data Reg 
    = Zero
    | One
    | Char Char
    | Plus Reg Reg
    | Times Reg Reg
    | Star Reg
  deriving Show

acc :: String -> Reg -> (String -> Bool) -> Bool
acc s Zero k = False
acc s One k = k s
acc [] (Char _) k = False
acc (c : s) (Char c') k = 
    if c == c' then k s else False
acc s (Plus r1 r2) k =
    (acc s r1 k) || (acc s r2 k)
acc s (Times r1 r2) k =
    acc s r1 (\s' -> acc s' r2 k)
acc s (Star r) k = 
    (k s) || (acc s r (\s' -> acc s' (Star r) k))

accept :: String -> Reg -> Bool
accept s r = acc s r (\s' -> if s' == [] then True else False)


bin :: String -> Bool
bin s = accept s (Times (Star (Plus (Char '0') (Char ('1'))))
		  (Plus (Char '0') (Char ('1'))))

one :: String -> Bool
one s = accept s (Char '1')