[blatant303]

> Identity is not equivalent to equivalence

When talking about identity/equivalence of types in the context of homotopy type theory, yes. This is literally what the univalence axiom states.

Auggierose, I'm curious about your thoughts on how we can provide more rigor to LLMs when it comes to large-scale program transformations and proof synthesis. Given the complexity and versatility of these systems, what kind of foundational framework do you believe would enable GPT and similar models to synthesize and execute proofs rigorously? How can we ensure that they are both reliable and adaptable while dealing with various mathematical and logical domains?

More importantly, how whould this relate to NLP tasks such as: alright, the story is good, but can you rewrite it in the style of Auggierose ?

[auggierose]

I am not a fan of HOTT, as nobody managed to explain to me its supposed advantages in terms that didn't border on mysticism.

Anyway, your question is very interesting! :-)