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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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Contributor : Tristan Crolard <>
Submitted on : Thursday, September 14, 2006 - 5:16:46 PM
Last modification on : Thursday, January 23, 2020 - 3:48:01 PM


  • HAL Id : hal-00094650, version 1



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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