License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2021.35
URN: urn:nbn:de:0030-drops-134696
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13469/
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Pistone, Paolo ; Tranchini, Luca

The Yoneda Reduction of Polymorphic Types

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LIPIcs-CSL-2021-35.pdf (0.7 MB)

Abstract

In this paper we explore a family of type isomorphisms in System F whose validity corresponds, semantically, to some form of the Yoneda isomorphism from category theory. These isomorphisms hold under theories of equivalence stronger than βη-equivalence, like those induced by parametricity and dinaturality. We show that the Yoneda type isomorphisms yield a rewriting over types, that we call Yoneda reduction, which can be used to eliminate quantifiers from a polymorphic type, replacing them with a combination of monomorphic type constructors. We establish some sufficient conditions under which quantifiers can be fully eliminated from a polymorphic type, and we show some application of these conditions to count the inhabitants of a type and to compute program equivalence in some fragments of System F.

BibTeX - Entry

@InProceedings{pistone_et_al:LIPIcs:2021:13469,
  author =	{Paolo Pistone and Luca Tranchini},
  title =	{{The Yoneda Reduction of Polymorphic Types}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{35:1--35:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-175-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{183},
  editor =	{Christel Baier and Jean Goubault-Larrecq},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13469},
  URN =		{urn:nbn:de:0030-drops-134696},
  doi =		{10.4230/LIPIcs.CSL.2021.35},
  annote =	{Keywords: System F, Type isomorphisms, Yoneda isomorphism, Program equivalence}
}

Keywords: System F, Type isomorphisms, Yoneda isomorphism, Program equivalence
Collection: 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)
Issue Date: 2021
Date of publication: 13.01.2021

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