Proof Recommendation System for the HOL4 Theorem Prover
This work addresses the challenge of improving efficiency for users of the HOL4 theorem prover, though it is incremental as it builds on existing transformer methods for a specific domain.
The authors tackled the problem of automating proof assistance in the HOL4 theorem prover by developing a transformer-based model that predicts optimal next tactics based on proof history, achieving accurate recommendations as demonstrated in their evaluation.
We introduce a proof recommender system for the HOL4 theorem prover. Our tool is built upon a transformer-based model [2] designed specifically to provide proof assistance in HOL4. The model is trained to discern theorem proving patterns from extensive libraries of HOL4 containing proofs of theorems. Consequently, it can accurately predict the next tactic(s) (proof step(s)) based on the history of previously employed tactics. The tool operates by reading a given sequence of tactics already used in a proof process (in our case, it contains at least three tactics), referred to as the current proof state, and provides recommendations for the next optimal proof step(s).