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HOL-$\lambda \sigma$ an intentional first-order expression of higher-order logic

Gilles Dowek Thérèse Hardin Claude Kirchner 1
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We propose a first-order presentation of higher-order logic based on explicit substitutions. It is intentionally equivalent to the usual presentation of higher-order logic based on $\lambda$-calculus, i.e. a proposition can be proved without the extensionality axioms in one theory if and only if it can in the other. The {\em Extended Narrowing and Resolution} first-order proof-search method can be applied to this theory. This allows to simulate higher-order resolution step by step and furthermore leaves room for further optimizations and extensions.
Mots-clés : logique d'ordre supérieur explicit substitutions higher-order logic substitutions explicites
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Conference papers
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https://hal.inria.fr/inria-00098847
Contributor : Publications Loria <>
Submitted on : Tuesday, September 26, 2006 - 8:39:13 AM
Last modification on : Thursday, January 11, 2018 - 6:19:58 AM

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  • HAL Id : inria-00098847, version 1

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INRIA | CNRS | LORIA | UNIV-LORRAINE

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Gilles Dowek, Thérèse Hardin, Claude Kirchner. HOL-$\lambda \sigma$ an intentional first-order expression of higher-order logic. Tenth International Conference on Rewriting Techniques & Applications - RTA'99, Jul 1999, Trento, Italy, 14 p. ⟨inria-00098847⟩

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