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.
@article{arxiv.2111.10873,
title = {The Central Valuations Monad},
author = {Xiaodong Jia and Michael Mislove and Vladimir Zamdzhiev},
journal= {arXiv preprint arXiv:2111.10873},
year = {2021}
}