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Parametric Polymorphism — Universally

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Logic, Language, Information, and Computation (WoLLIC 2015)

Part of the book series: Lecture Notes in Computer Science ((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.

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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Authors and Affiliations

  1. University of Strathclyde, Glasgow, UK

    Neil Ghani, Fredrik Nordvall Forsberg & Federico Orsanigo

Authors
  1. Neil Ghani
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  2. Fredrik Nordvall Forsberg
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  3. Federico Orsanigo
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Corresponding author

Correspondence to Federico Orsanigo .

Editor information

Editors and Affiliations

  1. Nuance Communications, Sunnyvale, California, USA

    Valeria de Paiva

  2. Universidade Federal de Pernambuco, Centro de Informática, Recife, Pernambuco, Brazil

    Ruy de Queiroz

  3. Department of Mathematics, Indiana University Bloomington, Bloomington, Indiana, USA

    Lawrence S. Moss

  4. nDepartment of Computer Science, Indiana University Bloomington, Bloomington, Indiana, USA

    Daniel Leivant

  5. Universidade Federal de Pernambuco, Centro de Informática, Recife, Pernambuco, Brazil

    Anjolina G. de Oliveira

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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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