Template-Based Conjecturing for Automated Induction in Isabelle/HOL

Proof by induction plays a central role in formal verification. However, its automation remains as a formidable challenge in Computer Science. To solve inductive problems, human engineers often have to provide auxiliary lemmas manually. We automate this laborious process with template-based conjecturing, a novel approach to generate auxiliary lemmas and use them to prove final goals. Our evaluation shows that our working prototype, TBC, achieved 40 percentage point improvement of success rates for problems at intermediate difficulty level.Comment: To appear at Fundamentals of Software engineering 2023 (http://fsen.ir/2023/

Lemma Discovery for Induction: A Survey

Automating proofs by induction can be challenging, not least because proofs might need auxiliary lemmas, which themselves need to be proved by induction. In this paper we survey various techniques for automating the discovery of such lemmas, including both top-down techniques attempting to generate a lemma from an ongoing proof attempt, as well as bottom-up theory exploration techniques trying to construct interesting lemmas about available functions and datatypes, thus constructing a richer background theory