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A trustful monad for axiomatic reasoning with probability and nondeterminism

Published online by Cambridge University Press:  15 July 2021

REYNALD AFFELDT Open the ORCID record for REYNALD AFFELDT [Opens in a new window] ,
JACQUES GARRIGUE ,
DAVID NOWAK  and
TAKAFUMI SAIKAWA
REYNALD AFFELDT
Affiliation:
National Institute of Advanced Industrial Science and Technology, Digital Architecture Research Center, Tokyo, Japan (e-mail: reynald.affeldt@aist.go.jp)
JACQUES GARRIGUE
Affiliation:
Nagoya University, Graduate School of Mathematics, Nagoya, Japan (e-mail: garrigue@math.nagoya-u.ac.jp)
DAVID NOWAK
Affiliation:
Univ. Lille, CNRS, Centrale Lille, UMR 9189 CRIStAL, F-59000 Lille, France
TAKAFUMI SAIKAWA
Affiliation:
Nagoya University, Graduate School of Mathematics, Nagoya, Japan (e-mail: tscompor@gmail.com)
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Abstract

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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.

Type
Research Article
Information
Journal of Functional Programming , Volume 31 , 2021 , e17
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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