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)


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.


Classical Logic Operational Semantic Simple Type Classical Setting Realizability Interpretation 
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© 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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