EDIT: To be clear, that's 10-15% of the total theorems in a test set, not a relative 10-15% improvement. Given that solve rates for tools are in the 10-30% range, that's much more than a relative 10-15% improvement.
EDIT: To be clear, that's 10-15% of the total theorems in a test set, not a relative 10-15% improvement. Given that solve rates for tools are in the 10-30% range, that's much more than a relative 10-15% improvement.
Other uses are: better autocomplete from comments for Coq and Lean VScode envs than generalist tools.
Translation from NL sketch to formal proof. This is different from autocomplete in that it should generate long attempts as an automated spitballer. Leave it running a a long time to see if it finds anything when you're stuck. This works for formal and informal proofs but the latter gets no feedback (this is imagining future tunes able to make better use of interactive prover feedback).
Translating formal proofs to natural language.
Combine it with RAG and have it pull in and summarize references from your personal paper collection and the internet. Particularly useful in place of search when you don't have the vocabulary for a concept. As a basis for non-code based autocomplete of mathematical work.
I see unbounded potential for this combination. And a natural setting where between cost of search and the symbolic prover doing the heavy lifting, it's one of those areas that naturally lends itself to specialist Open over API models.
https://www.cs.ru.nl/~freek/100/
Some people greatly hope that fully formal proofs become a routine part of math research and communication in the future.