mapM id [Just 1, Just 2, Just 3] result: Just [1,2,3]
mapM :: (a -> m b) -> [a] -> m [b] So in this case: a = Maybe Int (second arg in mapM id [Just1, Just 2, Just 3] and b = Int and m = Maybe. So id is :: Maybe Int -> Maybe Int
Right! So note here that 'm' is Maybe and 'b' is 'Int', thus mapM's return value is 'm [b]', i.e. 'Maybe [Int]'. The implication is that it somehow yields a Maybe of [Int], but no Maybe Int.
mapM id [Just 1, Nothing, Just 3] result: Nothing. My first guess for the result: Just [Just 1, Nothing, Just 3]
This is contingent of the semantics of the Maybe monad. First, mapM's definition:
mapM f as = sequence (map f as)
So the list is mapped onto the (monadic!) function, then sequenced:
sequence :: Monad m => [m a] -> m [a] sequence = foldr mcons (return []) where mcons p q = p >>= \x -> q >>= \y -> return (x : y)
Note that consecutive values are bound, so seeing this example should clarify why a single Nothing causes mapM to return Nothing for the lot:
Just 1 >> Just 2 Just 2 Nothing >> Just 2 Nothing
This falls simply out of Maybe's Monad instance definition for bind:
instance Monad Maybe where (Just x) >>= k = k x Nothing >>= k = Nothing
HTH. Arlen