License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CALCO.2021.13
URN: urn:nbn:de:0030-drops-153686
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Dahlqvist, Fredrik ; Schmid, Todd

How to Write a Coequation ((Co)algebraic pearls)

LIPIcs-CALCO-2021-13.pdf (1 MB)


There is a large amount of literature on the topic of covarieties, coequations and coequational specifications, dating back to the early seventies. Nevertheless, coequations have not (yet) emerged as an everyday practical specification formalism for computer scientists. In this review paper, we argue that this is partly due to the multitude of syntaxes for writing down coequations, which seems to have led to some confusion about what coequations are and what they are for. By surveying the literature, we identify four types of syntaxes: coequations-as-corelations, coequations-as-predicates, coequations-as-equations, and coequations-as-modal-formulas. We present each of these in a tutorial fashion, relate them to each other, and discuss their respective uses.

BibTeX - Entry

  author =	{Dahlqvist, Fredrik and Schmid, Todd},
  title =	{{How to Write a Coequation}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{13:1--13:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-212-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{211},
  editor =	{Gadducci, Fabio and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-153686},
  doi =		{10.4230/LIPIcs.CALCO.2021.13},
  annote =	{Keywords: Coalgebra, coequation, covariety}

Keywords: Coalgebra, coequation, covariety
Collection: 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)
Issue Date: 2021
Date of publication: 08.11.2021

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