Logical relations and parametricity - A Reynolds Programme for category theory and programming languages dedicated to the memory of John C. Reynolds, 1935-2013: in Proceedings of the Workshop on Algebra, Coalgebra and Topology (WACT 2013)

Claudio Hermida, Uday S. Reddy, Edmund P. Robinson

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

In his seminal paper on "Types, Abstraction and Parametric Polymorphism," John Reynolds called for homomorphisms to be generalized from functions to relations. He reasoned that such a generalization would allow type-based "abstraction" (representation independence, information hiding, naturality or parametricity) to be captured in a mathematical theory, while accounting for higher-order types. However, after 30 years of research, we do not yet know fully how to do such a generalization. In this article, we explain the problems in doing so, summarize the work carried out so far, and call for a renewed attempt at addressing the problem.

Original languageEnglish
Pages (from-to)149-180
Number of pages32
JournalElectronic Notes in Theoretical Computer Science
Volume303
DOIs
Publication statusPublished - 28 Mar 2014
EventProceedings of the Workshop on Algebra, Coalgebra and Topology (WACT 2013) - Bath, United Kingdom
Duration: 1 Mar 20131 Mar 2013

Keywords

  • Category Theory
  • Data abstraction
  • Definability
  • Fibrations
  • Homomorphisms
  • Information hiding
  • Logical Relations
  • Natural Transformations
  • Parametric polymorphism
  • Reflexive Graphs
  • Relation lifting
  • Relational Parametricity
  • Universal algebra

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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