How to write this case expression with the view pattern syntax?

Question

After I have read the example of a RPN calculator in "Learn You a Haskell for Great Good!" I wanted to rewrite it myself in a more general way.

In order to easily extend the available functions I put these in separated lists and pattern matched with the lookup function using the ViewPatterns syntax. To read the input with read I wrote this:

parse xs x = case readMaybe x of
  Just x  -> Right (x : xs)
  Nothing -> Left "Syntax error

but I'd rather avoid a case expression and use again the view pattern like this:

parse xs (readMaybe -> Just x ) = Right (x : xs)
parse xs (readMaybe -> Nothing) = Left "Syntax error"

However with the latter I'm getting this error: No instance for (Read a0) arising from a use of ‘readMaybe’

I don't understand why. Aren't they equivalent?

The whole code is here.

Answer 1

They're not equivalent. The case version has one readMaybe, the view pattern version has two. For every readMaybe, the compiler has to infer which type is the target of the attempt to read. When the code says

parse xs x = case readMaybe x of
  Just x  -> Right (x : xs)
  Nothing -> Left "Syntax error

the GHC detective notices that in your Just x case, x ends up consed to xs, and so must take whatever type the elements of xs have. And that's good work.

But when you write

parse xs (readMaybe -> Just x ) = Right (x : xs)
parse xs (readMaybe -> Nothing) = Left "Syntax error"

you create two separate find-the-target-type problems, one for each use of readMaybe. The first of these is solved in just the same way as in the case case, but for the second, read individually,

parse xs (readMaybe -> Nothing) = Left "Syntax error"

there is just no clue what it is that you are failing to read, and no reason to believe it is the same thing as in the line above.

Generally, it is inappropriate to use view patterns unless there is only one outcome of interest. They are the wrong syntax if you want to do an intermediate computation once, but analyse the result into more than one case. I am happy to remain on the record that I consider them a misfeature for this reason.