Constructing Induction Rules for Deductive Synthesis Proofs
01 Mar 2006-Electronic Notes in Theoretical Computer Science (Elsevier Science Publishers B. V.)-Vol. 153, Iss: 1, pp 3-21
TL;DR: It is shown that a combination of rippling and the use of meta-variables as a least-commitment device can provide novelty in induction rule construction techniques that can introduce novel recursive structures.
About: This article is published in Electronic Notes in Theoretical Computer Science.The article was published on 2006-03-01 and is currently open access. It has received 2969 citations till now. The article focuses on the topics: Recursion & Mathematical proof.
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TL;DR: The IsaPlanner as mentioned in this paper is a generic framework for proof planning in the interactive theorem prover Isabelle, which facilitates the encoding of reasoning techniques, which can be used to conjecture and prove theorems automatically.
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225 citations
TL;DR: It is shown how the failure if rippling can be used in bridging gaps in the search for inductive proofs, and a novel theorem-proving architecture for supporting the automatic discovery of eureka steps is presented.
Abstract: 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.
184 citations