Monads for Measurable Queries in Probabilistic Databases

Swaraj Dash
(University of Oxford)
Sam Staton
(University of Oxford)

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 illustrate that this is useful for generating probabilistic databases.

In Ana Sokolova: Proceedings 37th Conference on Mathematical Foundations of Programming Semantics (MFPS 2021), Hybrid: Salzburg, Austria and Online, 30th August - 2nd September, 2021, Electronic Proceedings in Theoretical Computer Science 351, pp. 34–50.
Published: 29th December 2021.

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