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Proof assistants offer tactics to apply proof by induction, but these tacticsrely on inputs given by human engineers. To automate this laborious process, wedeveloped SeLFiE, a boolean query language to represent experienced users'knowledge on how to apply the induct tactic in Isabelle/HOL: when we apply aninduction heuristic written in SeLFiE to an inductive problem and arguments tothe induct tactic, the SeLFiE interpreter judges whether the arguments areplausible for that problem according to the heuristic by examining both thesyntactic structure of the problem and definitions of the relevant constants.To examine the intricate interaction between syntactic analysis and analysis ofconstant definitions, we introduce definitional quantifiers. For evaluation webuild an automatic induction prover using SeLFiE. Our evaluation based on 347inductive problems shows that our new prover achieves 1.4 x 10^3% improvementover the corresponding baseline prover for 1.0 second of timeout and the medianvalue of speedup is 4.48x.

Definitional Quantifiers Realise Semantic Reasoning for Proof by Induction