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arXiv · 2003.09993

A Trustful Monad for Axiomatic Reasoning with Probability and Nondeterminism

Reynald Affeldt·Jacques Garrigue·David Nowak·Takafumi Saikawa
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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.

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Reynald Affeldt, Jacques Garrigue, David Nowak, Takafumi Saikawa. 2020-03-22. A Trustful Monad for Axiomatic Reasoning with Probability and Nondeterminism. https://doi.org/10.1017/s0956796821000137

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