Let ReadP carry a failure message

19 Nov 2020

      Firstly, I propose a new class. This class is like MonadFail, but with
"error bind" operator:

    class Monad m => FailMsg m where
    failMsg :: String -> m a
    (>?=) :: m a -> (String -> m a) -> m a

Laws are:

 * For every (x :: m a), if (x ≡ fail msg) for some (msg :: String),
msg shall be unique.
 * For (x ≡ fail msg), (x >?= f ≡ f msg). If such msg doesn't exist,
(x >?= _ ≡ x).

Basic instances are:

    instance e ~ String => FailMsg (Either e) where
        failMsg = Left
        Left msg >?= f = f msg
        x >?= _ = x

    instance FailMsg IO where
        failMsg = throwIO . userError
        action >?= f = catch action (f . ioeGetErrorString)

Now let's focus on ReadP. Let P carry a failure message:

    data P a
        = Get (Char -> P a)
        | Look (String -> P a)
        | Fail String
        | Result a (P a)
        | Final (NonEmpty (a,String))

Then we have:

    instance FailMsg P where
        fail = Fail
        Fail msg >?= f = f msg
        p >?= _ = p

    instance FailMsg ReadP where
        fail msg = R (\_ -> fail msg)
        R m >?= f = R (\k -> case m k of
            Fail msg -> let
                R n = f msg
            in n k
            p -> p
            )

This is incredibly useful. This can be used when there are multiple
types of parse error.

Let ReadP carry a failure message

Dannyu NDos