This module provides linear lenses.

A Lens s t a b is equivalent to a (s #-> (a,b #-> t). It is a way to cut up an instance of a product type s into an a and a way to take a b to fill the place of the a in s which yields a t. When a=b and s=t, this type is much more intuitive: (s #-> (a,a #-> s)). This is a traversal on exactly one a in a s.

Example

{-# LANGUAGE LinearTypes #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE NoImplicitPrelude #-}

import Control.Optics.Linear.Internal
import Prelude.Linear

import Control.Optics.Linear.Internal
import Prelude.Linear
-- We can use a lens to, for instance, linearly modify a sub-piece in
-- a nested record
modPersonZip :: Person %1-> Person
modPersonZip = over (personLocL .> locZipL)  (x -> x + 1)

-- A person has a name and location
data Person = Person String Location

-- A location is a zip code and address
data Location = Location Int String

personLocL :: Lens' Person Location
personLocL = lens ((Person s l) -> (l, l' -> Person s l'))

locZipL :: Lens' Location Int
locZipL = lens ((Location i s) -> (i, i' -> Location i' s))