Way cool. I have gained newfound respect for what I don't know. :)
Can there ever be more than one (observably different) valid definition
of pure for a given <*> that obeys all the laws? I would imagine that
there could be at most one.
Dan
Ryan Ingram wrote:
(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<weston...@imageworks.com> wrote:
-- 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
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