LIPIcs.CALCO.2021.18.pdf
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The Central Valuations Monad (Early Ideas)
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9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Conference on Algebra and Coalgebra in Computer Science (CALCO) - License:
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- Publication Date: 2021-11-08
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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).
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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)
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
- 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.
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