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

Does

h :: (Monad m, Num a) => a -> m a
h 0 = fail "Failed."
h a = return a

suit your needs? For example,

> [0,1,2,3] >>= h
[1,2,3]