Universal properties for universal types in bifibrational parametricity

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Ghani, Neil and Nordvall Forsberg, Fredrik and Orsanigo, Federico (2019) Universal properties for universal types in bifibrational parametricity. Mathematical Structures in Computer Science, 29 (6). 810–827. ISSN 1469-8072 (https://doi.org/10.1017/S0960129518000336)

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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.

ORCID iDs

Ghani, Neil ORCID logoORCID: https://orcid.org/0000-0002-3988-2560, Nordvall Forsberg, Fredrik ORCID logoORCID: https://orcid.org/0000-0001-6157-9288 and Orsanigo, Federico;
CORE (COnnecting REpositories)