module Pandora.Pattern.Morphism.Flip where

import Pandora.Pattern.Semigroupoid (Semigroupoid ((.)))
import Pandora.Pattern.Category (Category (identity))
import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-)))
import Pandora.Pattern.Functor.Contravariant (Contravariant ((>-|-)))

newtype Flip (v :: * -> * -> *) a e = Flip (v e a)

instance Semigroupoid m => Semigroupoid (Flip m) where
	Flip m c b
g . :: Flip m b c -> Flip m a b -> Flip m a c
. Flip m b a
f = m c a -> Flip m a c
forall (v :: * -> * -> *) a e. v e a -> Flip v a e
Flip (m b a
f m b a -> m c b -> m c a
forall (m :: * -> * -> *) b c a.
Semigroupoid m =>
m b c -> m a b -> m a c
. m c b
g)

instance Category m => Category (Flip m) where
	identity :: Flip m a a
identity = m a a -> Flip m a a
forall (v :: * -> * -> *) a e. v e a -> Flip v a e
Flip m a a
forall (m :: * -> * -> *) a. Category m => m a a
identity

instance (Category m, Covariant m m t) => Contravariant (Flip m) m t where
	>-|- :: Flip m a b -> m (t b) (t a)
(>-|-) (Flip m b a
f) = m b a -> m (t b) (t a)
forall (source :: * -> * -> *) (target :: * -> * -> *)
       (t :: * -> *) a b.
Covariant source target t =>
source a b -> target (t a) (t b)
(<-|-) m b a
f

instance (Category m, Covariant m m t) => Contravariant m (Flip m) t where
	>-|- :: m a b -> Flip m (t b) (t a)
(>-|-) m a b
f = m (t a) (t b) -> Flip m (t b) (t a)
forall (v :: * -> * -> *) a e. v e a -> Flip v a e
Flip (m a b -> m (t a) (t b)
forall (source :: * -> * -> *) (target :: * -> * -> *)
       (t :: * -> *) a b.
Covariant source target t =>
source a b -> target (t a) (t b)
(<-|-) m a b
f)

instance (Category m, Covariant m m t) => Covariant (Flip m) (Flip m) t where
	<-|- :: Flip m a b -> Flip m (t a) (t b)
(<-|-) (Flip m b a
f) = m (t b) (t a) -> Flip m (t a) (t b)
forall (v :: * -> * -> *) a e. v e a -> Flip v a e
Flip (m b a -> m (t b) (t a)
forall (source :: * -> * -> *) (target :: * -> * -> *)
       (t :: * -> *) a b.
Covariant source target t =>
source a b -> target (t a) (t b)
(<-|-) m b a
f)