Nijmegen Quantum Logic Group

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Affine Monads and Side-Effect-Freeness

04 Jun 2016 [ proceedings (CMCS 2016) · preprint ]

The notion of strongly affine monad is introduced and related to side-effect freeness of instruments which are associated with predicates.

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).