Data.Label.Point

The Point data type which generalizes the different lenses and forms the basis for vertical composition using the Applicative type class.

The point data type that generalizes lens.

data Point cat g i f o

Abstract Point datatype. The getter and modifier operations work in some category. The type of the value pointed to might change, thereby changing the type of the outer structure.

Constructors

Point (cat f o) (cat (cat o i, f) g)

Instances

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

Defined in Data.Label.Point

Methods

fmap :: (a -> b) -> Point arr f i f a -> Point arr f i f b

(<$) :: a -> Point arr f i f b -> Point arr f i f a

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

Defined in Data.Label.Point

Methods

pure :: a -> Point arr f i f a

(<*>) :: Point arr f i f (a -> b) -> Point arr f i f a -> Point arr f i f b

liftA2 :: (a -> b -> c) -> Point arr f i f a -> Point arr f i f b -> Point arr f i f c

(*>) :: Point arr f i f a -> Point arr f i f b -> Point arr f i f b

(<*) :: Point arr f i f a -> Point arr f i f b -> Point arr f i f a

Alternative (Point Partial f view f)

Defined in Data.Label.Point

Methods

empty :: Point Partial f view f a

(<|>) :: Point Partial f view f a -> Point Partial f view f a -> Point Partial f view f a

some :: Point Partial f view f a -> Point Partial f view f [a]

many :: Point Partial f view f a -> Point Partial f view f [a]

get :: Point cat g i f o -> cat f o

Get the getter category from a Point.

modify :: Point cat g i f o -> cat (cat o i, f) g

Get the modifier category from a Point.

set :: Arrow arr => Point arr g i f o -> arr (i, f) g

Get the setter category from a Point.

identity :: ArrowApply arr => Point arr f f o o

Identity Point. Cannot change the type.

compose :: ArrowApply cat => Point cat t i b o -> Point cat g t f b -> Point cat g i f o

Point composition.

Working with isomorphisms.

data Iso cat i o infix 8

An isomorphism is like a Category that works in two directions.

Constructors

Iso infix 8

Fields

• fw :: cat i o
• bw :: cat o i

Instances

Category cat => Category (Iso cat :: Type -> Type -> Type)

Isomorphisms are categories.

Defined in Data.Label.Point

Methods

id :: Iso cat a a

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

inv :: Iso cat i o -> Iso cat o i

Flip an isomorphism.

Specialized lens contexts.

type Total = (->)

Context that represents computations that always produce an output.

type Partial = Kleisli Maybe

Context that represents computations that might silently fail.

type Failing e = Kleisli (Either e)

Context that represents computations that might fail with some error.

Arrow type class for failing with some error.

class Arrow a => ArrowFail e a where

The ArrowFail class is similar to ArrowZero, but additionally embeds some error value in the computation instead of throwing it away.

Methods

failArrow :: a e c

Instances

ArrowFail e Partial

Defined in Data.Label.Point

Methods

failArrow :: Partial e c

ArrowFail e (Failing e)

Defined in Data.Label.Point

Methods

failArrow :: Failing e e c