A calculus for and termination of rippling

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. Funded by the German Ministry for Research and Technology under grant ITS 9102. Supported by a Human Capital and Mobility Research Fellowship from the European Commission. Both authors thank members of the Edinburgh Mathematical Reasoning Group, as well as Alan Bundy, Leo Bachmair, Dieter Hutter, and Michael Rusinowitch, for their comments on previous drafts. Additional support was also received from the MInd grant EC-US 019-76094.