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

@article{Jacobs15,
  title = {A Recipe for State-and-Effect Triangles},
  author = {Bart Jacobs},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 13, Issue 2},
  year = {2017},
  doi = {10.23638/lmcs-13(2:6)2017}
}