Control.Category.Cartesian

Documentation

class MonoidalProduct k => Cartesian k where

Minimal complete definition

consume, copy, fst', snd'

Methods

(&&&) :: (a `k` l) -> (a `k` r) -> a `k` (l, r)

consume :: a `k` ()

copy :: a `k` (a, a)

fst' :: (l, r) `k` l

snd' :: (l, r) `k` r

Instances

Cartesian ((->) :: Type -> Type -> Type)

Defined in Control.Category.Cartesian

Methods

(&&&) :: (a -> l) -> (a -> r) -> a -> (l, r)

consume :: a -> ()

copy :: a -> (a, a)

fst' :: (l, r) -> l

snd' :: (l, r) -> r

r ~ 'Req 'HasCategory 'HasSymmetricProduct symS 'HasMonoidalProduct monS 'HasCartesian cocart rec fix => Cartesian (Catalyst r c)

Defined in Control.Category.Free

Methods

(&&&) :: Catalyst r c a l -> Catalyst r c a r0 -> Catalyst r c a (l, r0)

consume :: Catalyst r c a ()

copy :: Catalyst r c a (a, a)

fst' :: Catalyst r c (l, r0) l

snd' :: Catalyst r c (l, r0) r0

class MonoidalSum k => Cocartesian k where

Minimal complete definition

injectL, injectR, unify, tag

Methods

(|||) :: (al `k` b) -> (ar `k` b) -> Either al ar `k` b

injectL :: a `k` Either a b

injectR :: a `k` Either b a

unify :: Either a a `k` a

tag :: k (Bool, a) (Either a a)

tags Right when True, Left when False

Instances

Cocartesian ((->) :: Type -> Type -> Type)

Defined in Control.Category.Cartesian

Methods

(|||) :: (al -> b) -> (ar -> b) -> Either al ar -> b

injectL :: a -> Either a b

injectR :: a -> Either b a

unify :: Either a a -> a

tag :: (Bool, a) -> Either a a

r ~ 'Req 'HasCategory symP 'HasSymmetricSum monP 'HasMonoidalSum cart 'HasCocartesian rec fix => Cocartesian (Catalyst r c)

Defined in Control.Category.Free

Methods

(|||) :: Catalyst r c al b -> Catalyst r c ar b -> Catalyst r c (Either al ar) b

injectL :: Catalyst r c a (Either a b)

injectR :: Catalyst r c a (Either b a)

unify :: Catalyst r c (Either a a) a

tag :: Catalyst r c (Bool, a) (Either a a)