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ITU  /  Research  /  Technical Reports  /  Technical Reports Archive  /  2010  /  Realizability Semantics of Parametric Polymorphism, General References, and Recursive Types
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    Realizability Semantics of Parametric Polymorphism, General References, and Recursive Types

    TR-2010-124, Authors: Lars Birkedal, Kristian Støvring and Jacob Thamsborg

    Lars Birkedal
    Kristian Støvring
    Jacob Thamsborg
    January 2010

    Abstract

    We present a realizability 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 (as needed for parametricity reasoning) that include general reference types. The interpretation uses a new approach to modeling 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.


    Technical report [TR-2010-124] in IT University Technical Report Series, January 2010.

    Available as PDF.


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