data Exp = Plus  Exp Exp
         | Minus Exp Exp
         | Times Exp Exp
         | Div   Exp Exp
         | Const Int
         deriving Show

eval :: Exp -> Int
eval (Plus  e1 e2) = (eval e1) + (eval e2)
eval (Minus e1 e2) = (eval e1) - (eval e2)
eval (Times e1 e2) = (eval e1) * (eval e2)
eval (Div   e1 e2) = (eval e1) `div` (eval e2)
eval (Const i)     = i

answer = (Div (Div (Const 1972) (Const 2)) (Const 23))
err    = (Div (Const 1) (Const 0))

-- VAR 1: Error handling

data M1 a = Raise Exception | Return a deriving Show
type Exception = String

evalE :: Exp -> M1 Int
-- Plus, Minus, Times cases omitted.
evalE (Div e1 e2) = 
   case evalE e1 of
      Return a -> 
        case evalE e2 of
          Return b -> if b == 0 then Raise "division by 0"
                   else Return (a `div` b)
          Raise s -> Raise s
      Raise s -> Raise s
evalE (Const i)     = Return i

-- VAR 2: State

type M2 a   = State -> (a, State)
type State = Int

evalS :: Exp -> M2 Int
-- Plus, Minus, Times cases omitted.
evalS (Div e1 e2) x = let (a, y) = evalS e1 x in
                        let (b, z) = evalS e2 y in
                           (a `div` b, z+1)
evalS (Const i)   x = (i, x)

-- VAR 3: Output

type M3 a    = (a, Output)
type Output = String

evalO :: Exp -> M3 Int
-- Plus, Minus, Times cases omitted.
evalO (Div e1 e2) = let (a, x) = evalO e1 in
                    let (b, y) = evalO e2 in
                    (a `div` b, 
                        x ++ y ++ line (Div e1 e2) (a `div` b))
evalO (Const i)   = (i, line (Const i) i)

line :: Exp -> Int -> Output
line e a = show e ++ "=" ++ show a ++ "\n"