FR: Allow UDFs to vary only in `data` annotations

[nsiccha]

Currently, defining the same function with the two signatures which are identical except for data annotations does not work (Stan will error during compilation with "Function '[...]' has already been declared for signature [...]`.

This is not usually a big issue, because the data annotations are optional and AFAIK don't provide a substantial benefit - except for allowing you to call other functions which only accept data arguments. Activity analysis (what's data, what's parameter) still happens AFAIK.

However, to work around #3224 , I now sometimes have to add data annotations, and I would like to just do it automatically (via code generation) whenever needed. However, this currently would lead to issues if the same function needs to get called with arguments that have different "activities". The data annotated function would of course not accept the parameter arguments, and defining the same function with more permissive data annotations is currently impossible.

[WardBrian]

I transferred this to stanc3. It's a reasonable request, but actually implementing it might be trickier than you would hope due to some of the way we do code generation etc. that currently doesn't really consider data-only arguments and would need to in order to allow this.

We could at the very least improve the error the typechecker gives in this case

[nsiccha]

Thanks! Yes, I was a bit unsure where exactly this belonged :)

[nsiccha]

For me, this would also only make it easier for me to implement the workaround for the other bugs. When these are fixed, then my "need" for this feature would also essentially disappear.

[WardBrian]

We might as well leave it open as a wishlist item, even if low priority.

I think I've got a fix for #1532

[nsiccha]

Oh, I accidentally closed this issue, and I'm not allowed to reopen it. Would you do that, @WardBrian ?:)

[nsiccha]

Thanks! Sorry, I must have used some hot key which I wasn't aware of 😅