Abstract
In theorem provers based on dependent type theory such as Coq and Lean, induction is a fundamental proof method and induction tactics are omnipresent in proof scripts. Yet the ergonomics of existing induction tactics are not ideal: they do not reliably support inductive predicates and relations; they sometimes generate overly specific or unnecessarily complex induction hypotheses; and they occasionally choose confusing names for the hypotheses they introduce.
This paper describes a new induction tactic, implemented in Lean 3, which addresses these issues. The tactic is particularly suitable for educational use, but experts should also find it more convenient than existing induction tactics. In addition, the tactic serves as a moderately complex case study for the metaprogramming framework of Lean 3. The paper describes some difficulties encountered during the implementation and suggests improvements to the framework.
This paper describes a new induction tactic, implemented in Lean 3, which addresses these issues. The tactic is particularly suitable for educational use, but experts should also find it more convenient than existing induction tactics. In addition, the tactic serves as a moderately complex case study for the metaprogramming framework of Lean 3. The paper describes some difficulties encountered during the implementation and suggests improvements to the framework.
| Original language | English |
|---|---|
| Title of host publication | CPP 2021 |
| Subtitle of host publication | Proceedings of the 10th ACM SIGPLAN International Conference on Certified Programs and Proofs |
| Editors | Catalin Hritcu, Andrei Popescu |
| Publisher | Association for Computing Machinery, Inc |
| Pages | 199-211 |
| Number of pages | 13 |
| ISBN (Electronic) | 9781450382991 |
| DOIs | |
| Publication status | Published - Jan 2021 |
