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Universal properties for universal types in bifibrational parametricity

Published online by Cambridge University Press:  22 March 2019

Neil Ghani ,
Fredrik Nordvall Forsberg  and
Federico Orsanigo
Neil Ghani*
Affiliation:
Department of Computer and Information Sciences, University of Strathclyde, Glasgow, UK
Fredrik Nordvall Forsberg
Affiliation:
Department of Computer and Information Sciences, University of Strathclyde, Glasgow, UK
Federico Orsanigo
Affiliation:
Department of Computer and Information Sciences, University of Strathclyde, Glasgow, UK
*
*Corresponding author. Email: neil.ghani@strath.ac.uk
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Abstract

In the 1980s, John Reynolds postulated that a parametrically polymorphic function is an ad-hoc polymorphic function satisfying a uniformity principle. This allowed him to prove that his set-theoretic semantics has a relational lifting which satisfies the Identity Extension Lemma and the Abstraction Theorem. However, his definition (and subsequent variants) has only been given for specific models. In contrast, we give a model-independent axiomatic treatment by characterising Reynolds’ definition via a universal property, and show that the above results follow from this universal property in the axiomatic setting.

Keywords

Relational parametricitycategorical semanticscomprehension categories

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 29 , Issue 6 , June 2019 , pp. 810 - 827
Copyright
© Cambridge University Press 2019 

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