Hi Tony On 29 Dec 2009, at 12:10, Tony Morris wrote:
Can (liftM join .) . mapM be improved? (Monad m) => (a -> m [b]) -> [a] -> m [b]
You can (a) generalize m from Monad to Applicative (b) generalize [b] to any Monoid (c) generalize [a] to f a for any Foldable f and write ala AppLift foldMap if you happen to have some of my usual kit. See below. Cheers Conor Here's the machinery.
class Newtype n where type Unwrap n wrap :: Unwrap n -> n unwrap :: n -> Unwrap n
ala :: Newtype v' => (t -> t') -> ((s -> t') -> u -> v') -> (s -> t) -> u -> Unwrap v' ala p h f u = unwrap (h (p . f) u)
Here's a rather useful newtype, capturing applicative lifting of monoids.
newtype AppLift a x = AppLift (a x)
instance (Applicative a, Monoid x) => Monoid (AppLift a x) where mempty = AppLift (pure mempty) mappend (AppLift ax) (AppLift ay) = AppLift (mappend <$> ax <*> ay)
instance Newtype (AppLift a x) where type Unwrap (AppLift a x) = a x wrap = AppLift unwrap (AppLift ax) = ax