Journal of Automated Reasoning

, Volume 16, Issue 1–2, pp 147–180 | Cite as

A calculus for and termination of rippling

  • David A. Basin
  • Toby Walsh
Article

Abstract

Rippling is a type of rewriting developed for inductive theorem proving that uses annotations to direct search. Rippling has many desirable properties: for example, it is highly goal directed, usually involves little search, and always terminates. In this paper we give a new and more general formalization of rippling. We introduce a simple calculus for rewriting annotated terms, close in spirit to first-order rewriting, and prove that is has the formal properties desired of rippling. Next we develop criteria for proving the termination of such annotated rewriting, and introduce orders on annotated terms that lead to termination. In addition, we show how to make rippling more flexible by adapting the termination orders to the problem domain. Our work has practical as well as theoretical advantages: it has led to a very simple implementation of rippling that has been integrated in the Edinburgh CLAM system.

Key words

Mathematical induction inductive theorem proving term rewriting 
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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • David A. Basin
    • 1
  • Toby Walsh
    • 2
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany
  2. 2.Mechanized Reasoning Group, DISTGenova and IRSTTrentoItaly

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