Safe Haskell	Safe
Language	Haskell2010

Control.Categorical.Functor

Synopsis

class (Category s, Category t) => Functor (s :: α -> α -> *) (t :: β -> β -> *) (f :: α -> β) where
- map :: s a b -> t (f a) (f b)
type EndoFunctor s = Functor s s
type Endofunctor s = Functor s s
(<$>) :: Functor s (->) f => s a b -> f a -> f b
newtype NT s f g = NT {
- nt :: forall a. s (f a) (g a)
}

Documentation

class (Category s, Category t) => Functor (s :: α -> α -> *) (t :: β -> β -> *) (f :: α -> β) where Source #

Laws:

map id = id
map (f . g) = map f . map g

Methods

map :: s a b -> t (f a) (f b) Source #

Instances

Functor s t f => Functor (Iso s :: α -> α -> Type) (t :: β -> β -> Type) (f :: α -> β) Source #
Instance details Defined in Data.Morphism.Iso Methods map :: Iso s a b -> t (f a) (f b) Source #
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 #
Monad s m => Functor (Kleisli s m :: β -> β -> Type) (s :: β -> β -> Type) (m :: β -> β) Source #
Instance details Defined in Control.Categorical.Monad Methods map :: Kleisli s m a b -> s (m a) (m b) Source #
Comonad s ɯ => Functor (Cokleisli s ɯ :: β -> β -> Type) (s :: β -> β -> Type) (ɯ :: β -> β) Source #
Instance details Defined in Control.Categorical.Monad Methods map :: Cokleisli s ɯ a b -> s (ɯ a) (ɯ b) Source #
Category s => Functor (s :: α -> α -> Type) ((->) :: Type -> Type -> Type) (s a :: α -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: s a0 b -> s a a0 -> s a b Source #
Category s => Functor (s :: α -> α -> Type) ((->) :: Type -> Type -> Type) (Proxy :: α -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: s a b -> Proxy a -> Proxy b Source #
Functor s ((->) :: Type -> Type -> Type) f => Functor (s :: k -> k -> Type) ((->) :: Type -> Type -> Type) (IdentityT f :: k -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: s a b -> IdentityT f a -> IdentityT f b Source #
Category s => Functor (s :: α -> α -> Type) ((->) :: Type -> Type -> Type) (Const a :: α -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: s a0 b -> Const a a0 -> Const a b Source #
(Functor s ((->) :: Type -> Type -> Type) f, Functor s ((->) :: Type -> Type -> Type) g) => Functor (s :: k -> k -> Type) ((->) :: Type -> Type -> Type) (Product f g :: k -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: s a b -> Product f g a -> Product f g b Source #
(Functor s ((->) :: Type -> Type -> Type) f, Functor s ((->) :: Type -> Type -> Type) g) => Functor (s :: k -> k -> Type) ((->) :: Type -> Type -> Type) (Sum f g :: k -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: s a b -> Sum f g a -> Sum f g b Source #
Functor s t m => Functor (s :: k2 -> k2 -> Type) ((->) :: Type -> Type -> Type) (Kleisli t m a :: k2 -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods map :: s a0 b -> Kleisli t m a a0 -> Kleisli t m a b Source #
Category s => Functor (s :: k2 -> k2 -> Type) ((->) :: Type -> Type -> Type) (Cokleisli s ɯ a :: k2 -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods map :: s a0 b -> Cokleisli s ɯ a a0 -> Cokleisli s ɯ a b Source #
(Functor ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) f, Functor s ((->) :: Type -> Type -> Type) (p w)) => Functor (s :: k2 -> k2 -> Type) ((->) :: Type -> Type -> Type) (WriterT p w f :: k2 -> Type) Source #
