Faced with the need to quantify software (un)reliability in the presence of faults, the semantics of state-based systems is urged to evolve towards quantified (e.g. probabilistic) nondeterminism. When one is approaching such semantics from a categorical perspective, this inevitably calls for some technical elaboration, in a monadic setting.#R##N##R##N#This paper proposes that such an evolution be undertaken without sacrificing the simplicity of the original (qualitative) definitions, by keeping quantification implicit rather than explicit. The approach is a monad lifting strategy whereby, under some conditions, definitions can be preserved provided the semantics moves to another category.#R##N##R##N#The technique is illustrated by showing how to introduce probabilism in an existing software component calculus, by moving to a suitable category of matrices and using linear algebra in the reasoning.#R##N##R##N#The paper also addresses the problem of preserving monadic strength in the move from original to target (Kleisli) categories, a topic which bears relationship to recent studies in categorial physics.
['José Nuno Fonseca Oliveira', 'Victor Cacciari Miraldo']
“Keep definition, change category” — A practical approach to state-based system calculi