Abstract
The usual monad laws can directly be used as rewrite rules for Isabelle’s
simplifier to normalise monadic HOL terms and decide equivalences.
In a commutative monad, however, the commutativity law is a
higher-order permutative rewrite rule that makes the simplifier loop.
This AFP entry implements a simproc that normalises monadic
expressions in commutative monads using ordered rewriting. The
simproc can also permute computations across control operators like if
and case.