Instance details Defined in Data.Functor.Trans.Writer Methods map :: s a b -> WriterT p w f a -> WriterT p w f b Source #
(Functor t ((->) :: Type -> Type -> Type) f, Functor ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (s r)) => Functor (t :: k2 -> k2 -> Type) ((->) :: Type -> Type -> Type) (ReaderT s r f :: k2 -> Type) Source #
Instance details Defined in Data.Functor.Trans.Reader Methods map :: t a b -> ReaderT s r f a -> ReaderT s r f b Source #
Functor s t f => Functor (s :: k2 -> k2 -> Type) ((->) :: Type -> Type -> Type) (ReaderT t r f :: k2 -> Type) Source #
Instance details Defined in Data.Functor.Trans.Reader Methods map :: s a b -> ReaderT t r f a -> ReaderT t r f b Source #
(Functor s (Kleisli ((->) :: Type -> Type -> Type) m) f, Endofunctor ((->) :: Type -> Type -> Type) m) => Functor (s :: k -> k -> Type) (Kleisli ((->) :: Type -> Type -> Type) m :: Type -> Type -> Type) (IdentityT f :: k -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods map :: s a b -> Kleisli (->) m (IdentityT f a) (IdentityT f b) Source #
(Functor s (Cokleisli ((->) :: Type -> Type -> Type) ɯ) f, Endofunctor ((->) :: Type -> Type -> Type) ɯ) => Functor (s :: k -> k -> Type) (Cokleisli ((->) :: Type -> Type -> Type) ɯ :: Type -> Type -> Type) (IdentityT f :: k -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods map :: s a b -> Cokleisli (->) ɯ (IdentityT f a) (IdentityT 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 #
Functor t (NT ((->) :: Type -> Type -> Type) :: (k2 -> Type) -> (k2 -> Type) -> Type) s => Functor (t :: k3 -> k3 -> Type) (NT (NT ((->) :: Type -> Type -> Type) :: (k1 -> Type) -> (k1 -> Type) -> Type) :: ((k1 -> k2) -> k1 -> Type) -> ((k1 -> k2) -> k1 -> Type) -> Type) (ReaderT s :: k3 -> (k1 -> k2) -> k1 -> Type) Source #
Instance details Defined in Data.Functor.Trans.Reader Methods map :: t a b -> NT (NT (->)) (ReaderT s a) (ReaderT s 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 #
Functor f => Functor ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (f :: Type -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: (a -> b) -> f a -> f b Source #
Functor ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) Identity Source #
Instance details Defined in Control.Categorical.Functor Methods map :: (a -> b) -> Identity a -> Identity b Source #
Functor ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Either a :: Type -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: (a0 -> b) -> Either a a0 -> Either a b Source #
Functor ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((,) a :: Type -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: (a0 -> b) -> (a, a0) -> (a, b) Source #
(Traversable f, Monad ((->) :: Type -> Type -> Type) m) => Functor (Kleisli ((->) :: Type -> Type -> Type) m :: Type -> Type -> Type) (Kleisli ((->) :: Type -> Type -> Type) m :: Type -> Type -> Type) (f :: Type -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods map :: Kleisli (->) m a b -> Kleisli (->) m (f a) (f b) Source #
