Compound Monads and Models of Computation

We consider the theory of “extended subsitutions” involving both angelic and demonic choice. For other related formal theories describing program semantics the implicit model of computation is based on a combination of monads by a distributive law. We show how the model of computation underlying extended subsitutions is based on a monad which, while not being a compound monad, has strong similarities to a compound monad based on a distributive law. We discuss these compound monads and monad morphisms between them. We have used the theorem prover Isabelle to formalise and machine-check our results.