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.CONCUR.2020.28
URN: urn:nbn:de:0030-drops-128407
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12840/
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Mio, Matteo ; Vignudelli, Valeria

Monads and Quantitative Equational Theories for Nondeterminism and Probability

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LIPIcs-CONCUR-2020-28.pdf (0.6 MB)


Abstract

The monad of convex sets of probability distributions is a well-known tool for modelling the combination of nondeterministic and probabilistic computational effects. In this work we lift this monad from the category of sets to the category of extended metric spaces, by means of the Hausdorff and Kantorovich metric liftings. Our main result is the presentation of this lifted monad in terms of the quantitative equational theory of convex semilattices, using the framework of quantitative algebras recently introduced by Mardare, Panangaden and Plotkin.

BibTeX - Entry

@InProceedings{mio_et_al:LIPIcs:2020:12840,
  author =	{Matteo Mio and Valeria Vignudelli},
  title =	{{Monads and Quantitative Equational Theories for Nondeterminism and Probability}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{28:1--28:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Igor Konnov and Laura Kov{\'a}cs},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12840},
  URN =		{urn:nbn:de:0030-drops-128407},
  doi =		{10.4230/LIPIcs.CONCUR.2020.28},
  annote =	{Keywords: Computational Effects, Monads, Metric Spaces, Quantitative Algebras}
}

Keywords: Computational Effects, Monads, Metric Spaces, Quantitative Algebras
Collection: 31st International Conference on Concurrency Theory (CONCUR 2020)
Issue Date: 2020
Date of publication: 26.08.2020


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