Monad ((->) :: Type -> Type -> Type) m => Functor (Kleisli ((->) :: Type -> Type -> Type) m :: Type -> Type -> Type) (Kleisli ((->) :: Type -> Type -> Type) m :: Type -> Type -> Type) ((,) a :: Type -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods map :: Kleisli (->) m a0 b -> Kleisli (->) m (a, a0) (a, b) Source #
Functor ((->) :: Type -> Type -> Type) (NT ((->) :: Type -> Type -> Type) :: (Type -> Type) -> (Type -> Type) -> Type) Either Source #
Instance details Defined in Control.Categorical.Functor Methods map :: (a -> b) -> NT (->) (Either a) (Either b) Source #
Functor ((->) :: Type -> Type -> Type) (NT ((->) :: Type -> Type -> Type) :: (Type -> Type) -> (Type -> Type) -> Type) (,) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: (a -> b) -> NT (->) ((,) a) ((,) b) Source #
Functor ((->) :: Type -> Type -> Type) (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) (Const :: Type -> k -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: (a -> b) -> NT (->) (Const a) (Const b) Source #
Functor ((->) :: Type -> Type -> Type) (NT (NT ((->) :: Type -> Type -> Type) :: (k2 -> Type) -> (k2 -> Type) -> Type) :: (k1 -> k2 -> Type) -> (k1 -> k2 -> Type) -> Type) (Const2 :: Type -> k1 -> k2 -> Type) Source #
Instance details Defined in Control.Category.Const2 Methods map :: (a -> b) -> NT (NT (->)) (Const2 a) (Const2 b) Source #
Monad ((->) :: Type -> Type -> Type) m => Functor (Kleisli ((->) :: Type -> Type -> Type) m :: Type -> Type -> Type) (NT (Kleisli ((->) :: Type -> Type -> Type) m) :: (Type -> Type) -> (Type -> Type) -> Type) (,) Source #
Instance details Defined in Control.Categorical.Monad Methods map :: Kleisli (->) m a b -> NT (Kleisli (->) m) ((,) a) ((,) b) Source #
Monad ((->) :: Type -> Type -> Type) m => Functor (Kleisli ((->) :: Type -> Type -> Type) m :: Type -> Type -> Type) (NT (NT (Kleisli ((->) :: Type -> Type -> Type) m) :: (k2 -> Type) -> (k2 -> Type) -> Type) :: (k1 -> k2 -> Type) -> (k1 -> k2 -> Type) -> Type) (Const2 :: Type -> k1 -> k2 -> Type) Source #
Instance details Defined in Control.Category.Const2 Methods map :: Kleisli (->) m a b -> NT (NT (Kleisli (->) m)) (Const2 a) (Const2 b) Source #
(Category s, Category t, Functor (NT s :: (k1 -> k4) -> (k1 -> k4) -> Type) (NT t :: (k2 -> k3) -> (k2 -> k3) -> Type) f) => Functor (NT (Dual s) :: (k1 -> k4) -> (k1 -> k4) -> Type) (NT (Dual t) :: (k2 -> k3) -> (k2 -> k3) -> Type) (f :: (k1 -> k4) -> k2 -> k3) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: NT (Dual s) a b -> NT (Dual t) (f a) (f b) Source #
Functor (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) (IdentityT :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: NT (->) a b -> NT (->) (IdentityT a) (IdentityT b) Source #
Functor (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) (NT (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) :: ((k -> Type) -> k -> Type) -> ((k -> Type) -> k -> Type) -> Type) (Product :: (k -> Type) -> (k -> Type) -> k -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: NT (->) a b -> NT (NT (->)) (Product a) (Product b) Source #
