Control.Category.Dual

Documentation

newtype Dual k a b

Constructors

Dual

Fields

• dual :: k b a

Instances

Functor α β s t f => Functor α β (Iso α s) (Dual β β t) f

Methods

map :: f a b -> t (f a) (f b)

Category k s => Functor k (k -> *) (Dual k k s) (NT * k * ((->) LiftedRep LiftedRep)) s

Methods

map :: s a b -> t (f a) (f b)

Category k1 k2 => Category k1 (Dual k1 k1 k2)

Methods

id :: cat a a

(.) :: cat b c -> cat a b -> cat a c

Groupoid k1 k2 => Groupoid k1 (Dual k1 k1 k2)

Methods

invert :: k a b -> k b a

Semigroup (k3 b a) => Semigroup (Dual k1 k2 k3 a b)

Methods

(<>) :: Dual k1 k2 k3 a b -> Dual k1 k2 k3 a b -> Dual k1 k2 k3 a b

sconcat :: NonEmpty (Dual k1 k2 k3 a b) -> Dual k1 k2 k3 a b

stimes :: Integral b => b -> Dual k1 k2 k3 a b -> Dual k1 k2 k3 a b

Monoid (k3 b a) => Monoid (Dual k1 k2 k3 a b)

Methods

mempty :: Dual k1 k2 k3 a b

mappend :: Dual k1 k2 k3 a b -> Dual k1 k2 k3 a b -> Dual k1 k2 k3 a b

mconcat :: [Dual k1 k2 k3 a b] -> Dual k1 k2 k3 a b

Group (k3 b a) => Group (Dual k1 k2 k3 a b)

Methods

invert :: Dual k1 k2 k3 a b -> Dual k1 k2 k3 a b