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

Acknowledgements

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

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.CALCO.2021.18

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.

Subject Classification

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

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References

  1. Jean Goubault-Larrecq, Xiaodong Jia, and Clément Théron. A Domain-Theoretic Approach to Statistical Programming Languages, 2021. Preprint. URL: https://arxiv.org/abs/2106.16190.
  2. Xiaodong Jia, Bert Lindenhovius, Michael Mislove, and Vladimir Zamdzhiev. Commutative monads for probabilistic programming languages. In Logic in Computer Science (LICS 2021), 2021. URL: http://arxiv.org/abs/2102.00510.
  3. C. Jones and Gordon D. Plotkin. A probabilistic powerdomain of evaluations. In Proceedings of the Fourth Annual Symposium on Logic in Computer Science (LICS '89), Pacific Grove, California, USA, June 5-8, 1989, pages 186-195. IEEE Computer Society, 1989. URL: https://doi.org/10.1109/LICS.1989.39173.
  4. Claire Jones. Probabilistic Non-determinism. PhD thesis, University of Edinburgh, UK, 1990. URL: http://hdl.handle.net/1842/413.
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