import Parsing
import Data.Char(isSpace)

-- Parsing Expressions using the monadic parser 

-------------------------------------------------------------------------
-- The expression datatype

data Expr
  = Num Int
  | Add Expr Expr
  | Mul Expr Expr
 deriving ( Show, Eq )
 
-------------------------------------------------------------------------
--

{- Parsed according to the grammar 
   expr ::= term + expr | term
   term ::= factor * term | factor
   factor ::= num | (expr) 

 -}


expr, term, factor, num :: Parser Expr

num    =  do n <- int
             return $ Num n

expr   = chain term '+' Add

term   = chain factor '*' Mul

factor =  num +++ 
          do char '('
             e <- expr
             char ')'
             return e

-- reading expressions

readExpr :: String -> Maybe Expr
readExpr s =
  case parse expr s' of
    Just (a,"") -> Just a
    _           -> Nothing
  where s' = filter (not.isSpace) s