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arXiv · 2111.10873

The Central Valuations Monad

Xiaodong Jia·Michael Mislove·Vladimir Zamdzhiev
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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 [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.

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Xiaodong Jia, Michael Mislove, Vladimir Zamdzhiev. 2021-11-21. The Central Valuations Monad. https://doi.org/10.4230/lipics.calco.2021.18

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