{-
  * Extend the data type so that expressions can contain multiplication
    and division.
-}
data Expr = Lit Int | Add Expr Expr | Sub Expr Expr | Mul Expr Expr | Div Expr Expr
            deriving (Show, Eq)         

{-
  * Create Expr values corresponding to the expressions
    (5 - 3) + 2 and 5 - (3 + 2)
-}

ex1 = Add (Sub (Lit 5) (Lit 3)) (Lit 2)
ex2 = Sub (Lit 5) (Add (Lit 3) (Lit 2))

{-
  * Write a function that evaluates an expression.
-}

eval :: Expr -> Int
eval (Lit n)   = n
eval (Add e1 e2) = (eval e1) + (eval e2)
eval (Sub e1 e2) = (eval e1) - (eval e2)
eval (Mul e1 e2) = (eval e1) * (eval e2)
eval (Div e1 e2) = (eval e1) `div` (eval e2)


{-
  * Write a fold function for expressions.                                        
-}

foldExpr
  :: (Int -> a)               -- Lit
    -> (a -> a -> a)          -- Add
    -> (a -> a -> a)          -- Sub
    -> (a -> a -> a)          -- Mul
    -> (a -> a -> a)          -- Div
    -> Expr
    -> a
foldExpr lit add sub mul div = go
  where
    go (Lit v) = lit v
    go (Add s t) = add (go s) (go t)
    go (Sub s t) = sub (go s) (go t)
    go (Mul s t) = mul (go s) (go t)
    go (Div s t) = div (go s) (go t)
    
{-
  * Use the fold function to reimplement the expression evaluator
-}

eval' = foldExpr id (+) (-) (*) div

{-
  * Write a function that returns the largest literal in an expression.
-}                                      

getMax = foldExpr id max max max max