Parametric polymorphism - universally

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Ghani, Neil and Nordvall Forsberg, Fredrik and Orsanigo, Federico; de Paiva, Valeria and de Queiroz, Ruy and Moss, Lawrence S. and Leivant, Daniel and de Oliveira, Anjolina G., eds. (2015) Parametric polymorphism - universally. In: Logic, Language, Information, and Computation. Lecture Notes in Computer Science . Springer Berlin/Heidelberg, USA, pp. 81-92. ISBN 978-3-662-47708-3 (https://doi.org/10.1007/978-3-662-47709-0_7)

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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) have 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; de Paiva, Valeria, de Queiroz, Ruy, Moss, Lawrence S., Leivant, Daniel and de Oliveira, Anjolina G.
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