On the signature of >>= Monad operator

Question

This is the signature of the well know >>= operator in Haskell

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

The question is why

Answer 1

As others have said, your bind is the fmap function of the Functor class, a.k.a <$>.

But why is it less powerful than >>=?

it seems not difficult to write a general "adapter"

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

You can indeed write a function with this type:

adapt f x = return (f x)

However, this function is not able to do everything that we might want >>='s argument to do. There are useful values that adapt cannot produce.

In the list monad, return x = [x], so adapt will always return a single-element list.

In the Maybe monad, return x = Some x, so adapt will never return None.

In the IO monad, once you retrieved the result of an operation, all you can do is compute a new value from it, you can't run a subsequent operation!

etc. So in short, fmap is able to do fewer things than >>=. That doesn't mean it's useless -- it wouldn't have a name if it was :) But it is less powerful.