import Data.Char

-------------------------------------------------------------------------
-- the expression datatype

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

type Parser a = String -> Maybe (a,String)

number :: Parser Int
number (c:s) | isDigit c = Just (digits 0 (c:s))
number _                 = Nothing

digits :: Int -> String -> (Int,String)
digits n (c:s) | isDigit c = digits (10*n + digitToInt c) s
digits n s                 = (n,s)

num :: Parser Expr
num s =
  case number s of
    Just (n,s') -> Just (Num n, s')
    Nothing     -> Nothing

-------------------------------------------------------------------------
-- expr and term

{-
* an expression is a '+'-chain of terms
* a term is a '*'-chain of factors
-}

expr, term :: Parser Expr
expr = chain term   '+' Add
term = chain factor '*' Mul

{-
chain p op f s1 parsers a "chain" of things.
The things are parsed by the parser p.
The things are separated by the symbol op.
The things are combined by the function f.
For example,
  12+23+1+172
is a chain of numbers, separated by the symbol '+'.
-}

chain :: Parser a -> Char -> (a -> a -> a) -> Parser a
chain p op f s1 =
  case p s1 of
     Just (a,s2) -> case s2 of
                      c:s3 | c == op -> case chain p op f s3 of
                                          Just (b,s4) -> Just (f a b, s4)
                                          Nothing     -> Just (a,s2)
                      _              -> Just (a,s2)
     Nothing     -> Nothing

-------------------------------------------------------------------------
-- factor

factor :: Parser Expr
factor ('(':s) =
   case expr s of
      Just (a, ')':s1) -> Just (a, s1)
      _                -> Nothing
factor s = num s

-------------------------------------------------------------------------
-- reading expressions

readExpr :: String -> Maybe Expr
readExpr s =
  case expr s of
    Just (a,"") -> Just a
    _           -> Nothing

-------------------------------------------------------------------------