[Forlien]

I feel a bit dumb asking this, but your explanation doesn't make it clear to me why you can't think of a bind on Maybe as a flatMap on a List with 0 (Nothing) or 1 (Just) elements. Could you elaborate further on how thinking of a bind on Maybe as null propagation eliminates it also being interpreted as a flatMap on a restricted-size list?

[fmap]

You're right, maybe is equivalent to the type of lists with at most one element. There are however monad instances which are genuinely different.

For example the state monad is defined as

  F(X) = S -> S*X

I.e., a value of type F(X) is a state transformer which takes a state argument of type S and produces the new state and a value of type X. In this case, bind is sequencing of state transformers.

Using the state monad you can write code that looks like it uses a global variable of type S, while being completely pure which makes testing and refactoring easier, and of course doesn't pollute the rest of the program.

[acomar]

Unfortunately, not all monads are list-like (though there are a lot that are). The most notorious example is probably Cont[1], the monad of delimited continuations. State, ST, and IO all struggle to be interpreted as lists as well.

[1]: http://blog.sigfpe.com/2008/12/mother-of-all-monads.html