Monad is a well designed little universe, where any composition of actions never escape. Hence, by monad, we separate the concrete real problem into severy disjoint sub problems, and solve them separately, in their own universe.
Correspondingly, Monad Transformer is a even bigger universe. Let MT be a monad transformer, M is a common little monad. Then the MT M is the universe which embraces everything in M. Viz.,M is a sub universe of MT M. For any action act in M, lift.act must be a member of MT M .
We say monad transformer is a sound way of composing monads. It is one-way relationship. Everything in M can be lifted to MT M, while the reversed way is totally forbidden. Besides, from the universe perspect, if we luckily find everything in M is in MT M, and everything in MT M in also in M, then oh, MT M will be identical with M. Universe M is as large as Universe MT M, viz. Then comes the problem, why you need two exactly same universe? That must be a stupid design.
