Backwards compatibility: We should allow functions to be named _jacobian that don't use the new feature to be called anywhere for a few versions

[WardBrian]

We took care to implement jacobian+= in a backwards-compatible way, but not _jacobian functions, of which there are some in the wild: https://github.com/search?q=language%3Astan+_jacobian%28&type=code

Because these functions don't need the jacobian += feature, ideally they would continue to be treated as FnPlains, with a warning. I'm not sure if this is actually implementable, however, due to the order-independence of the functions block.

First reported by @tillahoffmann https://discourse.mc-stan.org/t/planning-the-2-36-release/36382/15?u=wardbrian

[WardBrian]

@nhuurre -- do you have any sense of how this could be done in a way that isn't so horrible?

[WardBrian]

Options:

• we find a way to typecheck that allows both usages
• we don't allow _jacobian functions for 3 versions while we emit warnings, and then we do what we do now
• we just re-use the _lp function name?

Also pinging @SteveBronder

[nhuurre]

I think the easiest backwards-compatibility hack would be that right before calling Typechecker.add_userdefined_function you check if any of the user-defined _jacobian functions actually use jacobian += and if not, then frontent never creates FnJacobian, only FnPlain, ie, replace every Fun_kind.suffix_from_name in Typechecker with

let jacobian_compatibilty_mode = ref false
let suffix_from_name name =
  match Fun_kind.suffix_from_name name with
  | FnJacobian when !jacobian_compatibilty_mode -> Fun_kind.FnPlain
  | f -> f

Trying to do this on a per-function basis gets complicated if there are mutually recursive _jacobian functions.

[WardBrian]

I agree. I had just finished sketching out a graph search over the functions (while not entirely knowing how to resolve overloads to do so), when it occurred to me that for backwards compatibility purposes a global check is sufficient. If we see the new feature, we don’t have to worry about this being an old model…