There is an increasing use of (first- and higher-order) rewrite rules in many programming languages and logical systems. The recursive path ordering (RPO) is a well-known tool for proving termination of such rewrite rules in the first-order case. However, RPO has some weaknesses. For instance, since it is a simplification ordering, it can only handle simply terminating systems. Several techniques have been developed for overcoming these weaknesses of RPO. A very recent such technique is the monotonic semantic path ordering (MSPO), a simple and easily automatable ordering which generalizes other more ad-hoc methods. Another recent extension of RPO is its higher-order version HORPO. HORPO is an ordering on terms of a typed lambda-calculus generated by a signature of higher-order function symbols. Although many interesting examples can be proved terminating using HORPO, it inherits the weaknesses of the first-order RPO. Therefore, there is an obvious need for higher-order termination orderings without these weaknesses. Here we define the first such ordering, the monotonic higher-order semantic path ordering (MHOSPO), which is still automatable like MSPO. We give evidence of its power by means of several natural and non-trivial examples which cannot be handled by HORPO.
CITATION STYLE
Borralleras, C., & Rubio, A. (2001). A monotonic higher-order semantic path ordering. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2250, pp. 531–547). Springer Verlag. https://doi.org/10.1007/3-540-45653-8_37
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