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Parametric polymorphism - universally

Ghani, Neil and Nordvall Forsberg, Fredrik and Orsanigo, Federico (2015) Parametric polymorphism - universally. In: Logic, Language, Information, and Computation. Lecture Notes in Computer Science . Springer Berlin/Heidelberg, pp. 81-92. ISBN 978-3-662-47708-3

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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.