Functor (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) (NT (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) :: ((k -> Type) -> k -> Type) -> ((k -> Type) -> k -> Type) -> Type) (Sum :: (k -> Type) -> (k -> Type) -> k -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: NT (->) a b -> NT (NT (->)) (Sum a) (Sum b) Source #
Monad (Dual ((->) :: Type -> Type -> Type)) m => Functor (NT (Kleisli (Dual ((->) :: Type -> Type -> Type)) m) :: (k -> Type) -> (k -> Type) -> Type) (NT (Kleisli (Dual ((->) :: Type -> Type -> Type)) m) :: (k -> Type) -> (k -> Type) -> Type) (IdentityT :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods map :: NT (Kleisli (Dual (->)) m) a b -> NT (Kleisli (Dual (->)) m) (IdentityT a) (IdentityT b) Source #
Monad ((->) :: Type -> Type -> Type) m => Functor (NT (Kleisli ((->) :: Type -> Type -> Type) m) :: (k -> Type) -> (k -> Type) -> Type) (NT (Kleisli ((->) :: Type -> Type -> Type) m) :: (k -> Type) -> (k -> Type) -> Type) (IdentityT :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods map :: NT (Kleisli (->) m) a b -> NT (Kleisli (->) m) (IdentityT a) (IdentityT b) Source #
Comonad ((->) :: Type -> Type -> Type) ɯ => Functor (NT (Cokleisli ((->) :: Type -> Type -> Type) ɯ) :: (k -> Type) -> (k -> Type) -> Type) (NT (Cokleisli ((->) :: Type -> Type -> Type) ɯ) :: (k -> Type) -> (k -> Type) -> Type) (IdentityT :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods map :: NT (Cokleisli (->) ɯ) a b -> NT (Cokleisli (->) ɯ) (IdentityT a) (IdentityT b) Source #
Functor (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) (Product f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: NT (->) a b -> NT (->) (Product f a) (Product f b) Source #
Functor (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) (Sum f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: NT (->) a b -> NT (->) (Sum f a) (Sum f b) Source #
Functor (NT ((->) :: Type -> Type -> Type) :: (k1 -> Type) -> (k1 -> Type) -> Type) (NT (NT ((->) :: Type -> Type -> Type) :: (k2 -> Type) -> (k2 -> Type) -> Type) :: ((k2 -> k1) -> k2 -> Type) -> ((k2 -> k1) -> k2 -> Type) -> Type) (Compose :: (k1 -> Type) -> (k2 -> k1) -> k2 -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: NT (->) a b -> NT (NT (->)) (Compose a) (Compose b) Source #
Functor s ((->) :: Type -> Type -> Type) f => Functor (NT s :: (k1 -> k2) -> (k1 -> k2) -> Type) (NT ((->) :: Type -> Type -> Type) :: (k1 -> Type) -> (k1 -> Type) -> Type) (Compose f :: (k1 -> k2) -> k1 -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: NT s a b -> NT (->) (Compose f a) (Compose f b) Source #
Functor (NT ((->) :: Type -> Type -> Type) :: (k3 -> Type) -> (k3 -> Type) -> Type) (NT ((->) :: Type -> Type -> Type) :: (k2 -> Type) -> (k2 -> Type) -> Type) (WriterT p w :: (k3 -> Type) -> k2 -> Type) Source #
Instance details Defined in Data.Functor.Trans.Writer Methods map :: NT (->) a b -> NT (->) (WriterT p w a) (WriterT p w b) Source #
Functor t ((->) :: Type -> Type -> Type) (s r) => Functor (NT t :: (k1 -> k3) -> (k1 -> k3) -> Type) (NT ((->) :: Type -> Type -> Type) :: (k1 -> Type) -> (k1 -> Type) -> Type) (ReaderT s r :: (k1 -> k3) -> k1 -> Type) Source #
Instance details Defined in Data.Functor.Trans.Reader Methods map :: NT t a b -> NT (->) (ReaderT s r a) (ReaderT s r b) Source #

