In Problems.P75, askGoldbach could not output an error if the input was not a number or it was not an even number greater than 2. We could implement a function which returned Nothing when the input is not valid, such as in the following.

maybeGoldbach :: String -> Maybe (Int, (Int,Int))
maybeGoldbach s =
  case readMaybe s of
    Nothing -> Nothing
    Just n -> if n < 2 then Nothing else
                if odd n then Nothing else
                  Just (n, goldbach n)

Then we could take advantage of this function to print out an error if the input is not valid.

>>> :{
let format (n, (a,b)) = (show n) ++ "=" ++ (show a) ++ "+" ++ (show b)
    maybeAskGoldbach hIn hOut = do
      s <- hGetLine hIn
      case maybeGoldbach s of
        Nothing -> hPutStrLn hOut "error"
        Just x  -> hPutStrLn hOut $ format x
in do
  withFixedInput "104" stdout maybeAskGoldbach
  withFixedInput "not a number" stdout maybeAskGoldbach
:}
104=3+101
error

However, the implementation of maybeGoldbach above is a chain of conditional expressions. It is not problematic in this particular case, but can make things awkward when there are many conditions and successful operations that need to happen for a function to return a Maybe value.

Take advantage of the fact that Maybe is a monad and rewrite maybeGoldbach more succintly using do notation. The guard function, which in the Maybe monad returns Just () when its argument is true and Nothing when its argument is false, would be useful for making it even more succinct.

Examples

>>> maybeGoldbach "104"
Just (104,(3,101))

>>> maybeGoldbach "not a number"
Nothing

>>> maybeGoldbach "1"
Nothing

>>> maybeGoldbach "101"
Nothing

Parses a string into a number and returns a tuple of the number and its Goldbach pair. Returns Nothing if the input is not valid.

This is an implementation of maybeGoldbach without do notation.

Examples

>>> maybeGoldbach' "104"
Just (104,(3,101))

>>> maybeGoldbach' "not a number"
Nothing

>>> maybeGoldbach' "1"
Nothing

>>> maybeGoldbach' "101"
Nothing