A Recipe for State-and-Effect Triangles

Abstract

In the semantics of programming languages one can view programs as statetransformers, or as predicate transformers. Recently the author has introducedstate-and-effect triangles which capture this situation categorically,involving an adjunction between state- and predicate-transformers. The currentpaper exploits a classical result in category theory, part of Jon Beck'smonadicity theorem, to systematically construct such a state-and-effecttriangle from an adjunction. The power of this construction is illustrated inmany examples, covering many monads occurring in program semantics, including(probabilistic) power domains