Productive use of failure in inductive proof

Andrew Ireland, Alan Bundy

Research output: Contribution to journalArticlepeer-review

106 Citations (Scopus)


Proof by mathematical induction gives rise to various kinds of eureka steps, e.g., missing lemmata and generalization. Most inductive theorem provers rely upon user intervention in supplying the required eureka steps. In contrast, we present a novel theorem-proving architecture for supporting the automatic discovery of eureka steps. We build upon rippling, a search control heuristic designed for inductive reasoning. We show how the failure if rippling can be used in bridging gaps in the search for inductive proofs. © 1996 Kluwer Academic Publishers.

Original languageEnglish
Pages (from-to)79-111
Number of pages33
JournalJournal of Automated Reasoning
Issue number1-2
Publication statusPublished - 1996


  • Automated theorem proving
  • Mathematical induction
  • Proof patching


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