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.CALCO.2015.205
URN: urn:nbn:de:0030-drops-55351
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5535/
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Kurz, Alexander ; Pardo, Alberto ; Petrisan, Daniela ; Severi, Paula ; de Vries, Fer-Jan

Approximation of Nested Fixpoints – A Coalgebraic View of Parametric Dataypes

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Abstract

The question addressed in this paper is how to correctly approximate infinite data given by systems of simultaneous corecursive definitions. We devise a categorical framework for reasoning about regular datatypes, that is, datatypes closed under products, coproducts and fixpoints. We argue that the right methodology is on one hand coalgebraic (to deal with possible nontermination and infinite data) and on the other hand 2-categorical (to deal with parameters in a disciplined manner). We prove a coalgebraic version of Bekic lemma that allows us to reduce simultaneous fixpoints to a single fix point. Thus a possibly infinite object of interest is regarded as a final coalgebra of a many-sorted polynomial functor and can be seen as a limit of finite approximants. As an application, we prove correctness of a generic function that calculates the approximants on a large class of data types.

BibTeX - Entry

@InProceedings{kurz_et_al:LIPIcs:2015:5535,
  author =	{Alexander Kurz and Alberto Pardo and Daniela Petrisan and Paula Severi and Fer-Jan de Vries},
  title =	{{Approximation of Nested Fixpoints – A Coalgebraic View of Parametric Dataypes}},
  booktitle =	{6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)},
  pages =	{205--220},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-84-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{35},
  editor =	{Lawrence S. Moss and Pawel Sobocinski},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5535},
  URN =		{urn:nbn:de:0030-drops-55351},
  doi =		{10.4230/LIPIcs.CALCO.2015.205},
  annote =	{Keywords: coalgebra, Bekic lemma, infinite data, functional programming, type theory}
}

Keywords: coalgebra, Bekic lemma, infinite data, functional programming, type theory
Collection: 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)
Issue Date: 2015
Date of publication: 28.10.2015

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