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Classical program extraction in the calculus of constructions

Abstract : We show how to extract classical programs expressed in Krivine lambda-c-calculus from proof-terms built in a proof-irrelevant and classical version of the calculus of constructions with universes. For that, we extend Krivine's realisability model of classical second-order arithmetic to the calculus of constructions with universes using a structure of Pi-set which is reminiscent of omega-sets, and show that our realisability model validates Peirce's law and proof-irrelevance. Finally, we extend the extraction scheme to a primitive data-type of natural numbers in a way which preserves the whole compatibility with the classical realisability interpretation of second-order arithmetic.
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Contributor : Alexandre Miquel <>
Submitted on : Sunday, June 3, 2007 - 10:24:56 PM
Last modification on : Saturday, March 28, 2020 - 2:06:54 AM
Document(s) archivé(s) le : Friday, September 21, 2012 - 4:01:12 PM


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  • HAL Id : hal-00150889, version 1



Alexandre Miquel. Classical program extraction in the calculus of constructions. 2007. ⟨hal-00150889⟩



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