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Game Semantics and Normalization by Evaluation

  • Pierre Clairambault
  • Peter Dybjer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9034)

Abstract

We show that Hyland and Ong’s game semantics for PCF can be presented using normalization by evaluation (nbe). We use the bijective correspondence between innocent well-bracketed strategies and PCF Böhm trees, and show how operations on PCF Böhm trees, such as composition, can be computed lazily and simply by nbe. The usual equations characteristic of games follow from the nbe construction without reference to low-level game-theoretic machinery. As an illustration, we give a Haskell program computing the application of innocent strategies.

Keywords

Reduction Rule Semantic Domain Closed Term Game Semantic Recursive Type 
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-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Pierre Clairambault
    • 1
  • Peter Dybjer
    • 2
  1. 1.CNRS, ENS Lyon, Inria, UCBLUniversité de LyonLyonFrance
  2. 2.Chalmers Tekniska HögskolaGothenburgSweden

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