Faster Smarter Induction in Isabelle/HOL

Proof by induction plays a critical role in formal verification and mathematics at large. However, its automation remains as one of the long-standing challenges in Computer Science. To address this problem, we developed semind. Given inductive problem, semind recommends what arguments to pass to the induct method. To improve the accuracy of semind, we introduced definitional quantifiers, a new kind of quantifiers that allow us to investigate not only the syntactic structures of inductive problems but also the definitions of relevant constants in a domain-agnostic style. Our evaluation shows that compared to its predecessor semind improves the accuracy of recommendation from 20.1% to 38.2% for the most promising candidates within 5.0 seconds of timeout while decreasing the median value of execution time from 2.79 seconds to 1.06 seconds.