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On Bar Recursion and Choice in a Classical Setting

  • Valentin Blot
  • Colin Riba
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8301)

Abstract

We show how Modified Bar-Recursion, a variant of Spector’s Bar-Recursion due to Berger and Oliva can be used to realize the Axiom of Countable Choice in Parigot’s Lambda-Mu-calculus, a direct-style language for the representation and evaluation of classical proofs.

We rely on Hyland-Ong innocent games. They provide a model for the instances of the axiom of choice usually used in the realization of classical choice with Bar-Recursion, and where, moreover, the standard datatype of natural numbers is in the image of a CPS-translation.

Keywords

Classical Logic Operational Semantic Simple Type Classical Setting Realizability Interpretation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Valentin Blot
    • 1
  • Colin Riba
    • 1
  1. 1.ENS de LyonUniversité de Lyon, LIPFrance

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