implementation of transform using generics

generic-transform.hs

data Expr
  = Lit Int
  | Add Expr Expr
  | Mul Expr Expr
  | Div Expr Expr
  | Sub Expr Expr
  | Neg Expr
  deriving (Show, Eq, Generic)



-- Transform --

class GTransform a struct where
  gtransform :: (a -> a) -> struct x -> struct x

instance GTransform a U1 where
  gtransform _ U1 = U1

instance GTransform a V1 where
  gtransform _ x = x

instance {-# OVERLAPPING #-} Transform a => GTransform a (K1 _1 a) where
  gtransform f (K1 a) = K1 (f $ transform f a)

instance Transform b => GTransform a (K1 _1 b) where
  gtransform f (K1 b) = K1 (transform f b)

instance (GTransform a x, GTransform a y) => GTransform a (x :+: y) where
  gtransform f = \case
    L1 x -> L1 $ gtransform f x
    R1 y -> R1 $ gtransform f y

instance (GTransform a x, GTransform a y) => GTransform a (x :*: y) where
  gtransform f (x :*: y) = gtransform f x :*: gtransform f y

instance GTransform a struct => GTransform a (M1 _x _y struct) where
  gtransform f (M1 a) = M1 $ gtransform f a

class Transform x where
  transform :: (a -> a) -> x -> x
  default transform :: forall a. (Generic x, GTransform a (Rep x)) => (a -> a) -> x -> x
  transform f = to . gtransform f . from

instance Transform Int where
  transform = flip const

instance Transform Expr
{- ^
generics.hs:101:10: error:
    • Overlapping instances for GTransform a (K1 R Int)
        arising from a use of ‘Main.$dmtransform’
      Matching instances:
        two instances involving out-of-scope types
        (use -fprint-potential-instances to see them all)
      (The choice depends on the instantiation of ‘a’
       To pick the first instance above, use IncoherentInstances
       when compiling the other instance declarations)
    • In the expression: Main.$dmtransform @(Expr)
      In an equation for ‘transform’:
          transform = Main.$dmtransform @(Expr)
      In the instance declaration for ‘Transform Expr’
    |
101 | instance Transform Expr
    |          ^^^^^^^^^^^^^^

-}