The Central Valuations Monad (Early Ideas)

Authors Xiaodong Jia, Michael Mislove, Vladimir Zamdzhiev

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Author Details

Xiaodong Jia
  • School of Mathematics, Hunan University, Changsha, China
Michael Mislove
  • Department of Computer Science, Tulane University, New Orleans, LA, USA
Vladimir Zamdzhiev
  • Université de Lorraine, CNRS, Inria, LORIA, F 54000 Nancy, France


We thank the anonymous reviewers for their feedback which led to improvements of this paper. Xiaodong Jia acknowledges the support of NSFC (No. 12001181).

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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)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Denotational semantics
  • Valuations
  • Commutative Monad
  • DCPO
  • Probabilistic Choice
  • Recursion


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