Interpreting polymorphic FPC into domain theoretic models of parametric polymorphism

  • Authors:

  • Rasmus Ejlers Møgelberg

  • Affiliations:

  • DISI, Università di Genova

  • Venue:
  • ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
  • Year:
  • 2006

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Abstract

This paper shows how parametric PILLY (Polymorphic Intuitionistic / Linear Lambda calculus with a fixed point combinator Y) can be used as a metalanguage for domain theory, as originally suggested by Plotkin more than a decade ago. Using recent results about solutions to recursive domain equations in parametric models of PILLY, we show how to interpret FPC in these. Of particular interest is a model based on “admissible” pers over a reflexive domain, the theory of which can be seen as a domain theory for (impredicative) polymorphism. We show how this model gives rise to a parametric and computationally adequate model of PolyFPC, an extension of FPC with impredicative polymorphism. This is the first model of a language with parametric polymorphism, recursive terms and recursive types in a non-linear setting