Chapter

Foundations of Software Science and Computational Structures

Volume 6604 of the series Lecture Notes in Computer Science pp 108-122

Realizability and Parametricity in Pure Type Systems

  • Jean-Philippe BernardyAffiliated withLancaster UniversityChalmers University of TechnologyUniversity of Gothenburg
  • , Marc LassonAffiliated withLancaster UniversityLIP (UMR 5668 CNRS ENS Lyon UCBL INRIA), ENS Lyon, Université de Lyon

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.