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.2019.13
URN: urn:nbn:de:0030-drops-114414
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11441/
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Levy, Paul Blain ; Goncharov, Sergey

Coinductive Resumption Monads: Guarded Iterative and Guarded Elgot

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Abstract

We introduce a new notion of "guarded Elgot monad", that is a monad equipped with a form of iteration. It requires every guarded morphism to have a specified fixpoint, and classical equational laws of iteration to be satisfied. This notion includes Elgot monads, but also further examples of partial non-unique iteration, emerging in the semantics of processes under infinite trace equivalence.
We recall the construction of the "coinductive resumption monad" from a monad and endofunctor, that is used for modelling programs up to bisimilarity. We characterize this construction via a universal property: if the given monad is guarded Elgot, then the coinductive resumption monad is the guarded Elgot monad that freely extends it by the given endofunctor.

BibTeX - Entry

@InProceedings{levy_et_al:LIPIcs:2019:11441,
  author =	{Paul Blain Levy and Sergey Goncharov},
  title =	{{Coinductive Resumption Monads: Guarded Iterative and Guarded Elgot}},
  booktitle =	{8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
  pages =	{13:1--13:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-120-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{139},
  editor =	{Markus Roggenbach and Ana Sokolova},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11441},
  URN =		{urn:nbn:de:0030-drops-114414},
  doi =		{10.4230/LIPIcs.CALCO.2019.13},
  annote =	{Keywords: Guarded iteration, guarded monads, coalgebraic resumptions}
}

Keywords: Guarded iteration, guarded monads, coalgebraic resumptions
Collection: 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)
Issue Date: 2019
Date of publication: 25.11.2019

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