(I'm going to play fast and loose with constructors for this post,
treating MyList and ZipList as if they were [])
On Thu, Jul 16, 2009 at 4:10 PM, Dan Weston
-- different from [], sum rather than product instance Applicative MyList where pure x = x ::: Nil (<*>) (f ::: fs) (x ::: xs) = f x ::: (fs <*> xs) (<*>) _ _ = Nil
Unfortunately, this instance doesn't fulfill this Applicative law: pure id <*> f = f pure id <*> [1,2,3] = [id] <*> [1,2,3] = [id 1] = [1] Fortunately, the solution already exists in Control.Applicative:
-- | Lists, but with an 'Applicative' functor based on zipping, so that -- -- @f '<$>' 'ZipList' xs1 '<*>' ... '<*>' 'ZipList' xsn = 'ZipList' (zipWithn f xs1 ... xsn)@ -- newtype ZipList a = ZipList { getZipList :: [a] }
instance Functor ZipList where fmap f (ZipList xs) = ZipList (map f xs)
instance Applicative ZipList where pure x = ZipList (repeat x) ZipList fs <*> ZipList xs = ZipList (zipWith id fs xs)
In this case: pure id <*> [1,2,3] = [id, id, ...] <*> [1,2,3] = [id 1, id 2, id 3] = [1,2,3] -- ryan