# Definitional Quantifiers Realise Semantic Reasoning for Proof by Induction

arXiv: https://arxiv.org/abs/2010.10296 · HTML: https://mlsanity.com/paper/2010.10296/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2020.

## Built on by (most cited first, 1 of 1)

- [Genetic Algorithm for Program Synthesis](https://mlsanity.com/paper/2211.11937/) (2022)

## Abstract (arXiv)

Proof assistants offer tactics to apply proof by induction, but these tactics rely on inputs given by human engineers. To automate this laborious process, we developed SeLFiE, a boolean query language to represent experienced users' knowledge 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 judges whether the arguments are plausible for that problem according to the heuristic by examining both the syntactic structure of the problem and definitions of the relevant constants. To examine the intricate interaction between syntactic analysis and analysis of constant definitions, we introduce definitional quantifiers. For evaluation we build an automatic induction prover using SeLFiE. Our evaluation based on 347 inductive problems shows that our new prover achieves 1.4 x 10^3% improvement over the corresponding baseline prover for 1.0 second of timeout and the median value of speedup is 4.48x.