I am learning functional programming style. From this link http://channel9.msdn.com/shows/Going+Deep/Brian-Beckman-Dont-fear-the-Monads/, Brian Beckman gave a brilliant introduction about Monad. He mentioned that Monad is about composition of functions so as to address complexity.

A Monad includes a unit function that transfers type T to an amplified type M(T); and a Bind function that, given function from T to M(U), transforms type M(T) to another type M(U). (U can be T, but is not necessarily).

In my understanding, the language implementing monad should be type-checked statically. Otherwise, type errors cannot be found during compilation and "Complexity" is not controlled. Is my understanding correct?