Why use such a peculiar function type in monads?

Question

New to Haskell, and am trying to figure out this Monad thing. The monadic bind operator -- >>= -- has a very peculiar type signature:

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Answer 1

The thing that makes a monad a monad is how 'join' works. Recall that join has the type:

join :: m (m a) -> m a

What 'join' does is "interpret" a monad action that returns a monad action in terms of a monad action. So, you can think of it peeling away a layer of the monad (or better yet, pulling the stuff in the inner layer out into the outer layer). This means that the 'm''s form a "stack", in the sense of a "call stack". Each 'm' represents a context, and 'join' lets us join contexts together, in order.

So, what does this have to do with bind? Recall:

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

And now consider that for f :: a -> m b, and ma :: m a:

fmap f ma :: m (m b)

That is, the result of applying f directly to the a in ma is an (m (m b)). We can apply join to this, to get an m b. In short,

ma >>= f = join (fmap f ma)