Demonstration of how incorrect (Enum x, Enum y) => Enum (x, y) instance can be used for Enum a => Enum (a,a)

Enum.hs

{-# LANGUAGE FlexibleInstances #-}

-- See http://stackoverflow.com/questions/9967790/instance-in-haskell

instance (Enum a) => Enum (a, a) where
  fromEnum (x,y) =
    k^2 + 2*j + if permuted then 1 else 0
      where
        k = max (fromEnum x) (fromEnum y)
        j = min (fromEnum x) (fromEnum y)
        permuted = (fromEnum y) > (fromEnum x)
  toEnum n =
    let k = floor . sqrt $ fromIntegral n
        (j, permdAdd) = (n-k^2) `divMod` 2
        permute (x,y) | permdAdd>0  = (toEnum y, toEnum x)
                      | otherwise   = (toEnum x, toEnum y)
    in permute (k, j)

data A = A1 | A2 deriving (Show, Enum)
data B = B1 | B2 | B3 deriving (Show, Enum)

main = do
  print [(A1,A1)..(A2,A2)]
  print [(B1,B1)..(B3,B3)]


-- $ runhaskell tupleenum.hs 
-- [(A1,A1),(A2,A1),(A1,A2),(A2,A2)]
-- [(B1,B1),(B2,B1),(B1,B2),(B2,B2),(B3,B1),(B1,B3),(B3,B2),(B2,B3),(B3,B3)]