[Haskell-beginners] explanation

[Daniel Fischer]

On Wednesday 01 December 2010 20:34:31, John Moore wrote:
> 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 reduces the Expression one step unless it's a Val, which is 
irreducible.

> evalStep :: Expression ->  Expression
> evalStep (Val x)=  (Val x)

Can't reduce a Val, so leave it as is.

> evalStep (Add x y)

For a non-atomic Expression (here Add), look at the first component/left 
branch (an Expression is a binary tree with Vals at the leaves and 
arithmetic operations at the branch nodes).

>   = case x of
>       (Val a) -> case y of

If the left branch is irreducible, look at the right

>                    (Val b) -> Val (a+b)

If that is also irreducible, add the values and return the irreducible 
Expression

>                    left -> Add x (evalStep y)

otherwise reduce the right branch one step (recur).

>       right -> Add (evalStep x)y

If the left branch is reducible, reduce it one step (recur), leaving the 
right unchanged.

> 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