module Data.Comp.Ops where
import Data.Foldable
import Data.Traversable
import Control.Applicative
import Control.Monad hiding (sequence, mapM)
import Data.Comp.SubsumeCommon
import Prelude hiding (foldl, mapM, sequence, foldl1, foldr1, foldr)
infixr 6 :+:
data (f :+: g) e = Inl (f e)
| Inr (g e)
fromInl :: (f :+: g) e -> Maybe (f e)
fromInl = caseF Just (const Nothing)
fromInr :: (f :+: g) e -> Maybe (g e)
fromInr = caseF (const Nothing) Just
caseF :: (f a -> b) -> (g a -> b) -> (f :+: g) a -> b
caseF f g x = case x of
Inl x -> f x
Inr x -> g x
instance (Functor f, Functor g) => Functor (f :+: g) where
fmap f (Inl e) = Inl (fmap f e)
fmap f (Inr e) = Inr (fmap f e)
instance (Foldable f, Foldable g) => Foldable (f :+: g) where
fold (Inl e) = fold e
fold (Inr e) = fold e
foldMap f (Inl e) = foldMap f e
foldMap f (Inr e) = foldMap f e
foldr f b (Inl e) = foldr f b e
foldr f b (Inr e) = foldr f b e
foldl f b (Inl e) = foldl f b e
foldl f b (Inr e) = foldl f b e
foldr1 f (Inl e) = foldr1 f e
foldr1 f (Inr e) = foldr1 f e
foldl1 f (Inl e) = foldl1 f e
foldl1 f (Inr e) = foldl1 f e
instance (Traversable f, Traversable g) => Traversable (f :+: g) where
traverse f (Inl e) = Inl <$> traverse f e
traverse f (Inr e) = Inr <$> traverse f e
sequenceA (Inl e) = Inl <$> sequenceA e
sequenceA (Inr e) = Inr <$> sequenceA e
mapM f (Inl e) = Inl `liftM` mapM f e
mapM f (Inr e) = Inr `liftM` mapM f e
sequence (Inl e) = Inl `liftM` sequence e
sequence (Inr e) = Inr `liftM` sequence e
infixl 5 :<:
infixl 5 :=:
type family Elem (f :: * -> *) (g :: * -> *) :: Emb where
Elem f f = Found Here
Elem (f1 :+: f2) g = Sum' (Elem f1 g) (Elem f2 g)
Elem f (g1 :+: g2) = Choose (Elem f g1) (Elem f g2)
Elem f g = NotFound
type family Choose (e1 :: Emb) (r :: Emb) :: Emb where
Choose (Found x) (Found y) = Ambiguous
Choose Ambiguous y = Ambiguous
Choose x Ambiguous = Ambiguous
Choose (Found x) y = Found (Le x)
Choose x (Found y) = Found (Ri y)
Choose x y = NotFound
type family Sum' (e1 :: Emb) (r :: Emb) :: Emb where
Sum' (Found x) (Found y) = Found (Sum x y)
Sum' Ambiguous y = Ambiguous
Sum' x Ambiguous = Ambiguous
Sum' NotFound y = NotFound
Sum' x NotFound = NotFound
data Proxy a = P
class Subsume (e :: Emb) (f :: * -> *) (g :: * -> *) where
inj' :: Proxy e -> f a -> g a
prj' :: Proxy e -> g a -> Maybe (f a)
instance Subsume (Found Here) f f where
inj' _ = id
prj' _ = Just
instance Subsume (Found p) f g => Subsume (Found (Le p)) f (g :+: g') where
inj' _ = Inl . inj' (P :: Proxy (Found p))
prj' _ (Inl x) = prj' (P :: Proxy (Found p)) x
prj' _ _ = Nothing
instance Subsume (Found p) f g => Subsume (Found (Ri p)) f (g' :+: g) where
inj' _ = Inr . inj' (P :: Proxy (Found p))
prj' _ (Inr x) = prj' (P :: Proxy (Found p)) x
prj' _ _ = Nothing
instance (Subsume (Found p1) f1 g, Subsume (Found p2) f2 g)
=> Subsume (Found (Sum p1 p2)) (f1 :+: f2) g where
inj' _ (Inl x) = inj' (P :: Proxy (Found p1)) x
inj' _ (Inr x) = inj' (P :: Proxy (Found p2)) x
prj' _ x = case prj' (P :: Proxy (Found p1)) x of
Just y -> Just (Inl y)
_ -> case prj' (P :: Proxy (Found p2)) x of
Just y -> Just (Inr y)
_ -> Nothing
type f :<: g = (Subsume (ComprEmb (Elem f g)) f g)
inj :: forall f g a . (f :<: g) => f a -> g a
inj = inj' (P :: Proxy (ComprEmb (Elem f g)))
proj :: forall f g a . (f :<: g) => g a -> Maybe (f a)
proj = prj' (P :: Proxy (ComprEmb (Elem f g)))
type f :=: g = (f :<: g, g :<: f)
spl :: (f :=: f1 :+: f2) => (f1 a -> b) -> (f2 a -> b) -> f a -> b
spl f1 f2 x = case inj x of
Inl y -> f1 y
Inr y -> f2 y
infixr 8 :*:
data (f :*: g) a = f a :*: g a
ffst :: (f :*: g) a -> f a
ffst (x :*: _) = x
fsnd :: (f :*: g) a -> g a
fsnd (_ :*: x) = x
infixr 7 :&:
data (f :&: a) e = f e :&: a
instance (Functor f) => Functor (f :&: a) where
fmap f (v :&: c) = fmap f v :&: c
instance (Foldable f) => Foldable (f :&: a) where
fold (v :&: _) = fold v
foldMap f (v :&: _) = foldMap f v
foldr f e (v :&: _) = foldr f e v
foldl f e (v :&: _) = foldl f e v
foldr1 f (v :&: _) = foldr1 f v
foldl1 f (v :&: _) = foldl1 f v
instance (Traversable f) => Traversable (f :&: a) where
traverse f (v :&: c) = liftA (:&: c) (traverse f v)
sequenceA (v :&: c) = liftA (:&: c)(sequenceA v)
mapM f (v :&: c) = liftM (:&: c) (mapM f v)
sequence (v :&: c) = liftM (:&: c) (sequence v)
class DistAnn s p s' | s' -> s, s' -> p where
injectA :: p -> s a -> s' a
projectA :: s' a -> (s a, 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 c v = v :&: c
projectA (v :&: p) = (v,p)
instance (DistAnn s p s') => DistAnn (f :+: s) p ((f :&: p) :+: s') where
injectA c (Inl v) = Inl (v :&: c)
injectA c (Inr v) = Inr $ injectA c v
projectA (Inl (v :&: p)) = (Inl v,p)
projectA (Inr v) = let (v',p) = projectA v
in (Inr v',p)