type EndoFunctor s = Functor s s Source #

Deprecated: Use Endofunctor

type Endofunctor s = Functor s s Source #

(<$>) :: Functor s (->) f => s a b -> f a -> f b infixl 4 Source #

newtype NT s f g Source #

Constructors

NT
Fields nt :: forall a. s (f a) (g a)

Instances

(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 #
Functor t (NT ((->) :: Type -> Type -> Type) :: (k2 -> Type) -> (k2 -> Type) -> Type) s => Functor (t :: k3 -> k3 -> Type) (NT (NT ((->) :: Type -> Type -> Type) :: (k1 -> Type) -> (k1 -> Type) -> Type) :: ((k1 -> k2) -> k1 -> Type) -> ((k1 -> k2) -> k1 -> Type) -> Type) (ReaderT s :: k3 -> (k1 -> k2) -> k1 -> Type) Source #
Instance details Defined in Data.Functor.Trans.Reader Methods map :: t a b -> NT (NT (->)) (ReaderT s a) (ReaderT s 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 #
Functor ((->) :: Type -> Type -> Type) (NT ((->) :: Type -> Type -> Type) :: (Type -> Type) -> (Type -> Type) -> Type) Either Source #
Instance details Defined in Control.Categorical.Functor Methods map :: (a -> b) -> NT (->) (Either a) (Either b) Source #
Functor ((->) :: Type -> Type -> Type) (NT ((->) :: Type -> Type -> Type) :: (Type -> Type) -> (Type -> Type) -> Type) (,) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: (a -> b) -> NT (->) ((,) a) ((,) b) Source #
Functor ((->) :: Type -> Type -> Type) (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) (Const :: Type -> k -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: (a -> b) -> NT (->) (Const a) (Const b) Source #
Functor ((->) :: Type -> Type -> Type) (NT (NT ((->) :: Type -> Type -> Type) :: (k2 -> Type) -> (k2 -> Type) -> Type) :: (k1 -> k2 -> Type) -> (k1 -> k2 -> Type) -> Type) (Const2 :: Type -> k1 -> k2 -> Type) Source #
Instance details Defined in Control.Category.Const2 Methods map :: (a -> b) -> NT (NT (->)) (Const2 a) (Const2 b) Source #
Monad ((->) :: Type -> Type -> Type) m => Functor (Kleisli ((->) :: Type -> Type -> Type) m :: Type -> Type -> Type) (NT (Kleisli ((->) :: Type -> Type -> Type) m) :: (Type -> Type) -> (Type -> Type) -> Type) (,) Source #
Instance details Defined in Control.Categorical.Monad Methods map :: Kleisli (->) m a b -> NT (Kleisli (->) m) ((,) a) ((,) b) Source #
Monad ((->) :: Type -> Type -> Type) m => Functor (Kleisli ((->) :: Type -> Type -> Type) m :: Type -> Type -> Type) (NT (NT (Kleisli ((->) :: Type -> Type -> Type) m) :: (k2 -> Type) -> (k2 -> Type) -> Type) :: (k1 -> k2 -> Type) -> (k1 -> k2 -> Type) -> Type) (Const2 :: Type -> k1 -> k2 -> Type) Source #
Instance details Defined in Control.Category.Const2 Methods map :: Kleisli (->) m a b -> NT (NT (Kleisli (->) m)) (Const2 a) (Const2 b) Source #
(Category s, Category t, Functor (NT s :: (k1 -> k4) -> (k1 -> k4) -> Type) (NT t :: (k2 -> k3) -> (k2 -> k3) -> Type) f) => Functor (NT (Dual s) :: (k1 -> k4) -> (k1 -> k4) -> Type) (NT (Dual t) :: (k2 -> k3) -> (k2 -> k3) -> Type) (f :: (k1 -> k4) -> k2 -> k3) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: NT (Dual s) a b -> NT (Dual t) (f a) (f b) Source #
Functor (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) (IdentityT :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: NT (->) a b -> NT (->) (IdentityT a) (IdentityT b) Source #
Functor (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) (NT (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) :: ((k -> Type) -> k -> Type) -> ((k -> Type) -> k -> Type) -> Type) (Product :: (k -> Type) -> (k -> Type) -> k -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: NT (->) a b -> NT (NT (->)) (Product a) (Product b) Source #
