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Early Ideas
DOI: 10.4230/LIPIcs.CALCO.2021.18
The Central Valuations Monad (Early Ideas)

Authors: Xiaodong Jia, Michael Mislove, and Vladimir Zamdzhiev

Published in: LIPIcs, Volume 211, 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)

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.
Cite as

Xiaodong Jia, Michael Mislove, and Vladimir Zamdzhiev. The Central Valuations Monad (Early Ideas). In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 18:1-18:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2021.18},
  URN =		{urn:nbn:de:0030-drops-153733},
  doi =		{10.4230/LIPIcs.CALCO.2021.18},
  annote =	{Keywords: Valuations, Commutative Monad, DCPO, Probabilistic Choice, Recursion}
}
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