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Polynomial Interpretations for Higher-Order Rewriting

Authors Carsten Fuhs, Cynthia Kop



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LIPIcs.RTA.2012.176.pdf
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Carsten Fuhs
Cynthia Kop

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Carsten Fuhs and Cynthia Kop. Polynomial Interpretations for Higher-Order Rewriting. In 23rd International Conference on Rewriting Techniques and Applications (RTA'12). Leibniz International Proceedings in Informatics (LIPIcs), Volume 15, pp. 176-192, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2012)
https://doi.org/10.4230/LIPIcs.RTA.2012.176

Abstract

The termination method of weakly monotonic algebras, which has been defined for higher-order rewriting in the HRS formalism, offers a lot of power, but has seen little use in recent years. We adapt and extend this method to the alternative formalism of algebraic functional systems, where the simply-typed lambda-calculus is combined with algebraic reduction. Using this theory, we define higher-order polynomial interpretations, and show how the implementation challenges of this technique can be tackled. A full implementation is provided in the termination tool Wanda.
Keywords
  • higher-order rewriting
  • termination
  • polynomial interpretations
  • weakly monotonic algebras
  • automation

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