LensStore.hs

module LensStore where

import Control.Comonad
import Control.Comonad.Store

type Coalg s a = s -> Store a s

_1 :: (a, b) -> Store a (a, b)
_1 (a, b) = store set get
  where
    set a' = (a' , b)
    get = a

_2 :: (a, b) -> Store b (a, b)
_2 (a, b) = store set get
  where
    set b' = (a , b')
    get = b

view :: Coalg s a -> s -> a
view l = pos . l

set :: Coalg s a -> a -> s -> s
set l a = peek a . l

comp :: Coalg a b -> Coalg b c -> Coalg a c
comp f g a = store (ba . cb) c
  where
    (ba, b) = runStore $ f a
    (cb, c) = runStore $ g b

ex1 :: Bool
ex1 =  view _1 (True, ())

ex2 :: (Bool, ())
ex2 = set _1 False (True, ())

ex3 :: Bool
ex3 = view (_2 `comp` _1) ((), (True, ()))