Question

If I define the “bind” function like this:

(>>=) :: M a -> (a -> M' b) -> M' b

Will this definition help me if I want the result to be of a new Monad type, or I should use same Monad but with b in the same Monad box as before?

Answer 1

As I’ve mentioned in the comment, I don’t think such operation can be safely defined for general monads (e.g. M = IO, M' = Maybe).

However, if the M is safely convertible to M’, then this bind can be defined as:

convert :: M1 a -> M2 a
...

(>>=*) :: M1 a -> (a -> M2 b) -> M2 b
x >>=* f = convert x >>= f

And conversely,

convert x = x >>=* return

Some of such safe conversion methods are maybeToList (Maybe → []), listToMaybe ([] → Maybe), stToIO (ST RealWorld → IO), … note that there isn’t a generic convert method for any monads.