While we can't *zip* sums generically, we can *unzip* them. Here's a rewrite:
genericmzipWith :: (Generic1 m, GMonadZip (Rep1 m)) => (a -> b -> c)
-> m a -> m b -> m c
genericmzipWith f m1 m2 = to1 $ gmzipWith f (from1 m1) (from1 m2)
genericmunzip :: (Generic1 m, GMonadUnzip (Rep1 m)) => m (a, b) -> (m a, m b)
genericmunzip m = case gmunzip (from1 m) of
(p, q) -> (to1 p, to1 q)
class GMonadZip f where
gmzipWith :: (a -> b -> c) -> f a -> f b -> f c
class GMonadUnzip f where
gmunzip :: f (a, b) -> (f a, f b)
instance MonadZip f => GMonadZip (Rec1 f) where
gmzipWith f (Rec1 fa) (Rec1 fb) = Rec1 (mzipWith f fa fb)
instance MonadZip f => GMonadUnzip (Rec1 f) where
gmunzip (Rec1 fab) = (Rec1 fa, Rec1 fb)
where
-- We want to be lazy here, because this might actually
-- be recursive. We do a lot of NOINLINE to get selector
-- thunks to avoid space leaks.
{-# NOINLINE mufab #-}
{-# NOINLINE fa #-}
{-# NOINLINE fb #-}
mufab = munzip fab
(fa, fb) = mufab
nstance (MonadZip f, GMonadZip g) => GMonadZip (f :.: g) where
gmzipWith f (Comp1 fga1) (Comp1 fga2) = Comp1 $ mzipWith (gmzipWith
f) fga1 fga2
instance (Functor g, MonadZip f, GMonadUnzip g) => GMonadUnzip (f :.: g) where
gmunzip (Comp1 fgc) = case munzip . fmap gmunzip $ fgc of
(p, q) -> (Comp1 p, Comp1 q)
instance GMonadZip U1 where
gmzipWith _ _ _ = U1
instance GMonadUnzip U1 where
gmunzip _ = (U1, U1)
instance GMonadZip Par1 where
gmzipWith = coerce
instance GMonadUnzip Par1 where
gmunzip = coerce
deriving instance GMonadZip f => GMonadZip (M1 i c f)
deriving instance GMonadUnzip f => GMonadUnzip (M1 i c f)
instance (GMonadZip f, GMonadZip g) => GMonadZip (f :*: g) where
gmzipWith f (x1 :*: y1) (x2 :*: y2) = gmzipWith f x1 x2 :*:
gmzipWith f y1 y2
instance (GMonadUnzip f, GMonadUnzip g) => GMonadUnzip (f :*: g) where
-- Why don't we need to be lazy in this munzip? If we're working with
-- Rep1, then laziness will be added by the Rec1 instance. If we're working
-- with Rep, then we can't have any K1s because K1 isn't an instance of
-- Monad, let alone MonadZip!
gmunzip (fab :*: gab)
| (fa, fb) <- gmunzip fab
, (ga, gb) <- gmunzip gab
= (fa :*: ga, fb :*: gb)
instance (GMonadUnzip f, GMonadUnzip g) => GMonadUnzip (f :+: g) where
gmunzip (L1 x) = case gmunzip x of
(l, r) -> (L1 l, L1 r)
gmunzip (R1 x) = case gmunzip x of
(l, r) -> (R1 l, R1 r)
On Sat, Aug 21, 2021 at 9:44 PM David Feuer
We can offer generic helpers for writing MonadZip instances:
genericmzipWith :: (Generic1 m, GMonadZip (Rep1 m)) => (a -> b -> c) -> m a -> m b -> m c genericmzipWith f m n = to1 $ gmzipWith f (from1 m) (from1 n)
genericmunzip :: (Generic1 m, GMonadZip (Rep1 m)) => m (a, b) -> (m a, m b) genericmunzip m = case gmunzip (from1 m) of (r1, r2) -> (to1 r1, to1 r2)
These can be used with appropriate product types (there's no way to zip sums generically). I propose adding these to Control.Monad.Zip. The GMonadZip class and its instances are below.
class GMonadZip f where gmzipWith :: (a -> b -> c) -> f a -> f b -> f c gmunzip :: f (a, b) -> (f a, f b)
instance MonadZip f => GMonadZip (Rec1 f) where gmzipWith f (Rec1 fa) (Rec1 fb) = Rec1 (mzipWith f fa fb) gmunzip (Rec1 fab) = (Rec1 fa, Rec1 fb) where -- We want to be lazy here, because this might actually -- be recursive. We do a lot of NOINLINE to get selector -- thunks to avoid space leaks. {-# NOINLINE mufab #-} {-# NOINLINE fa #-} {-# NOINLINE fb #-} mufab = munzip fab (fa, fb) = mufab
instance (Functor g, MonadZip f, GMonadZip g) => GMonadZip (f :.: g) where gmzipWith f (Comp1 fga1) (Comp1 fga2) = Comp1 $ mzipWith (gmzipWith f) fga1 fga2 gmunzip (Comp1 fgc) = case munzip . fmap gmunzip $ fgc of (p, q) -> (Comp1 p, Comp1 q)
-- | @since 4.9.0.0 instance GMonadZip U1 where gmzipWith _ _ _ = U1 gmunzip _ = (U1, U1)
-- | @since 4.9.0.0 instance GMonadZip Par1 where gmzipWith = coerce gmunzip = coerce
-- | @since 4.9.0.0 deriving instance GMonadZip f => GMonadZip (M1 i c f)
-- | @since 4.9.0.0 instance (GMonadZip f, GMonadZip g) => GMonadZip (f :*: g) where gmzipWith f (x1 :*: y1) (x2 :*: y2) = gmzipWith f x1 x2 :*: gmzipWith f y1 y2 -- Why don't we need to be lazy in this munzip? If we're working with -- Rep1, then laziness will be added by the Rec1 instance. If we're working -- with Rep, then we can't have any K1s because K1 isn't an instance of -- Monad, let alone MonadZip! gmunzip (fab :*: gab) | (fa, fb) <- gmunzip fab , (ga, gb) <- gmunzip gab = (fa :*: ga, fb :*: gb)