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).
https://hal.inria.fr/hal-01446033 Contributor : Hal IfipConnect in order to contact the contributor Submitted on : Wednesday, January 25, 2017 - 3:24:27 PM Last modification on : Wednesday, January 25, 2017 - 3:31:57 PM Long-term archiving on: : Wednesday, April 26, 2017 - 3:07:29 PM