Data.Label.Abstract

Documentation

data Point (~>) f i o

Abstract Point datatype. The getter and setter functions work in some arrow.

Constructors

Point

Fields

_get :: f ~> o

_set :: (i, f) ~> f

Instances

Arrow ~> => Functor (Point ~> f i)

Arrow ~> => Applicative (Point ~> f i)

_modify :: ArrowApply ~> => Point ~> f i o -> (o ~> i, f) ~> f

Modification as a compositon of a getter and setter. Unfortunately, ArrowApply is needed for this composition.

newtype Lens (~>) f a

Abstract Lens datatype. The getter and setter functions work in some arrow. Arrows allow for effectful lenses, for example, lenses that might fail or use state.

Constructors

Lens

Fields

unLens :: Point ~> f a a

Instances

Arrow ~> => Iso ~> (Lens ~> f)

We can diverge Lenses using an isomorphism.

ArrowApply ~> => Category (Lens ~>)

lens :: (f ~> a) -> ((a, f) ~> f) -> Lens ~> f a

Create a lens out of a getter and setter.

get :: Arrow ~> => Lens ~> f a -> f ~> a

Get the getter arrow from a lens.

set :: Arrow ~> => Lens ~> f a -> (a, f) ~> f

Get the setter arrow from a lens.

modify :: ArrowApply ~> => Lens ~> f o -> (o ~> o, f) ~> f

Get the modifier arrow from a lens.

bimap :: Arrow ~> => (o' ~> o) -> (i ~> i') -> Point ~> f i' o' -> Point ~> f i o

Make a Point diverge in two directions.

for :: Arrow ~> => (i ~> o) -> Lens ~> f o -> Point ~> f i o

data Bijection (~>) a b

The bijections datatype, an arrow that works in two directions.

Constructors

Bij

Fields

fw :: a ~> b

bw :: b ~> a

Instances

Arrow ~> => Iso ~> (Bijection ~> a)

We can diverge Bijections using an isomorphism.

Category ~> => Category (Bijection ~>)

Bijections as categories.

liftBij :: Functor f => Bijection (->) a b -> Bijection (->) (f a) (f b)

Lifting Bijections.

class Iso (~>) f where

The isomorphism type class is like a Functor but works in two directions.

Methods

iso :: Bijection ~> a b -> f a ~> f b

Instances

Arrow ~> => Iso ~> (Bijection ~> a)

We can diverge Bijections using an isomorphism.

Arrow ~> => Iso ~> (Lens ~> f)

We can diverge Lenses using an isomorphism.