newtype Parser a = P { getParser :: String -> Maybe (a, String) }

instance Applicative Parser where
    pure = success

    P p <*> P p' = P $ \\s -> case p s of
        Just (f, s') -> fmap (applyToFirst f) $ p' s'
        Nothing      -> Nothing

{-|
    Applies a function to the first component of a pair.
-}
applyToFirst :: (a -> b) -> (a, c) -> (b, c)
applyToFirst f (x, y) = (f x, y)

instance Applicative Parser where
    pure v = P (\\s -> Just (v, s))

    P p <*> P p' = P $ \\s -> case p s of
        Just (f, s') -> case p' s' of
          Just (v, s'') -> Just (f v, s'')
          Nothing -> Nothing
        Nothing      -> Nothing