Relating Classical Realizability and Negative Translation for Existential Witness Extraction

  • Alexandre Miquel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5608)


Friedman showed how to turn a classical proof of a \(\Sigma^0_1\) formula into an intuitionistic proof of the same formula, thus giving an effective method to extract witnesses from classical proofs of such formulae. In this paper we show how to achieve the same goal efficiently using Krivine realizability with primitive numerals, and prove that the corresponding program is but the direct-style equivalent (using call-cc) of the CPS-style program underlying Friedman’s method.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Alexandre Miquel
    • 1
  1. 1.Université Paris 7 & LIP (ENS Lyon)France

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