import Control.Monad.Except
import Control.Monad.State

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

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

-- variants of eval using standard mtl library monads

-- MONAD LIBRARY VAR 1: Error Handling 

type MLE = Either String

evalMLE :: Exp -> MLE Int
evalMLE (Div e1 e2) = do 
               a <- evalMLE e1;
               b <- evalMLE e2;
               if b == 0 then (throwError "division by 0")
                         else return (a `div` b)
evalMLE (Const i)   = return i

-- MONAD LIBRARY VAR 2: State

type MLS = State Int

tick :: (Num s, MonadState s m) => m ()
tick = do st <- get;
          put (st+1)

evalMLS :: Exp -> MLS Int
evalMLS (Div e1 e2) = do a <- evalMLS e1;
                         b <- evalMLS e2;
                         tick;
                         return (a `div` b)
evalMLS (Const i)   = return i

runMLS s exp = runState (evalMLS exp) s