Abstract The algebraic properties of the combination of probabilistic choice and nondeterministic choice have long been a research topic in program semantics. This paper explains a formalization in the Coq proof assistant of a monad equipped with both choices: the geometrically convex monad. This formalization has an immediate application: it provides a model for a monad that implements a nontrivial interface, which allows for proofs by equational reasoning using probabilistic and nondeterministic effects. We explain the technical choices we made to go from the literature to a complete Coq formalization, from which we identify reusable theories about mathematical structures such as convex spaces and concrete categories, and that we integrate in a framework for monadic equational reasoning.

@article{paperbot1229,
  title = {A trustful monad for axiomatic reasoning with probability and nondeterminism},
  author = {REYNALD AFFELDT and JACQUES GARRIGUE and DAVID NOWAK and TAKAFUMI SAIKAWA},
  journal = {Journal of Functional Programming},
  volume = {31},
  year = {2021},
  doi = {10.1017/s0956796821000137}
}