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.2021.18
URN: urn:nbn:de:0030-drops-153733
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/15373/
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Jia, Xiaodong ; Mislove, Michael ; Zamdzhiev, Vladimir

The Central Valuations Monad (Early Ideas)

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LIPIcs-CALCO-2021-18.pdf (0.5 MB)

Abstract

We give a commutative valuations monad Z on the category DCPO of dcpo’s and Scott-continuous functions. Compared to the commutative valuations monads given in [Xiaodong Jia et al., 2021], our new monad Z is larger and it contains all push-forward images of valuations on the unit interval [0, 1] along lower semi-continuous maps. We believe that this new monad will be useful in giving domain-theoretic denotational semantics for statistical programming languages with continuous probabilistic choice.

BibTeX - Entry

@InProceedings{jia_et_al:LIPIcs.CALCO.2021.18,
  author =	{Jia, Xiaodong and Mislove, Michael and Zamdzhiev, Vladimir},
  title =	{{The Central Valuations Monad}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{18:1--18:5},
  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 =		{https://drops.dagstuhl.de/opus/volltexte/2021/15373},
  URN =		{urn:nbn:de:0030-drops-153733},
  doi =		{10.4230/LIPIcs.CALCO.2021.18},
  annote =	{Keywords: Valuations, Commutative Monad, DCPO, Probabilistic Choice, Recursion}
}

Keywords: Valuations, Commutative Monad, DCPO, Probabilistic Choice, Recursion
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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