We consider the problem of establishing a relationship between two interpretations of base type terms of a λ c -calculus extended with algebraic operations. We show that the given relationship holds if it satisfies a set of natural conditions. We apply this result to 1) comparing two monadic semantics related by a strong monad morphism, and 2) comparing two monadic semantics of fresh name creation: Stark's new name creation monad [32] , and the global counter monad. We also consider the same

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... blem, relating semantics of computational effects, in the presence of recursive functions. We apply this additional by extending the previous monad morphism comparison result to the recursive case.