I would dearly love to make Yatima a usable theorem prover, and Lean has been a huge inspiration particularly regarding syntax. But building a usable theorem prover is a huge project, and at minimum will require substantial work on our theory, on type-inference (which is fairly minimal right now) and on advanced features like quotient types or univalence.

On that point, we've done a little exploration on encoding the Path types from Cubical Type Theory as self-types, and I think there's some promising work to be done there. But I know my limits and while I feel very comfortable building a useful programming language that can do a little bit of basic theorem proving, I know that doing a proper job on a real theorem is going to require larger scale resources.

As far as the link from the Self-Types paper, our theory is similar to their System S, but is not the same. Not 100% sure but I think the main relevant difference here is about Leibniz equality, which iirc allows for saying `a == b` when `a` and `b` are of different types. Yatima's Equal type https://github.com/yatima-inc/introit/blob/main/Equal.ya, implements the more standard homogenous/Martin-Löf equality, but this is just a library, not a language builtin.

We really do need to write an actual paper for Yatima's theory though, especially considering that we've combined the self-types from System S with a variation of Quantitative Types a la Idris 2. Writing that paper is likely step 0 of any Yatima as a theorem prover project, until then we should view Yatima as just an unsound functional programming language with some nice type-level features