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Mechanizing Weakly Ground Termination Proving of Term Rewriting Systems by Structural and Cover-Set Inductions

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Abstract

The paper presents three formal proving methods for generalized weakly ground terminating property, i.e., weakly terminating property in a restricted domain of a term rewriting system, one with structural induction, one with cover-set induction, and the third without induction, and describes their mechanization based on a meta-computation model for term rewriting systems—dynamic term rewriting calculus. The methods can be applied to non-terminating, non-confluent and/or non-left-linear term rewriting systems. They can do “forward proving” by applying propositions in the proof, as well as “backward proving” by discovering lemmas during the proof.

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Authors and Affiliations

  1. Department of Computer Science, Beijing Normal University, Beijing, 100875, P.R. China

    Su Feng

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  1. Su Feng
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Correspondence to Su Feng.

Additional information

This work is supported partially by the National Natural Science Foundation of China under Grant No.60273015 and the Scientific Research Foundation for Returned Overseas Chinese Scholars, Ministry of Education of China.

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Feng, S. Mechanizing Weakly Ground Termination Proving of Term Rewriting Systems by Structural and Cover-Set Inductions. J Comput Sci Technol 20, 496–513 (2005). https://doi.org/10.1007/s11390-005-0496-0

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  • DOI: https://doi.org/10.1007/s11390-005-0496-0

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