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The Central Valuations Monad

Abstract : We give a commutative valuations monad $\mathcal{Z}$ on the category DCPO of dcpo's and Scott-continuous functions. Compared to the commutative valuations monads given in [2], 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.
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https://hal.inria.fr/hal-03258065
Contributor : Vladimir Zamdzhiev <>
Submitted on : Friday, June 11, 2021 - 12:06:27 PM
Last modification on : Saturday, June 12, 2021 - 3:33:20 AM

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Xiaodong Jia, Michael Mislove, Vladimir Zamdzhiev. The Central Valuations Monad. 2021. ⟨hal-03258065⟩

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