Unlike a Functor, a Monad can change shape?

Question

I\'ve always enjoyed the following intuitive explanation of a monad\'s power relative to a functor: a monad can change shape; a functor cannot.

For example: length

Answer 1

The key combinator for monads is (>>=). Knowing that it composes two monadic values and reading its type signature, the power of monads becomes more apparent:

(>>=) :: Monad m => m a -> (a -> m b) -> m b

The future action can depend entirely on the outcome of the first action, because it is a function of its result. This power comes at a price though: Functions in Haskell are entirely opaque, so there is no way for you to get any information about a composed action without actually running it. As a side note, this is where arrows come in.