Lemma Mining over HOL Light
This work addresses the challenge of lemma reusability in formal mathematics, which is incremental as it builds on existing methods for automated theorem proving.
The authors tackled the problem of identifying useful lemmas in large formal mathematical libraries by developing criteria to estimate lemma usefulness and applying them to the HOL Light library, resulting in the addition of thousands of new lemmas that improved automated theorem proving performance.
Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such statements is named and re-used in later proofs by formal mathematicians. In this work, we suggest and implement criteria defining the estimated usefulness of the HOL Light lemmas for proving further theorems. We use these criteria to mine the large inference graph of all lemmas in the core HOL Light library, adding thousands of the best lemmas to the pool of named statements that can be re-used in later proofs. The usefulness of the new lemmas is then evaluated by comparing the performance of automated proving of the core HOL Light theorems with and without such added lemmas.