data AST = C String | Seq AST AST | Star AST | Plus AST AST deriving Show

parsePar :: String -> (AST, String)
parsePar (x:str)
    | not (null excess) = (parse token, tail excess)
    | otherwise       = error "Incorrect parentheses"
        where
            token = takeWhile (\e -> (not (elem e ")"))) (x:str)
            excess = dropWhile (\e -> (not (elem e ")"))) (x:str)

parseEl :: String -> (AST, String)
parseEl ('(':str) = (ast, excess)
        where
            (ast, excess) = parsePar str
parseEl (x:str)
    | isDigit x = ((C [x]), str)
    | isLetter x = ((C [x]), str)
    | otherwise = error $ "Feil: " ++ [x]

parseBa :: String -> (AST, String)
parseBa str
    | null excess = (ast, [])
    | head excess == '*' = (Star ast, tail excess)
    | otherwise = (ast, excess)
        where
            (ast, excess) = parseEl str

parseSq :: String -> (AST, String)
parseSq str
    | null excess = (ast, [])
    | not (elem (head excess) "+*") = (Seq ast ast2, excess2)
    | otherwise =  (ast, excess)
        where
            (ast, excess) = parseBa str
            (ast2, excess2) = parseSq excess

parseRe :: String -> (AST, String)
parseRe str
   | null excess = (ast, [])
   | head excess == '+' = (Plus ast ast2, excess2)
   | otherwise   = (ast, excess)
        where
         (ast, excess) = parseSq str
         (ast2, excess2) = parseRe (tail excess)

parse :: String -> AST
parse str = fst (parseRe str)