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A proof-theoretic treatment of λ-reduction with cut-elimination: λ-calculus as a logic programming language

Published online by Cambridge University Press:  12 March 2014

Michael Gabbay
Michael Gabbay*
Affiliation:
Department of Philosophy, Kings College London, Strand, WC2R 2LS, UK, E-mail: [email protected]
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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).

Keywords

term-sequentcut-eliminationlambda-calculuslogic programming
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 2 , June 2011 , pp. 673 - 699
Copyright
Copyright © Association for Symbolic Logic 2011

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References

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