Completeness of combinations of constructor systems

Aart Middeldorp, Yoshihito Toyama

Research output: Chapter in Book/Report/Conference proceedingConference contribution

20 Citations (Scopus)


A term rewriting system is called complete if it is both confluent and strongly normalizing. Barendregt and Klop showed that the disjoint union of complete term rewriting systems does not need to be complete. In other words, completeness is not a modular property of term rewriting systems. Toyama, Klop and Barendregt showed that completeness is a modular property of left-linear TRS’s. In this paper we show that it is sufficient to impose the constructor discipline for obtaining the modularity of completeness. This result is a simple consequence of a quite powerful divide and conquer technique for establishing completeness of such constructor systems. Our approach is not limited to systems which are composed of disjoint parts. The importance of our method is that we may decompose a given constructor system into parts which possibly share function symbols and rewrite rules in order to infer completeness. We obtain a similar technique for semi-completeness, i.e. the combination of confluence and weak normalization.

Original languageEnglish
Title of host publicationRewriting Techniques and Applications - 4th International Conference, RTA-1991, Proceedings
EditorsRonald V. Book
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783540539049
Publication statusPublished - 1991
Externally publishedYes
Event4th International Conference on Rewriting Techniques and Applications, RTA-1991 - