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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.
|Title of host publication||Logic, Language, Information, and Computation|
|Subtitle of host publication||22nd International Workshop, WoLLIC 2015, Bloomington, IN, USA, July 20-23, 2015, Proceedings|
|Editors||Valeria de Paiva, Ruy de Queiroz, Lawrence S. Moss, Daniel Leivant, Anjolina G. de Oliveira|
|Number of pages||12|
|Publication status||Published - 24 Jun 2015|
|Event||Workshop on Logic, Language and Information (WoLLIC 2015) - Indiana University, Bloomington, IN, United States|
Duration: 20 Jul 2015 → 23 Jul 2015
|Name||Lecture Notes in Computer Science|
|Conference||Workshop on Logic, Language and Information (WoLLIC 2015)|
|Period||20/07/15 → 23/07/15|
- parametric polymorphism
- type theory
Ghani, N., Nordvall Forsberg, F. & Orsanigo, F., 30 Jun 2019, In: Mathematical Structures in Computer Science. 29, 6, p. 810–827 18 p.
Research output: Contribution to journal › Article › peer-reviewOpen AccessFile4 Downloads (Pure)