Data.Functor.Day.Profunctor

class Profunctor p  where

A profunctor in the category of functors and natural transformations.

Members

• dimap :: forall b a t s. (s ~> a) -> (b ~> t) -> p a b -> p s t

Instances

• Profunctor NT

class (Profunctor p) <= Strong p  where

A strong profunctor with respect to Day convolution.

Members

• first :: forall x b a. p a b -> p (a ⊗ x) (b ⊗ x)
• second :: forall x b a. p a b -> p (x ⊗ a) (x ⊗ b)

Instances

• Strong NT

newtype NT f g

Natural transformations form a Strong profunctor.

Constructors

• NT (f ~> g)

Instances

• Profunctor NT
• Strong NT

runNT :: forall g f. NT f g -> f ~> g

type Optic p (s :: Type -> Type) (t :: Type -> Type) a b = p a b -> p s t

A general type for profunctor optics in the functor category.

type Iso s t a b = forall p. Profunctor p => Optic p s t a b

An isomorphism of functors.

type Lens s t a b = forall p. Strong p => Optic p s t a b

A lens with respect to Day convolution, which identifies one functor as a Day convolution of another with a third, unknown functor.

lens :: forall b a t s. Functor b => (s ~> a ⊗ (Hom b t)) -> Lens s t a b

Create a profunctor lens from a getter-setter pair.

hoistOf :: forall b a t s. Optic NT s t a b -> (a ~> b) -> s ~> t

Hoist a natural transformation over the specified optic.