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G. Plotkin and the author have worked out the equivalence between statetransformer semantics and predicate transformer semantics in a domaintheoretical setting for programs combining nondeterminism and probability.Works of C. Morgan and co-authors, Keimel, Rosenbusch and Streicher, already goin the same direction using only discrete state spaces. It is the aim of thispaper to exhibit a general framework in which one can hope that statetransformer semantics and predicate transformer semantics are equivalent. Weuse a notion of entropicity borrowed from universal algebra and a relaxedsetting adapted to the domain theoretical situation.

On the equivalence of state transformer semantics and predicate transformer semantics