Parametric Polymorphism — Universally

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9160)


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.


Parametric Polymorphism Abstraction Theorem Polymorphic Functions Universal Property Axiomatic Setting 
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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.University of StrathclydeGlasgowUK

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