Data.Category.Kleisli

This is an attempt at the Kleisli category, and the construction of an adjunction for each monad.

Documentation

data Kleisli m a b where

Constructors

Kleisli :: (Functor m, Dom m ~ k, Cod m ~ k) => Monad m -> Obj k b -> k a (m :% b) -> Kleisli m a b

Instances

Category (Kleisli m :: Type -> Type -> Type)

The category of Kleisli arrows.

Defined in Data.Category.Kleisli

Methods

src :: Kleisli m a b -> Obj (Kleisli m) a

tgt :: Kleisli m a b -> Obj (Kleisli m) b

(.) :: Kleisli m b c -> Kleisli m a b -> Kleisli m a c

kleisliId :: (Functor m, Dom m ~ k, Cod m ~ k) => Monad m -> Obj k a -> Kleisli m a a

newtype KleisliFree m

Constructors

KleisliFree (Monad m)

Instances

(Functor m, Dom m ~ k, Cod m ~ k) => Functor (KleisliFree m)

Defined in Data.Category.Kleisli

Associated Types

type Dom (KleisliFree m) :: Type -> Type -> Type

type Cod (KleisliFree m) :: Type -> Type -> Type

type (KleisliFree m) :% a :: Type

Methods

(%) :: KleisliFree m -> Dom (KleisliFree m) a b -> Cod (KleisliFree m) (KleisliFree m :% a) (KleisliFree m :% b)

type Dom (KleisliFree m)

Defined in Data.Category.Kleisli

type Dom (KleisliFree m) = Dom m

type Cod (KleisliFree m)

Defined in Data.Category.Kleisli

type Cod (KleisliFree m) = Kleisli m

type (KleisliFree m) :% a

Defined in Data.Category.Kleisli

type (KleisliFree m) :% a = a

data KleisliForget m

Constructors

KleisliForget

Instances

(Functor m, Dom m ~ k, Cod m ~ k) => Functor (KleisliForget m)

Defined in Data.Category.Kleisli

Associated Types

type Dom (KleisliForget m) :: Type -> Type -> Type

type Cod (KleisliForget m) :: Type -> Type -> Type

type (KleisliForget m) :% a :: Type

Methods

(%) :: KleisliForget m -> Dom (KleisliForget m) a b -> Cod (KleisliForget m) (KleisliForget m :% a) (KleisliForget m :% b)

type Dom (KleisliForget m)

Defined in Data.Category.Kleisli

type Dom (KleisliForget m) = Kleisli m

type Cod (KleisliForget m)

Defined in Data.Category.Kleisli

type Cod (KleisliForget m) = Dom m

type (KleisliForget m) :% a

Defined in Data.Category.Kleisli

type (KleisliForget m) :% a = m :% a

kleisliAdj :: (Functor m, Dom m ~ k, Cod m ~ k) => Monad m -> Adjunction (Kleisli m) k (KleisliFree m) (KleisliForget m)