Strange.hs

{-# LANGUAGE NoMonomorphismRestriction #-}

data N = A | B | C | D

instance Num N where
    fromInteger 0 = C
    fromInteger 1 = B
    A + B = B
    A + C = C
    A + D = B
    B + C = B
    B + D = C
    C + A = C
    C + B = B
    C + C = C
    C + D = B
    D + C = C
    x + y = error (show x ++ "+" ++ show y)

instance Eq N where
    A == C = True
    C == C = True
    B == B = True
    B == D = True
    C == B = True
    D == B = True
    D == C = True
    x == y = error (show x ++ "==" ++ show y)

instance Ord N
instance Enum N
instance Real N

instance Integral N where
    toInteger n = case n of
                    B -> 1; _ -> 0

instance Show N where
    show C = "1"

main = do
    print $ a + c == 0     -- True
    print $ a == c         -- True
    print $ c == 0         -- True
    print $ a + d == 1     -- True
    print $ b + c == 1     -- True
    print $ b + d == 0     -- True
    print $ b == d         -- True
    print $ d == 0         -- True
    print $ sum([a, b, c]) -- 1
    print $ sum([a, b, d]) -- 1
    print $ [a, b, c] !! a -- 0
    print $ [a, b, c] !! b -- 1
    print $ [a, b, c] !! c -- 0
  where a = fromInteger . toInteger $ A
        b = fromInteger . toInteger $ B
        c = fromInteger . toInteger $ C
        d = D