Safe Haskell	Safe
Language	Haskell2010

Control.Categorical.Monad

Documentation

class Endofunctor s m => Monad s m where Source #

Minimal complete definition

unit

Methods

unit :: a `s` m a Source #

join :: m (m a) `s` m a Source #

bind :: (a `s` m b) -> m a `s` m b Source #

Instances

Comonad s f => Monad (Dual s :: β -> β -> Type) (f :: β -> β) Source #
Instance details Defined in Control.Categorical.Monad Methods unit :: Dual s a (f a) Source # join :: Dual s (f (f a)) (f a) Source # bind :: Dual s a (f b) -> Dual s (f a) (f b) Source #
Monad m => Monad ((->) :: Type -> Type -> Type) (m :: Type -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods unit :: a -> m a Source # join :: m (m a) -> m a Source # bind :: (a -> m b) -> m a -> m b Source #
Monad ((->) :: Type -> Type -> Type) f => Monad ((->) :: Type -> Type -> Type) (IdentityT f :: Type -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods unit :: a -> IdentityT f a Source # join :: IdentityT f (IdentityT f a) -> IdentityT f a Source # bind :: (a -> IdentityT f b) -> IdentityT f a -> IdentityT f b Source #
Monad ((->) :: Type -> Type -> Type) f => Monad ((->) :: Type -> Type -> Type) (WriterT Either w f :: Type -> Type) Source #
Instance details Defined in Data.Functor.Trans.Writer Methods unit :: a -> WriterT Either w f a Source # join :: WriterT Either w f (WriterT Either w f a) -> WriterT Either w f a Source # bind :: (a -> WriterT Either w f b) -> WriterT Either w f a -> WriterT Either w f b Source #
(Monoid w, Monad ((->) :: Type -> Type -> Type) f) => Monad ((->) :: Type -> Type -> Type) (WriterT (,) w f :: Type -> Type) Source #
Instance details Defined in Data.Functor.Trans.Writer Methods unit :: a -> WriterT (,) w f a Source # join :: WriterT (,) w f (WriterT (,) w f a) -> WriterT (,) w f a Source # bind :: (a -> WriterT (,) w f b) -> WriterT (,) w f a -> WriterT (,) w f b Source #
Monad ((->) :: Type -> Type -> Type) f => Monad ((->) :: Type -> Type -> Type) (ReaderT ((->) :: Type -> Type -> Type) r f :: Type -> Type) Source #
Instance details Defined in Data.Functor.Trans.Reader Methods unit :: a -> ReaderT (->) r f a Source # join :: ReaderT (->) r f (ReaderT (->) r f a) -> ReaderT (->) r f a Source # bind :: (a -> ReaderT (->) r f b) -> ReaderT (->) r f a -> ReaderT (->) r f b 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 (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 #
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 #

(<=<) :: Monad s m => (b `s` m c) -> (a `s` m b) -> a `s` m c infixr 1 Source #

(>=>) :: Monad s m => (a `s` m b) -> (b `s` m c) -> a `s` m c infixr 1 Source #

newtype Kleisli s m a b Source #

Constructors

Kleisli
Fields kleisli :: a `s` m b

Instances

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 #
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 #
(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 #
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 #
Monad s m => Category (Kleisli s m :: k -> k -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods id :: Kleisli s m a a # (.) :: Kleisli s m b c -> Kleisli s m a b -> Kleisli s m a c #
(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 #
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 #
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 #
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 #
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 #

class Endofunctor s ɯ => Comonad s ɯ where Source #

Minimal complete definition

counit

Methods

counit :: ɯ a `s` a Source #

cut :: ɯ a `s` ɯ (ɯ a) Source #

cobind :: (ɯ a `s` b) -> ɯ a `s` ɯ b Source #

Instances

Comonad ((->) :: Type -> Type -> Type) Identity Source #
Instance details Defined in Control.Categorical.Monad Methods counit :: Identity a -> a Source # cut :: Identity a -> Identity (Identity a) Source # cobind :: (Identity a -> b) -> Identity a -> Identity b Source #
Comonad ((->) :: Type -> Type -> Type) NonEmpty Source #
Instance details Defined in Control.Categorical.Monad Methods counit :: NonEmpty a -> a Source # cut :: NonEmpty a -> NonEmpty (NonEmpty a) Source # cobind :: (NonEmpty a -> b) -> NonEmpty a -> NonEmpty b Source #
Comonad ((->) :: Type -> Type -> Type) ((,) a :: Type -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods counit :: (a, a0) -> a0 Source # cut :: (a, a0) -> (a, (a, a0)) Source # cobind :: ((a, a0) -> b) -> (a, a0) -> (a, b) Source #
Comonad ((->) :: Type -> Type -> Type) (Arg a :: Type -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods counit :: Arg a a0 -> a0 Source # cut :: Arg a a0 -> Arg a (Arg a a0) Source # cobind :: (Arg a a0 -> b) -> Arg a a0 -> Arg a b Source #
Comonad ((->) :: Type -> Type -> Type) f => Comonad ((->) :: Type -> Type -> Type) (IdentityT f :: Type -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods counit :: IdentityT f a -> a Source # cut :: IdentityT f a -> IdentityT f (IdentityT f a) Source # cobind :: (IdentityT f a -> b) -> IdentityT f a -> IdentityT f b Source #
Monoid m => Comonad ((->) :: Type -> Type -> Type) ((->) m :: Type -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods counit :: (m -> a) -> a Source # cut :: (m -> a) -> (m -> (m -> a)) Source # cobind :: ((m -> a) -> b) -> (m -> a) -> (m -> b) Source #
(Comonad ((->) :: Type -> Type -> Type) (p w), Comonad ((->) :: Type -> Type -> Type) f) => Comonad ((->) :: Type -> Type -> Type) (WriterT p w f :: Type -> Type) Source #
Instance details Defined in Data.Functor.Trans.Writer Methods counit :: WriterT p w f a -> a Source # cut :: WriterT p w f a -> WriterT p w f (WriterT p w f a) Source # cobind :: (WriterT p w f a -> b) -> WriterT p w f a -> WriterT p w f b Source #
Comonad ((->) :: Type -> Type -> Type) ɯ => Comonad ((->) :: Type -> Type -> Type) (ReaderT (,) r ɯ :: Type -> Type) Source #
Instance details Defined in Data.Functor.Trans.Reader Methods counit :: ReaderT (,) r ɯ a -> a Source # cut :: ReaderT (,) r ɯ a -> ReaderT (,) r ɯ (ReaderT (,) r ɯ a) Source # cobind :: (ReaderT (,) r ɯ a -> b) -> ReaderT (,) r ɯ a -> ReaderT (,) r ɯ 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 #
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 #

(=<=) :: Comonad s ɯ => (ɯ b `s` c) -> (ɯ a `s` b) -> ɯ a `s` c infixr 1 Source #

(=>=) :: Comonad s ɯ => (ɯ a `s` b) -> (ɯ b `s` c) -> ɯ a `s` c infixr 1 Source #

newtype Cokleisli s ɯ a b Source #

Constructors

Cokleisli
Fields cokleisli :: ɯ a `s` b

Instances

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 :: 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 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 #
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 #
Comonad s ɯ => Category (Cokleisli s ɯ :: k -> k -> Type) Source #
Instance details Defined in Control.Categorical.Monad Methods id :: Cokleisli s ɯ a a # (.) :: Cokleisli s ɯ b c -> Cokleisli s ɯ a b -> Cokleisli s ɯ a c #
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 #
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 #
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 #