Realisability semantics of parametric polymorphism, general references and recursive types

Author:

BIRKEDAL LARS,STØVRING KRISTIAN,THAMSBORG JACOB

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.

Publisher

Cambridge University Press (CUP)

Subject

Computer Science Applications,Mathematics (miscellaneous)

Cited by 13 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A Logical Approach to Type Soundness;Journal of the ACM;2024-07-10

2. A Kripke logical relation for effect-based program transformations;Information and Computation;2016-08

3. Trace semantics for polymorphic references;Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science;2016-07-05

4. Realizability models for a linear dependent PCF;Theoretical Computer Science;2015-06

5. Specification patterns for reasoning about recursion through the store;Information and Computation;2013-10

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