There is an existing implementation validating this idea, and the plan is to make it publicly available at some point.

> It seems to me that such an idea would be workable on a given language with a given type system, but it seems to me there would be a black magic step to train a model that would work in a language-agnostic manner.

That's correct. The blog post alludes to infrastructure building as a necessary component of making that happen for that exact reason. I.e. while it's "easy" to generate a dependent pair in this way, generating an entire dependently typed AST is much more difficult. On the positive side, this is more of a software engineering effort rather than a research one.