The Central Valuations Monad

TL;DR

This paper introduces a new commutative valuations monad Z on dcpo's that extends previous models by including push-forward images of valuations, aiming to improve domain-theoretic semantics for probabilistic programming.

Contribution

It presents a larger, more comprehensive valuations monad Z that encompasses all push-forward images of valuations on [0,1], enhancing semantic modeling capabilities.

Findings

The monad Z is larger than previous models.

It contains all push-forward images of valuations on [0,1].

Potential applications in probabilistic programming semantics.

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.