International Conference on Foundations of Software Science and Computational Structures

FoSSaCS 2011: Foundations of Software Science and Computational Structures pp 108-122

Realizability and Parametricity in Pure Type Systems

  • Jean-Philippe Bernardy
  • Marc Lasson
Conference paper

DOI: 10.1007/978-3-642-19805-2_8

Volume 6604 of the book series Lecture Notes in Computer Science (LNCS)

Abstract

We describe a systematic method to build a logic from any programming language described as a Pure Type System (PTS). The formulas of this logic express properties about programs. We define a parametricity theory about programs and a realizability theory for the logic. The logic is expressive enough to internalize both theories. Thanks to the PTS setting, we abstract most idiosyncrasies specific to particular type theories. This confers generality to the results, and reveals parallels between parametricity and realizability.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jean-Philippe Bernardy
    • 1
    • 2
  • Marc Lasson
    • 3
  1. 1.Chalmers University of TechnologySweden
  2. 2.University of GothenburgSweden
  3. 3.LIP (UMR 5668 CNRS ENS Lyon UCBL INRIA)ENS Lyon, Université de LyonFrance