Functor (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) (NT (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) :: ((k -> Type) -> k -> Type) -> ((k -> Type) -> k -> Type) -> Type) (Sum :: (k -> Type) -> (k -> Type) -> k -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: NT (->) a b -> NT (NT (->)) (Sum a) (Sum b) Source #
Monad (Dual ((->) :: Type -> Type -> Type)) m => Functor (NT (Kleisli (Dual ((->) :: Type -> Type -> Type)) m) :: (k -> Type) -> (k -> Type) -> Type) (NT (Kleisli (Dual ((->) :: Type -> Type -> Type)) m) :: (k -> Type) -> (k -> Type) -> Type) (IdentityT :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods map :: NT (Kleisli (Dual (->)) m) a b -> NT (Kleisli (Dual (->)) m) (IdentityT a) (IdentityT b) Source #
Monad ((->) :: Type -> Type -> Type) m => Functor (NT (Kleisli ((->) :: Type -> Type -> Type) m) :: (k -> Type) -> (k -> Type) -> Type) (NT (Kleisli ((->) :: Type -> Type -> Type) m) :: (k -> Type) -> (k -> Type) -> Type) (IdentityT :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods map :: NT (Kleisli (->) m) a b -> NT (Kleisli (->) m) (IdentityT a) (IdentityT b) Source #
Comonad ((->) :: Type -> Type -> Type) ɯ => Functor (NT (Cokleisli ((->) :: Type -> Type -> Type) ɯ) :: (k -> Type) -> (k -> Type) -> Type) (NT (Cokleisli ((->) :: Type -> Type -> Type) ɯ) :: (k -> Type) -> (k -> Type) -> Type) (IdentityT :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods map :: NT (Cokleisli (->) ɯ) a b -> NT (Cokleisli (->) ɯ) (IdentityT a) (IdentityT b) Source #
Functor (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) (Product f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: NT (->) a b -> NT (->) (Product f a) (Product f b) Source #
Functor (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) (Sum f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: NT (->) a b -> NT (->) (Sum f a) (Sum f b) Source #
Functor (NT ((->) :: Type -> Type -> Type) :: (k1 -> Type) -> (k1 -> Type) -> Type) (NT (NT ((->) :: Type -> Type -> Type) :: (k2 -> Type) -> (k2 -> Type) -> Type) :: ((k2 -> k1) -> k2 -> Type) -> ((k2 -> k1) -> k2 -> Type) -> Type) (Compose :: (k1 -> Type) -> (k2 -> k1) -> k2 -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: NT (->) a b -> NT (NT (->)) (Compose a) (Compose b) Source #
Functor s ((->) :: Type -> Type -> Type) f => Functor (NT s :: (k1 -> k2) -> (k1 -> k2) -> Type) (NT ((->) :: Type -> Type -> Type) :: (k1 -> Type) -> (k1 -> Type) -> Type) (Compose f :: (k1 -> k2) -> k1 -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods map :: NT s a b -> NT (->) (Compose f a) (Compose f b) Source #
Functor (NT ((->) :: Type -> Type -> Type) :: (k3 -> Type) -> (k3 -> Type) -> Type) (NT ((->) :: Type -> Type -> Type) :: (k2 -> Type) -> (k2 -> Type) -> Type) (WriterT p w :: (k3 -> Type) -> k2 -> Type) Source #
Instance details Defined in Data.Functor.Trans.Writer Methods map :: NT (->) a b -> NT (->) (WriterT p w a) (WriterT p w b) Source #
Functor t ((->) :: Type -> Type -> Type) (s r) => Functor (NT t :: (k1 -> k3) -> (k1 -> k3) -> Type) (NT ((->) :: Type -> Type -> Type) :: (k1 -> Type) -> (k1 -> Type) -> Type) (ReaderT s r :: (k1 -> k3) -> k1 -> Type) Source #
Instance details Defined in Data.Functor.Trans.Reader Methods map :: NT t a b -> NT (->) (ReaderT s r a) (ReaderT s r b) Source #
Category s => Category (NT s :: (k1 -> k2) -> (k1 -> k2) -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods id :: NT s a a # (.) :: NT s b c -> NT s a b -> NT s a c #
Groupoid s => Groupoid (NT s :: (k1 -> k2) -> (k1 -> k2) -> Type) Source #
Instance details Defined in Control.Categorical.Functor Methods invert :: NT s a b -> NT s b a Source #
