-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Adjunctions
--   
--   Adjunctions
@package adjunctions
@version 0.3

module Data.Functor.Contravariant.DualAdjunction

-- | An adjunction from Hask to Hask^op
--   
--   <pre>
--   Hask (f a) b ~ Op a (g b)
--   </pre>
--   
--   <pre>
--   rightAdjunct unit = id
--   leftAdjunct counit = id
--   </pre>
class (Contravariant f, Contravariant g) => DualAdjunction f g | f -> g, g -> f
unitOp :: DualAdjunction f g => g (f a) -> a
counitOp :: DualAdjunction f g => f (g a) -> a
leftAdjunctOp :: DualAdjunction f g => (f a -> b) -> g b -> a
rightAdjunctOp :: DualAdjunction f g => (g b -> a) -> f a -> b

module Data.Functor.Contravariant.Adjunction

-- | An adjunction from Hask^op to Hask
--   
--   <pre>
--   Op (f a) b ~ Hask a (g b)
--   </pre>
--   
--   <pre>
--   rightAdjunct unit = id
--   leftAdjunct counit = id
--   </pre>
class (Contravariant f, Contravariant g) => Adjunction f g | f -> g, g -> f
unit :: Adjunction f g => a -> g (f a)
counit :: Adjunction f g => a -> f (g a)
leftAdjunct :: Adjunction f g => (b -> f a) -> a -> g b
rightAdjunct :: Adjunction f g => (a -> g b) -> b -> f a

-- | A representation of a contravariant functor
data Representation f x
Representation :: (forall a. (a -> x) -> f a) -> (forall a. f a -> (a -> x)) -> Representation f x
rep :: Representation f x -> forall a. (a -> x) -> f a
unrep :: Representation f x -> forall a. f a -> (a -> x)

-- | Represent a contravariant functor that has a left adjoint
repAdjunction :: Adjunction f g => Representation g (f ())
repFlippedAdjunction :: Adjunction f g => Representation f (g ())
instance Adjunction Predicate Predicate
instance Adjunction (Op r) (Op r)


module Data.Functor.Adjunction

-- | An adjunction between Hask and Hask.
--   
--   <pre>
--   rightAdjunct unit = id
--   leftAdjunct counit = id 
--   </pre>
class (Functor f, Functor g) => Adjunction f g | f -> g, g -> f
unit :: Adjunction f g => a -> g (f a)
counit :: Adjunction f g => f (g a) -> a
leftAdjunct :: Adjunction f g => (f a -> b) -> a -> g b
rightAdjunct :: Adjunction f g => (a -> g b) -> f a -> b
data Representation f x
Representation :: (forall a. (x -> a) -> f a) -> (forall a. f a -> x -> a) -> Representation f x
rep :: Representation f x -> forall a. (x -> a) -> f a
unrep :: Representation f x -> forall a. f a -> x -> a
repAdjunction :: Adjunction f g => Representation g (f ())
instance (Adjunction f g, DualAdjunction f' g') => Adjunction (Compose f' f) (Compose g g')
instance (Adjunction f g, Adjunction f' g') => Adjunction (Compose f' f) (Compose g g')
instance Adjunction w m => Adjunction (EnvT e w) (ReaderT e m)
instance Adjunction f g => Adjunction (IdentityT f) (IdentityT g)
instance Adjunction Identity Identity
instance Adjunction ((,) e) ((->) e)


module Control.Monad.Trans.Adjoint
type Adjoint f g = AdjointT f g Identity
runAdjoint :: Functor g => Adjoint f g a -> g (f a)
adjoint :: Functor g => g (f a) -> Adjoint f g a
newtype AdjointT f g m a
AdjointT :: g (m (f a)) -> AdjointT f g m a
runAdjointT :: AdjointT f g m a -> g (m (f a))
instance (Adjunction f g, Traversable f) => MonadTrans (AdjointT f g)
instance (Adjunction f g, Monad m) => Monad (AdjointT f g m)
instance (Adjunction f g, Monad m) => Applicative (AdjointT f g m)
instance (Adjunction f g, Monad m) => Functor (AdjointT f g m)


module Control.Comonad.Trans.Adjoint
type Adjoint f g = AdjointT f g Identity
runAdjoint :: Functor f => Adjoint f g a -> f (g a)
adjoint :: Functor f => f (g a) -> Adjoint f g a
newtype AdjointT f g w a
AdjointT :: f (w (g a)) -> AdjointT f g w a
runAdjointT :: AdjointT f g w a -> f (w (g a))
instance (Adjunction f g, Distributive g) => ComonadTrans (AdjointT f g)
instance (Adjunction f g, Comonad m) => Comonad (AdjointT f g m)
instance (Adjunction f g, Functor m) => Functor (AdjointT f g m)


module Data.Functor.Zap
newtype Zap f g
Zap :: (forall a b c. (a -> b -> c) -> f a -> g b -> c) -> Zap f g
zapWith :: Zap f g -> forall a b c. (a -> b -> c) -> f a -> g b -> c
zap :: Zap f g -> f (a -> b) -> g a -> b
flipZap :: Zap f g -> Zap g f
zapAdjunction :: Adjunction f g => Zap g f
composeZap :: Zap f g -> Zap h i -> Zap (Compose f h) (Compose g i)
newtype Bizap p q
Bizap :: (forall a b c d e. (a -> c -> e) -> (b -> d -> e) -> p a b -> q c d -> e) -> Bizap p q
bizapWith :: Bizap p q -> forall a b c d e. (a -> c -> e) -> (b -> d -> e) -> p a b -> q c d -> e
bizap :: Bizap p q -> p (a -> c) (b -> c) -> q a b -> c
flipBizap :: Bizap p q -> Bizap q p
bizapProductSum :: Bizap (,) Either


-- | Use a contravariant adjunction to Hask^op to build a <a>Comonad</a> to
--   <a>Monad</a> transformer.
module Control.Monad.Contra
type Contra f g = ContraT f g Identity
runContra :: Contravariant g => Contra f g a -> g (f a)
contra :: Contravariant g => g (f a) -> Contra f g a
newtype ContraT f g w a
ContraT :: g (w (f a)) -> ContraT f g w a
runContraT :: ContraT f g w a -> g (w (f a))
instance (Adjunction f g, Comonad w) => Monad (ContraT f g w)
instance (Adjunction f g, Comonad w) => Applicative (ContraT f g w)
instance (Adjunction f g, Functor w) => Functor (ContraT f g w)