License	BSD-style (see the file LICENSE)
Maintainer	sjoerd@w3future.com
Stability	experimental
Portability	non-portable
Safe Haskell	None
Language	Haskell2010

Data.Category.Kleisli

Description

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

Documentation

data Kleisli m a b where Source #

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) Source #	The category of Kleisli arrows.
Instance details Defined in Data.Category.Kleisli Methods src :: Kleisli m a b -> Obj (Kleisli m) a Source # tgt :: Kleisli m a b -> Obj (Kleisli m) b Source # (.) :: Kleisli m b c -> Kleisli m a b -> Kleisli m a c Source #

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

Constructors

Instances

(Functor m, Dom m ~ k, Cod m ~ k) => Functor (KleisliFree m) Source #
Instance details Defined in Data.Category.Kleisli Associated Types type Dom (KleisliFree m) :: Type -> Type -> Type Source # type Cod (KleisliFree m) :: Type -> Type -> Type Source # type (KleisliFree m) :% a :: Type Source # Methods (%) :: KleisliFree m -> Dom (KleisliFree m) a b -> Cod (KleisliFree m) (KleisliFree m :% a) (KleisliFree m :% b) Source #
type Dom (KleisliFree m) Source #
Instance details Defined in Data.Category.Kleisli type Dom (KleisliFree m) = Dom m
type Cod (KleisliFree m) Source #
Instance details Defined in Data.Category.Kleisli type Cod (KleisliFree m) = Kleisli m
type (KleisliFree m) :% a Source #
Instance details Defined in Data.Category.Kleisli type (KleisliFree m) :% a = a

Constructors

Instances

(Functor m, Dom m ~ k, Cod m ~ k) => Functor (KleisliForget m) Source #
Instance details Defined in Data.Category.Kleisli Associated Types type Dom (KleisliForget m) :: Type -> Type -> Type Source # type Cod (KleisliForget m) :: Type -> Type -> Type Source # type (KleisliForget m) :% a :: Type Source # Methods (%) :: KleisliForget m -> Dom (KleisliForget m) a b -> Cod (KleisliForget m) (KleisliForget m :% a) (KleisliForget m :% b) Source #
type Dom (KleisliForget m) Source #
Instance details Defined in Data.Category.Kleisli type Dom (KleisliForget m) = Kleisli m
type Cod (KleisliForget m) Source #
Instance details Defined in Data.Category.Kleisli type Cod (KleisliForget m) = Dom m
type (KleisliForget m) :% a Source #
Instance details Defined in Data.Category.Kleisli type (KleisliForget m) :% a = m :% a