Summary: A Termination Ordering for Higher Order Rewrite
Olav Lysne ? and Javier Piris ??
Laboratoire de Recherche en Informatique
Bat. 490 91405 Orsay Cedex
Olav Lysne, Department of informatics, University of Oslo
P.O. box 1080 Blindern, 0316 Oslo, NORWAY
Phone: +47 22 85 24 34, Fax: +47 22 85 24 01
Abstract. We present an extension of the recursive path ordering for the purpose
of showing termination of higher order rewrite systems. Keeping close to the general
path ordering of Dershowitz and Hoot, we demonstrate the necessary properties of
the termination functions for our method to apply, thus describe a class of different
orderings. We also give a counterexample to a previously published extension of the
recursive path ordering into the higher order setting.
During the last two decades a lot of work has been done on techniques for first order
rewriting. There are still many open problems for the first order case, but even so we have in