module Data.Comp.Multi.Ops where
import Data.Comp.Multi.HFunctor
import Data.Comp.Multi.HFoldable
import Data.Comp.Multi.HTraversable
import qualified Data.Comp.Ops as O
import Control.Monad
import Control.Applicative
infixr 5 :+:
data (f :+: g) (h :: * -> *) e = Inl (f h e)
| Inr (g h e)
instance (HFunctor f, HFunctor g) => HFunctor (f :+: g) where
hfmap f (Inl v) = Inl $ hfmap f v
hfmap f (Inr v) = Inr $ hfmap f v
instance (HFoldable f, HFoldable g) => HFoldable (f :+: g) where
hfold (Inl e) = hfold e
hfold (Inr e) = hfold e
hfoldMap f (Inl e) = hfoldMap f e
hfoldMap f (Inr e) = hfoldMap f e
hfoldr f b (Inl e) = hfoldr f b e
hfoldr f b (Inr e) = hfoldr f b e
hfoldl f b (Inl e) = hfoldl f b e
hfoldl f b (Inr e) = hfoldl f b e
hfoldr1 f (Inl e) = hfoldr1 f e
hfoldr1 f (Inr e) = hfoldr1 f e
hfoldl1 f (Inl e) = hfoldl1 f e
hfoldl1 f (Inr e) = hfoldl1 f e
instance (HTraversable f, HTraversable g) => HTraversable (f :+: g) where
htraverse f (Inl e) = Inl <$> htraverse f e
htraverse f (Inr e) = Inr <$> htraverse f e
hmapM f (Inl e) = Inl `liftM` hmapM f e
hmapM f (Inr e) = Inr `liftM` hmapM f e
class (sub :: (* -> *) -> * -> *) :<: sup where
inj :: sub a :-> sup a
proj :: NatM Maybe (sup a) (sub a)
instance (:<:) f f where
inj = id
proj = Just
instance (:<:) f (f :+: g) where
inj = Inl
proj (Inl x) = Just x
proj (Inr _) = Nothing
instance (f :<: g) => (:<:) f (h :+: g) where
inj = Inr . inj
proj (Inr x) = proj x
proj (Inl _) = Nothing
infixr 8 :*:
data (f :*: g) a = f a :*: g a
fst :: (f :*: g) a -> f a
fst (x :*: _) = x
snd :: (f :*: g) a -> g a
snd (_ :*: x) = x
infixr 7 :&:
data (f :&: a) (g :: * -> *) e = f g e :&: a
instance (HFunctor f) => HFunctor (f :&: a) where
hfmap f (v :&: c) = hfmap f v :&: c
instance (HFoldable f) => HFoldable (f :&: a) where
hfold (v :&: _) = hfold v
hfoldMap f (v :&: _) = hfoldMap f v
hfoldr f e (v :&: _) = hfoldr f e v
hfoldl f e (v :&: _) = hfoldl f e v
hfoldr1 f (v :&: _) = hfoldr1 f v
hfoldl1 f (v :&: _) = hfoldl1 f v
instance (HTraversable f) => HTraversable (f :&: a) where
htraverse f (v :&: c) = (:&: c) <$> (htraverse f v)
hmapM f (v :&: c) = liftM (:&: c) (hmapM f v)
class DistAnn (s :: (* -> *) -> * -> *) p s' | s' -> s, s' -> p where
injectA :: p -> s a :-> s' a
projectA :: s' a :-> (s a O.:&: p)
class RemA (s :: (* -> *) -> * -> *) s' | s -> s' where
remA :: s a :-> s' a
instance (RemA s s') => RemA (f :&: p :+: s) (f :+: s') where
remA (Inl (v :&: _)) = Inl v
remA (Inr v) = Inr $ remA v
instance RemA (f :&: p) f where
remA (v :&: _) = v
instance DistAnn f p (f :&: p) where
injectA p v = v :&: p
projectA (v :&: p) = v O.:&: p
instance (DistAnn s p s') => DistAnn (f :+: s) p ((f :&: p) :+: s') where
injectA p (Inl v) = Inl (v :&: p)
injectA p (Inr v) = Inr $ injectA p v
projectA (Inl (v :&: p)) = (Inl v O.:&: p)
projectA (Inr v) = let (v' O.:&: p) = projectA v
in (Inr v' O.:&: p)