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

Gilles Dowek; Thérèse Hardin; Claude Kirchner

Conference papers

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

Document type :

Conference papers

Domain :

Computer Science [cs] / Other [cs.OH]

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https://hal.inria.fr/inria-00098847
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Submitted on : Tuesday, September 26, 2006 - 8:39:13 AM
Last modification on : Friday, February 4, 2022 - 3:30:28 AM

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

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

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