Affine Monads and Side-Effect-Freeness

Abstract : The notions of side-effect-freeness and commutativity are typical for probabilistic models, as subclass of quantum models. This paper connects these notions to properties in the theory of monads. A new property of a monad (‘strongly affine’) is introduced. It is shown that for such strongly affine monads predicates are in bijective correspondence with side-effect-free instruments. Also it is shown that these instruments are commutative, in a suitable sense, for monads which are commutative (monoidal).
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Bart Jacobs. Affine Monads and Side-Effect-Freeness. 13th International Workshop on Coalgebraic Methods in Computer Science (CMCS), Apr 2016, Eindhoven, Netherlands. pp.53-72, ⟨10.1007/978-3-319-40370-0_5⟩. ⟨hal-01446033⟩

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