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A Calculus for and Termination of Rippling

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Basin,  David A.
Programming Logics, MPI for Informatics, Max Planck Society;

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Walsh,  Toby
Programming Logics, MPI for Informatics, Max Planck Society;

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Citation

Basin, D. A., & Walsh, T. (1996). A Calculus for and Termination of Rippling. Journal of Automated Reasoning, 16(1/2), 147-180.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-ABBB-7
Abstract
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.