Higher-order orderings for normal rewriting

Authors:
Jean-Pierre Jouannaud;Albert Rubio
Affiliations:
École Polytechnique, LIX, Palaiseau, France;Technical University of Catalonia, Barcelona, Spain
Venue:
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Year:
2006

Citing 12
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Abstract

We extend the termination proof methods based on reduction orderings to higher-order rewriting systems à la Nipkow using higher-order pattern matching for firing rules, and accommodate for any use of eta, as a reduction, as an expansion or as an equation. As a main novelty, we provide with a mechanism for transforming any reduction ordering including beta-reduction, such as the higher-order recursive path ordering, into a reduction ordering for proving termination of rewriting à la Nipkow. Non-trivial examples are carried out.