Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-00150889
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

File

extract.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00150889, version 1

Collections

Citation

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

Share

Metrics

Record views

165

Files downloads

261