Monads for Measurable Queries in Probabilistic Databases

@inproceedings{Dash2021MonadsFM,
  title={Monads for Measurable Queries in Probabilistic Databases},
  author={Swaraj Dash and Sam Staton},
  booktitle={MFPS},
  year={2021}
}
We consider a bag (multiset) monad on the category of standard Borel spaces, and show that it gives a free measurable commutative monoid. Firstly, we show that a recent measurability result for probabilistic database queries (Grohe and Lindner, ICDT 2020) follows quickly from the fact that queries can be expressed in monad-based terms. We also extend this measurability result to a fuller query language. Secondly, we discuss a distributive law between probability and bag monads, and we… 

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This paper uses finite colimits and what the authors call uniform states in such Markov categories to define a (fixed size) multiset functor, with basic operations for sums and zips of multisets, and a graded monad structure.

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