data Logic = O | I | A | B | C | Not Logic | And Logic Logic | Or Logic Logic deriving (Eq, Show, Read)

eval :: Logic -> Logic


eval (Not O) = I
eval (Not I) = O
eval (Not (Not x)) = eval x

eval (And O _) = O
eval (And _ O) = O
eval (And I x) = eval x
eval (And x I) = eval x
eval (And x y)
    | x == y       = x
    | x == (Not y) = O
    | (Not x) == y = O
    | otherwise    = (And (eval x) (eval y))

eval (Or I _) = I
eval (Or _ I) = I
eval (Or O x) = eval x
eval (Or x O) = eval x
eval (Or x y)
    | x == y       = x
    | x == (Not y) = I
    | (Not x) == y = I
    | otherwise    = (Or (eval x) (eval y))

eval x = x