770

Abstract

We build on an existing a term-sequent logic for the λ-calculus. We formulate a general sequent system that fully integrates αβη-reductions between untyped λ-terms into first order logic.

We prove a cut-elimination result and then offer an application of cut-elimination by giving a notion of uniform proof for λ-terms. We suggest how this allows us to view the calculus of untyped αβ-reductions as a logic programming language (as well as a functional programming language, as it is traditionally seen).

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Michael Gabbay. "A proof-theoretic treatment of λ-reduction with cut-elimination: λ-calculus as a logic programming language." J. Symbolic Logic 76 (2) 673 - 699, June 2011. https://doi.org/10.2178/jsl/1305810770

Information

Published: June 2011
First available in Project Euclid: 19 May 2011

zbMATH: 1223.03038
MathSciNet: MR2830422
Digital Object Identifier: 10.2178/jsl/1305810770

Rights: Copyright © 2011 Association for Symbolic Logic

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Vol.76 • No. 2 • June 2011
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