Syntax for Free: Representing Syntax with Binding Using Parametricity

  • Authors:
  • Robert Atkey

  • Affiliations:
  • School of Informatics, University of Edinburgh,

  • Venue:
  • TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications
  • Year:
  • 2009

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Abstract

We show that, in a parametric model of polymorphism, the type *** *** . ((*** ****** ) ****** ) ***(*** ****** ****** ) ****** is isomorphic to closed de Bruijn terms. That is, the type of closed higher-order abstract syntax terms is isomorphic to a concrete representation. To demonstrate the proof we have constructed a model of parametric polymorphism inside the Coq proof assistant. The proof of the theorem requires parametricity over Kripke relations. We also investigate some variants of this representation.