A Type Theory which is complete for Kreisel's Modified Realizability

Abstract : We define a type theory with a strong elimination rule for existential quantification. As in Martin-Löf's type theory, the “axiom of choice” is thus derivable. Proofs are also annotated by realizers which are simply typed lambda-terms. A new rule called “type extraction” which extracts the type of a realizer allows us to derive the so-called “independance of premisses” schema. Consequently, any formula which is realizable in HA^omega according to Kreisel's modified realizability, is derivable in this type theory.
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Article dans une revue
Electronic Notes in Theoretical Computer Science, Elsevier, 1999, 23, pp.1-16
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https://hal.archives-ouvertes.fr/hal-00094650
Contributeur : Tristan Crolard <>
Soumis le : jeudi 14 septembre 2006 - 17:16:46
Dernière modification le : jeudi 11 janvier 2018 - 06:19:28

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  • HAL Id : hal-00094650, version 1

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Tristan Crolard. A Type Theory which is complete for Kreisel's Modified Realizability. Electronic Notes in Theoretical Computer Science, Elsevier, 1999, 23, pp.1-16. 〈hal-00094650〉

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