Termination and Confluence of Higher-Order Rewrite Systems

  • Frédéric Blanqui
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1833)


In the last twenty years, several approaches to higher-order rewriting have been proposed, among which Klop’s Combinatory Rewrite Systems (CRSs), Nipkow’s Higher-order Rewrite Systems (HRSs) and Jouannaud and Okada’s higher-order algebraic specification languages, of which only the last one considers typed terms. The later approach has been extended by Jouannaud, Okada and the present author into Inductive Data Type Systems (IDTSs). In this paper, we extend IDTSs with the CRS higher-order pattern-matching mechanism, resulting in simply-typed CRSs. Then, we show how the termination criterion developed for IDTSs with first-order pattern-matching, called the General Schema, can be extended so as to prove the strong normalization of IDTSs with higher-order pattern-matching. Next, we compare the unified approach with HRSs. We first prove that the extended General Schema can also be applied to HRSs. Second, we show how Nipkow’s higher-order critical pair analysis technique for proving local confluence can be applied to IDTSs.

Appendices A, B and C (proofs) are available from the web page.


Induction Hypothesis General Schema Function Symbol Critical Pair Process Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Frédéric Blanqui
    • 1
  1. 1.LRIUniversité de Paris-Sud, Bât. 490OrsayFrance

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