First, instead of `const id` I will use `const`, that is, we shall prove
const = liftM2 const :: M a -> M b -> M a
which I believe should be equivalent to your property.
My belief was wrong, which is evident when using do-notation. Kim-Ee stated do {_ <- b; x <- a; return x} = a while I examined do {x <- a; _ <- b; return x} = a Since do {x <- a; return x} = a holds for any monad, Kim-Ee's property can be reduced to do {_ <- b; a} = a or more concisely b >> a = a which I called Kleisli-const in my previous post. As we seemed to have settled for "occlusive" I suggest calling b >> a = a "right-occlusive" or "occlusive from the right" because the right action occludes the side-effects of the left action, and do {x <- a; _ <- b; return x} = a should be called "left-occlusive" or "occlusive from the left" because the left action hides the effect of the right action. Under commutativity, both are the same but in general these might be different properties. I do not have a distinguishing counterexample, though, because all monads I come up with are commutative. David Feuer hinted at the possibility to define occlusiveness more generally for Applicative functors. Commutativity might be stated for Applicatives as liftA2 f a b = liftA2 (flip f) b a So far I can only see two classes of occlusive monads: The reader-like (Identity ~ Reader ()) and the set-like monads. Olaf