Derandomizing probabilistic semantics through Eilenberg-Moore algebras for the Giry monad

A simple language is defined, a probabilistic semantics and a partial correctness logic is proposed in terms of probabilistic relations. It is shown how a derandomized semantics can be constructed through the Eilenberg-Moore algebras. We investigate the category of EilenbergMoore algebras for the Giry monad associated with stochastic relations over Polish spaces with continuous maps as morphisms. The algebras are characterized through strongly convex structures on the base space.

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