A Trustful Monad for Axiomatic Reasoning with Probability and Nondeterminism
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 non-trivial 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.
Cite
@article{arxiv.2003.09993,
title = {A Trustful Monad for Axiomatic Reasoning with Probability and Nondeterminism},
author = {Reynald Affeldt and Jacques Garrigue and David Nowak and Takafumi Saikawa},
journal= {arXiv preprint arXiv:2003.09993},
year = {2023}
}
Comments
28 pages, submitted