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Rippling is a type of rewriting developed for inductive theorem proving that uses annotations to direct search. 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 it has the formal properties desired of rippling. We then develop the 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. |
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calculus, rewriting systems, search problems, theorem proving, calculus, rippling termination, term rewriting, inductive theorem proving, direct search, termination orders, Edinburgh CLAM system, mathematical induction |
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