Am Sonntag 10 Mai 2009 07:24:43 schrieb Brandon S. Allbery KF8NH:
I can't tell where I'm making the mistake here.
In the thread where (>>=) and fmap were being confused, the error cited a type (Maybe a) which was supposed to be in typeclass Num. As far as I can tell, if the typechecker gets to the point where Num and Maybe are both present and (m) is Maybe, it has to (1) be focused on the (m b) part of (a -> m b), and therefore (2) must have already unified (a) and (b). But that means (m b) must unify with (Num a => a), which is unified with (b), resulting in the attempt to unify (Num a => a) with (Maybe a); since we get the error about (Maybe a) not being a Num, it must not have gotten there. But that means it can't have related Num to (m a) with (m) bound to Maybe, which is why I assumed it had unified (m) with ((->) r) instead.
Can the typechecker really get the Num to the other end of (a -> m b) without also getting the (a) there? Or is it checking for the Num constraint before it has fully evaluated the type of (m b)? I thought typeclass constraints happened later than basic type unification.
Just in case it hasn't been answered yet: Just 3 >>= (1+) Just 3 :: (Num n1) => Maybe n1 (>>=) :: (Monad m) => m a -> (a -> m b) -> m b (1+) :: (Num n2) => n2 -> n2 (Just 3 >>=) :: (Num n1) => (n1 -> Maybe b) -> Maybe b Now we must unify the type of (1+) with (Just 3 >>=)'s argument's type, that is (Num n2) => n2 -> n2 with (Num n1) => n1 -> Maybe b n2 = n1 n2 = Maybe b giving (Just 3 >>=) :: (Num (Maybe b)) => (Maybe b -> Maybe b) -> Maybe b Just 3 >>= (1+) :: Num (Maybe b) => Maybe b ================================================= module MaybeNum where import Control.Monad instance Num a => Num (Maybe a) where (+) = liftM2 (+) (-) = liftM2 (-) (*) = liftM2 (*) signum = fmap signum abs = fmap abs negate = fmap negate fromInteger = Just . fromInteger ================================================= *MaybeNum> Just 3 >>= (1+) Just 4 or, weirder: ================================================= instance Num (Maybe Bool) where (+) = liftM2 (/=) (-) = (+) (*) = liftM2 (&&) signum = (`mplus` Just False) abs = signum negate = id fromInteger = Just . odd ================================================= *MaybeNum> Just 3 >>= (1+) :: Maybe Bool Just False