{-# LANGUAGE FlexibleInstances #-}

{-

needs to mapping

F1 ----> G1
F2 ----> G2
F3 ----> G3

-}

data F1 = F1
data F2 = F2
data F3 = F3

data G = G1 | G2 | G3 deriving (Show)

data Wrapper a = Wrapper a

data Mapping r
  = GF1 !(Wrapper F1)
  | GF2 !(Wrapper F2)
  | GF3 !(Wrapper F3)

class ToMapping a where
  toMapping :: a -> Mapping a

toG :: Mapping a -> G
toG (GF1 _) = G1
toG (GF2 _) = G2
toG (GF3 _) = G3

instance ToMapping F1 where
  toMapping x = GF1 $ Wrapper x

instance ToMapping F2 where
  toMapping x = GF2 $ Wrapper x

instance ToMapping F3 where
  toMapping x = GF3 $ Wrapper x

convert :: ToMapping a => a -> G
convert = toG . toMapping