I can into simple Lenses!

gistfile1.hs

{-# LANGUAGE ExistentialQuantification #-}


data Point = Point { x :: Int, y :: Int } deriving (Show)
data Rect = Rect { a :: Point, b :: Point, c :: Point, d :: Point } deriving (Show)


data Lens s a = Lens { get :: s -> a, set :: s -> a -> s}



getA :: Rect -> Point
getA = a

setA :: Rect -> Point -> Rect
setA (Rect a b c d) a' = Rect a' b c d

lensA :: Lens Rect Point
lensA = Lens getA setA



getX :: Point -> Int
getX = x

setX :: Point -> Int -> Point
setX (Point x y) x' = Point x' y

lensX :: Lens Point Int
lensX = Lens getX setX



cl :: Lens c b -> Lens b a -> Lens c a
cl (Lens getB setB) (Lens getA setA) = Lens get set
    where
        get = getA . getB
        set c = setB c . setA (getB c)

lensAX = cl lensA lensX


setl :: s -> Lens s a -> a -> s
setl s (Lens _ set') = set' s



r1 = Rect (Point 0 0) (Point 1 0) (Point 1 1) (Point 0 1)
r2 = setl r1 lensAX 5