haskell for lenses

lens.hs

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

type Lens' a b =
  forall f. Functor f => (b -> f b) -> a -> f a

newtype Identity a =
  Identity { runIdentity :: a } 

newtype Const x a =
  Const { runConst :: x }

class Functor f where
  fmap :: (a -> b) -> f a -> f b
  
instance Functor (Const x) where
  fmap f (Const x) = Const x
  
instance Functor Identity where
  fmap f (Identity a) = Identity (f a)

get'' :: Lens' a b -> a -> b
get'' l a =
  let x = Const   -- :: b -> Const b b
      y = l x     -- :: a -> Const b a
      z = y a     -- :: Const b a
   in runConst z


set'' :: Lens’ a b -> b -> a -> a
set'' l b a = 
  let x = const $ Identity b -- :: b -> Identity b
      y = l x                -- :: a -> Identity a
      z = y a                -- :: Identity a
  in runIdentity z