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An effective proof of the well-foundedness of the multiset path ordering

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Abstract

The main contribution of this paper is an effective proof of the well-foundedness of MPO, as a term of the Calculus of Inductive Constructions. This proof is direct, short and simple. It is a sequence of nested inductions and it only relies on the fact that the multiset order, restricted to a well-founded part of the base set, is well-founded. In particular, it does not require to establish preliminarily the transitivity of the relation, although we prove it as an additional property. The terms we consider are not supposed to be ground nor the signature to be finite. All the proofs have been carried out in the Coq proof-assistant.

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Authors and Affiliations

  1. Centre de Mathématiques et d’Informatique, 39, rue Frédéric Joliot-Curie, 13453, Marseille Cedex 13, France

    Solange Coupet-Grimal & William Delobel

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  1. Solange Coupet-Grimal
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  2. William Delobel
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Correspondence to Solange Coupet-Grimal.

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Laboratoire d’Informatique Fondamentale de Marseille, UMR 6166.

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Coupet-Grimal, S., Delobel, W. An effective proof of the well-foundedness of the multiset path ordering. AAECC 17, 453–469 (2006). https://doi.org/10.1007/s00200-006-0020-y

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  • DOI: https://doi.org/10.1007/s00200-006-0020-y

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