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

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 :
Type de document :
Communication dans un congrès
Tenth International Conference on Rewriting Techniques & Applications - RTA'99, Jul 1999, Trento, Italy, 14 p, 1999
Domaine :

https://hal.inria.fr/inria-00098847
Contributeur : Publications Loria <>
Soumis le : mardi 26 septembre 2006 - 08:39:13
Dernière modification le : jeudi 11 janvier 2018 - 06:19:58

### Identifiants

• HAL Id : inria-00098847, version 1

### Citation

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, 1999. 〈inria-00098847〉

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