Parameterized Abstractions used for Proof-Planning

c Deutsches Forschungszentrum f ¨ ur K ¨ unstliche Intelligenz 1997 This work may not be copied or reproduced in whole of part for any commercial purpose. Permission to copy in whole or part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of the Deutsche Forschungszentrum f ¨ ur K ¨ unstliche Intelligenz, Kaiserslautern, Federal Republic of Germany; an acknowledgement of the authors and individual contributors to the work; all applicable portions of this copyright notice. Copying, reproducing, or republishing for any other purpose shall require a licence with payment of fee to Deutsches Forschungszentrum f ¨ ur K ¨ unstliche Intelligenz. Abstract In order to cope with large case studies arising from the application of formal methods in an industrial setting, this paper presents new techniques to support hierarchical proof planning. Following the paradigm of diierence reduction, proofs are obtained by removing syntactical diier-ences between parts of the formula to be proven step by step. To guide this manipulation we introduce dynamic abstractions of terms. These abstractions are parameterized by the individual goals of the manipulation and are especially designed to ease the proof search based on heuristics. The hierarchical approach and thus the decomposition of the original goal into several subgoals enables the use of diierent abstractions or diierent parameters of an abstraction within the proof search. In this paper we will present one of these dynamic abstractions together with heuristics to guide the proof search in the abstract space.