(Category s, Comonad (NT s :: (k1 -> k2) -> (k1 -> k2) -> Type) f) => Monad (NT (Dual s) :: (k1 -> k2) -> (k1 -> k2) -> Type) (f :: (k1 -> k2) -> k1 -> k2) Source #
Instance details Defined in Control.Categorical.Monad Methods unit :: NT (Dual s) a (f a) Source # join :: NT (Dual s) (f (f a)) (f a) Source # bind :: NT (Dual s) a (f b) -> NT (Dual s) (f a) (f b) Source #
Monad ((->) :: Type -> Type -> Type) m => Comonad (NT (Kleisli ((->) :: Type -> Type -> Type) m) :: (k -> Type) -> (k -> Type) -> Type) (IdentityT :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods counit :: NT (Kleisli (->) m) (IdentityT a) a Source # cut :: NT (Kleisli (->) m) (IdentityT a) (IdentityT (IdentityT a)) Source # cobind :: NT (Kleisli (->) m) (IdentityT a) b -> NT (Kleisli (->) m) (IdentityT a) (IdentityT b) Source #
Comonad (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) (IdentityT :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods counit :: NT (->) (IdentityT a) a Source # cut :: NT (->) (IdentityT a) (IdentityT (IdentityT a)) Source # cobind :: NT (->) (IdentityT a) b -> NT (->) (IdentityT a) (IdentityT b) Source #
Comonad ((->) :: Type -> Type -> Type) ɯ => Comonad (NT (Cokleisli ((->) :: Type -> Type -> Type) ɯ) :: (k -> Type) -> (k -> Type) -> Type) (IdentityT :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods counit :: NT (Cokleisli (->) ɯ) (IdentityT a) a Source # cut :: NT (Cokleisli (->) ɯ) (IdentityT a) (IdentityT (IdentityT a)) Source # cobind :: NT (Cokleisli (->) ɯ) (IdentityT a) b -> NT (Cokleisli (->) ɯ) (IdentityT a) (IdentityT b) Source #
Monad (NT ((->) :: Type -> Type -> Type) :: (k -> Type) -> (k -> Type) -> Type) (IdentityT :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods unit :: NT (->) a (IdentityT a) Source # join :: NT (->) (IdentityT (IdentityT a)) (IdentityT a) Source # bind :: NT (->) a (IdentityT b) -> NT (->) (IdentityT a) (IdentityT b) Source #
Monad ((->) :: Type -> Type -> Type) m => Monad (NT (Kleisli ((->) :: Type -> Type -> Type) m) :: (k -> Type) -> (k -> Type) -> Type) (IdentityT :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods unit :: NT (Kleisli (->) m) a (IdentityT a) Source # join :: NT (Kleisli (->) m) (IdentityT (IdentityT a)) (IdentityT a) Source # bind :: NT (Kleisli (->) m) a (IdentityT b) -> NT (Kleisli (->) m) (IdentityT a) (IdentityT b) Source #
Comonad ((->) :: Type -> Type -> Type) ɯ => Monad (NT (Cokleisli ((->) :: Type -> Type -> Type) ɯ) :: (k -> Type) -> (k -> Type) -> Type) (IdentityT :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods unit :: NT (Cokleisli (->) ɯ) a (IdentityT a) Source # join :: NT (Cokleisli (->) ɯ) (IdentityT (IdentityT a)) (IdentityT a) Source # bind :: NT (Cokleisli (->) ɯ) a (IdentityT b) -> NT (Cokleisli (->) ɯ) (IdentityT a) (IdentityT b) Source #
Comonad ((->) :: Type -> Type -> Type) (s r) => Comonad (NT ((->) :: Type -> Type -> Type) :: (k1 -> Type) -> (k1 -> Type) -> Type) (ReaderT s r :: (k1 -> Type) -> k1 -> Type) Source #
Instance details Defined in Data.Functor.Trans.Reader Methods counit :: NT (->) (ReaderT s r a) a Source # cut :: NT (->) (ReaderT s r a) (ReaderT s r (ReaderT s r a)) Source # cobind :: NT (->) (ReaderT s r a) b -> NT (->) (ReaderT s r a) (ReaderT s r b) Source #
Monad ((->) :: Type -> Type -> Type) (s r) => Monad (NT ((->) :: Type -> Type -> Type) :: (k1 -> Type) -> (k1 -> Type) -> Type) (ReaderT s r :: (k1 -> Type) -> k1 -> Type) Source #
Instance details Defined in Data.Functor.Trans.Reader Methods unit :: NT (->) a (ReaderT s r a) Source # join :: NT (->) (ReaderT s r (ReaderT s r a)) (ReaderT s r a) Source # bind :: NT (->) a (ReaderT s r b) -> NT (->) (ReaderT s r a) (ReaderT s r b) Source #