Control.Categorical.Monad

Documentation

class Endofunctor s m => Monad s m where

Minimal complete definition

unit

Methods

unit :: a `s` m a

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

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

Instances

Monad m => Monad ((->) :: Type -> Type -> Type) (m :: Type -> Type)

Defined in Control.Categorical.Monad

Methods

unit :: a -> m a

join :: m (m a) -> m a

bind :: (a -> m b) -> m a -> m b

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

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

newtype Kleisli s m a b

Constructors

Kleisli

Fields

• kleisli :: a `s` m b

Instances

Monad s m => Category (Kleisli s m :: k -> k -> Type)

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

class Endofunctor s ɯ => Comonad s ɯ where

Minimal complete definition

counit

Methods

counit :: ɯ a `s` a

cut :: ɯ a `s` ɯ (ɯ a)

cobind :: (ɯ a `s` b) -> ɯ a `s` ɯ b

Instances

Comonad ((->) :: Type -> Type -> Type) Identity

Defined in Control.Categorical.Monad

Methods

counit :: Identity a -> a

cut :: Identity a -> Identity (Identity a)

cobind :: (Identity a -> b) -> Identity a -> Identity b

Comonad ((->) :: Type -> Type -> Type) NonEmpty

Defined in Control.Categorical.Monad

Methods

counit :: NonEmpty a -> a

cut :: NonEmpty a -> NonEmpty (NonEmpty a)

cobind :: (NonEmpty a -> b) -> NonEmpty a -> NonEmpty b

Comonad ((->) :: Type -> Type -> Type) ((,) a :: Type -> Type)

Defined in Control.Categorical.Monad

Methods

counit :: (a, a0) -> a0

cut :: (a, a0) -> (a, (a, a0))

cobind :: ((a, a0) -> b) -> (a, a0) -> (a, b)

Comonad ((->) :: Type -> Type -> Type) (Arg a :: Type -> Type)

Defined in Control.Categorical.Monad

Methods

counit :: Arg a a0 -> a0

cut :: Arg a a0 -> Arg a (Arg a a0)

cobind :: (Arg a a0 -> b) -> Arg a a0 -> Arg a b

Monoid m => Comonad ((->) :: Type -> Type -> Type) ((->) m :: Type -> Type)

Defined in Control.Categorical.Monad

Methods

counit :: (m -> a) -> a

cut :: (m -> a) -> (m -> (m -> a))

cobind :: ((m -> a) -> b) -> (m -> a) -> (m -> b)

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

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

newtype Cokleisli s ɯ a b

Constructors

Cokleisli

Fields

• cokleisli :: ɯ a `s` b

Instances

Comonad s ɯ => Category (Cokleisli s ɯ :: k -> k -> Type)

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