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Article Dans Une Revue Mathematical Structures in Computer Science Année : 2001

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

Gilles Dowek
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Thérèse Hardin
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Claude Kirchner
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Résumé

We give a first-order presentation of higher-order logic based on explicit substitutions. This presentation is intentionally equivalent to the usual presentation of higher-order logic based on λ-calculus, that is, a proposition can be proved without the extensionality axioms in one theory if and only if it can be in the other. We show that the Extended Narrowing and Resolution first-order proof-search method can be applied to this theory. In this way we get a step-by-step simulation of higher-order resolution. Hence, expressing higher-order logic as a first-order theory and applying a first-order proof search method is a relevant alternative to a direct implementation. In particular, the well-studied improvements of proof search for first-order logic could be reused at no cost for higher-order automated deduction. Moreover, as we stay in a first-order setting, extensions, such as equational higher-order resolution, may be easier to handle.
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Dates et versions

hal-01199524 , version 1 (15-09-2015)

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  • HAL Id : hal-01199524 , version 1

Citer

Gilles Dowek, Thérèse Hardin, Claude Kirchner. HOL-lambda-sigma: an intentional first-order expression of higher-order logic. Mathematical Structures in Computer Science, 2001, 11, pp.21-45. ⟨hal-01199524⟩
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