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Realisability semantics of parametric polymorphism, general references and recursive types

Published online by Cambridge University Press:  02 July 2010

LARS BIRKEDAL ,
KRISTIAN STØVRING  and
JACOB THAMSBORG
LARS BIRKEDAL
Affiliation:
IT University of Copenhagen, Rued Langgaards Vej 7, 2300 Copenhagen S, Denmark Email: birkedal@itu.dk; kss@itu.dk; thamsborg@itu.dk
KRISTIAN STØVRING
Affiliation:
IT University of Copenhagen, Rued Langgaards Vej 7, 2300 Copenhagen S, Denmark Email: birkedal@itu.dk; kss@itu.dk; thamsborg@itu.dk
JACOB THAMSBORG
Affiliation:
IT University of Copenhagen, Rued Langgaards Vej 7, 2300 Copenhagen S, Denmark Email: birkedal@itu.dk; kss@itu.dk; thamsborg@itu.dk
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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.

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 20 , Issue 4 , August 2010 , pp. 655 - 703
Copyright
Copyright © Cambridge University Press 2010

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