Safe Haskell	None
Language	Haskell2010

Control.Category.Dual

Documentation

newtype Dual k a b Source #

Constructors

Dual
Fields dual :: k b a

Instances

Functor s t f => Functor (Iso s :: α -> α -> Type) (Dual t :: β -> β -> Type) (f :: α -> β) Source #
Instance details Defined in Data.Morphism.Iso Methods map :: Iso s a b -> Dual t (f a) (f b) Source #
Functor s t f => Functor (Dual s :: α -> α -> Type) (Dual t :: β -> β -> Type) (f :: α -> β) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: Dual s a b -> Dual t (f a) (f b) Source #
(Category s, Category t, Functor s (NT (Dual t) :: (k1 -> k2) -> (k1 -> k2) -> Type) f) => Functor (s :: α -> α -> Type) (Dual (NT t :: (k1 -> k2) -> (k1 -> k2) -> Type) :: (k1 -> k2) -> (k1 -> k2) -> Type) (f :: α -> k1 -> k2) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: s a b -> Dual (NT t) (f a) (f b) Source #
(Category t, Functor s (NT t :: (k1 -> k2) -> (k1 -> k2) -> Type) f) => Functor (Dual s :: α -> α -> Type) (NT (Dual t) :: (k1 -> k2) -> (k1 -> k2) -> Type) (f :: α -> k1 -> k2) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: Dual s a b -> NT (Dual t) (f a) (f b) Source #
Category s => Functor (Dual s :: k -> k -> Type) (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) (s :: k -> k -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: Dual s a b -> NT (->) (s a) (s b) Source #
Category s => Functor (Dual s :: k2 -> k2 -> Type) (NT ((->) :: Type -> Type -> Type) :: (k1 -> Type) -> (k1 -> Type) -> Type) (Kleisli s m :: k2 -> k1 -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods map :: Dual s a b -> NT (->) (Kleisli s m a) (Kleisli s m b) Source #
Functor s t ɯ => Functor (Dual s :: k2 -> k2 -> Type) (NT ((->) :: Type -> Type -> Type) :: (k1 -> Type) -> (k1 -> Type) -> Type) (Cokleisli t ɯ :: k2 -> k1 -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods map :: Dual s a b -> NT (->) (Cokleisli t ɯ a) (Cokleisli t ɯ b) Source #
Category k2 => Category (Dual k2 :: k1 -> k1 -> Type) Source #
Instance details Defined in Control.Category.Dual Methods id :: Dual k2 a a # (.) :: Dual k2 b c -> Dual k2 a b -> Dual k2 a c #
Groupoid k2 => Groupoid (Dual k2 :: k1 -> k1 -> Type) Source #
Instance details Defined in Control.Category.Dual Methods invert :: Dual k2 a b -> Dual k2 b a Source #
Semigroup (k3 b a) => Semigroup (Dual k3 a b) Source #
Instance details Defined in Control.Category.Dual Methods (<>) :: Dual k3 a b -> Dual k3 a b -> Dual k3 a b # sconcat :: NonEmpty (Dual k3 a b) -> Dual k3 a b # stimes :: Integral b0 => b0 -> Dual k3 a b -> Dual k3 a b #
Monoid (k3 b a) => Monoid (Dual k3 a b) Source #
Instance details Defined in Control.Category.Dual Methods mempty :: Dual k3 a b # mappend :: Dual k3 a b -> Dual k3 a b -> Dual k3 a b # mconcat :: [Dual k3 a b] -> Dual k3 a b #
Group (k3 b a) => Group (Dual k3 a b) Source #
Instance details Defined in Control.Category.Dual Methods invert :: Dual k3 a b -> Dual k3 a b #