Faster Smarter Induction in Isabelle/HOL
This work addresses a long-standing problem in computer science for formal verification practitioners, but it is incremental as it builds on a predecessor method.
The paper tackles the challenge of automating proof by induction in formal verification by developing sem_ind, a method that recommends arguments for the induct method, resulting in an accuracy improvement from 20.1% to 38.2% and a reduction in median execution time from 2.79 to 1.06 seconds.
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 sem_ind. Given inductive problem, sem_ind recommends what arguments to pass to the induct method. To improve the accuracy of sem_ind, 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 sem_ind 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.