Monads are not commutative. A structure that would tell the compiler that it's commutative, would give it more leeway for optimization (and parallel execution).

Perhaps if you search for Abelian Monad or so, you will find interesting things in the category theory literature. Some of them may be transplantable to Haskell --- but you probably don't want a completely commutative structure. Arrows seem to express the dependencies between operations more fine-grained than the sequencing that Monads require. (I meant to look into arrows for ages..) Matthias.