[Haskell-beginners] explanation

[John Moore]

Hi ,
     Havent used haskell in a while can someone explain just whats happening
here. I know what it does, I just can't workout how it does it. Only need to
explain how the red area works and I can work out the rest myself

Regards

John


module Rollback where


data Expression = Val Double
               | Add Expression Expression
               | Subtract Expression Expression
               | Multiply Expression Expression
               | Divide Expression Expression
        deriving Show
demo1 = (Add(Multiply(Divide(Subtract(Val 25)(Val 5))(Val 10))(Val 7))(Val
30))
evalStep :: Expression ->  Expression
evalStep (Val x)=  (Val x)
evalStep (Add x y)
  = case x of
      (Val a) -> case y of
                   (Val b) -> Val (a+b)
                   left -> Add x (evalStep y)
      right -> Add (evalStep x)y
evalStep (Subtract x y)
  = case x of
      (Val a) -> case y of
                   (Val b) -> Val (a-b)
                   left -> Subtract x (evalStep y)
      right -> Subtract (evalStep x)y
evalStep (Multiply x y)
  = case x of
      (Val a) -> case y of
                   (Val b) -> Val (a*b)
                   left -> Multiply x (evalStep y)
      right -> Multiply (evalStep x)y

evalStep (Divide x y)
  = case x of
      (Val a) -> case y of
                   (Val b) -> Val (a/b)
                   left -> Divide x (evalStep y)
      right -> Divide (evalStep x)y
type Stack = [Expression]
evaluate :: Expression -> IO ()
evaluate exp = do
     stk <- evalWithStack exp [exp]
     putStrLn "End of Equation"


evalWithStack :: Expression -> Stack -> IO Stack
-- Base case
evalWithStack (Val a) stk = return stk
-- Recursive case
evalWithStack e stk = do
     putStrLn "Evaluating one more step"
     let e' =  (evalStep e)
     putStrLn ("Result is "++(show e'))
     putStrLn "Do another step (y/n) or rollback (r)? :"
     c <- getLine
     case c of
       "y" -> evalWithStack e' (e':stk)
       "r" -> let (a,stk') = stackBack stk in evalWithStack a stk'
       "n"  -> do { putStrLn ("Ok you said :" ++ show c
                                           ++ "so that's it "
                                           ++ "You went as deep as " ++ show
(getCount stk) ++"  levels")
                 ; return (e': stk)
                 }

stackBack :: Stack -> (Expression,Stack)
stackBack [a]    = (a,[a])
stackBack (a:as) = (a,as)
stackBack []     = error "Nothing there"

getCount :: Stack -> Int
getCount stk = length stk
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