Proof by induction is a long-standing challenge in Computer Science. Induction tactics of proof assistants facilitate proof by induction, but rely on humans to manually specify how to apply induction. In this paper, we present SeLFiE, a domain-specific language to encode experienced users' expertise on how to apply the induct tactic in Isabelle/HOL: when we apply an induction heuristic written in SeLFiE to an inductive problem and arguments to the induct tactic, the SeLFiE interpreter examines both the syntactic structure of the problem and semantics of the relevant constants to judge whether the arguments to the induct tactic are plausible according to the heuristic. Then, we present semantic_induct, an automatic tool to recommend how to apply the induct tactic. Given an inductive problem, semantic_induct produces candidate arguments to the induct tactic and selects promising ones using heuristics written in SeLFiE. Our evaluation based on 254 inductive problems from nine problem domains show that semantic_induct achieved 15.7 percentage points of improvements in coincidence rates for the three most promising recommendations while achieving 43% of reduction in the median value for the execution time when compared to an existing tool, smart_induct.

通过引理归纳在正式验证和数学中发挥了关键作用，但其自动化仍然是计算机科学中长期存在的问题，使用定义量词我们开发了sem_ind，它可以推荐需要通过归纳予以验证的参数

在Isabelle/HOL中更快更智能的归纳