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Parametric Polymorphism — Universally

Part of the Lecture Notes in Computer Science book series (LNTCS,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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This work was partially supported by SICSA, and EPSRC grant EP/K023837/1.

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  1. 1.

    The category \(\mathsf {Rel}\) has as objects relations and as morphisms functions which preserve relatedness. This category will be introduced in detail in Sect. 2.


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Correspondence to Federico Orsanigo .

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Ghani, N., Forsberg, F.N., Orsanigo, F. (2015). Parametric Polymorphism — Universally. In: de Paiva, V., de Queiroz, R., Moss, L., Leivant, D., de Oliveira, A. (eds) Logic, Language, Information, and Computation. WoLLIC 2015. Lecture Notes in Computer Science(), vol 9160. Springer, Berlin, Heidelberg.

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