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Parametric Polymorphism — Universally

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9160)

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.

Keywords

  • Parametric Polymorphism
  • Abstraction Theorem
  • Polymorphic Functions
  • Universal Property
  • Axiomatic Setting

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This work was partially supported by SICSA, and EPSRC grant EP/K023837/1.

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Notes

  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. https://doi.org/10.1007/978-3-662-47709-0_7

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  • DOI: https://doi.org/10.1007/978-3-662-47709-0_7

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