Faster Smarter Induction in Isabelle/HOL

TL;DR

This paper introduces sem_ind, a tool that automates inductive proof argument selection in Isabelle/HOL, significantly improving accuracy and efficiency through definitional quantifiers.

Contribution

The paper presents sem_ind, a novel method that enhances inductive proof automation by integrating definitional quantifiers for better argument recommendation.

Findings

Recommendation accuracy increased from 20.1% to 38.2%.

Execution time median decreased from 2.79s to 1.06s.

Improved performance within 5 seconds timeout.

Abstract

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.