Realisability semantics of parametric polymorphism, general references and recursive types

  • Authors:

  • Lars Birkedal;Kristian StØ/vring;Jacob Thamsborg

  • Affiliations:

  • It university of copenhagen, rued langgaards vej 7, 2300 copenhagen s, denmark email: birkedal@itu.dk/ kss@itu.dk/ thamsborg@itu.dk;It university of copenhagen, rued langgaards vej 7, 2300 copenhagen s, denmark email: birkedal@itu.dk/ kss@itu.dk/ thamsborg@itu.dk;It university of copenhagen, rued langgaards vej 7, 2300 copenhagen s, denmark email: birkedal@itu.dk/ kss@itu.dk/ thamsborg@itu.dk

  • Venue:
  • Mathematical Structures in Computer Science
  • Year:
  • 2010

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Abstract

We present a realisability model for a call-by-value, higher-order programming language with parametric polymorphism, general first-class references, and recursive types. The main novelty is a relational interpretation of open types that include general reference types. The interpretation uses a new approach to modelling references. The universe of semantic types consists of world-indexed families of logical relations over a universal predomain. In order to model general reference types, worlds are finite maps from locations to semantic types: this introduces a circularity between semantic types and worlds that precludes a direct definition of either. Our solution is to solve a recursive equation in an appropriate category of metric spaces. In effect, types are interpreted using a Kripke logical relation over a recursively defined set of worlds. We illustrate how the model can be used to prove simple equivalences between different implementations of imperative abstract data types.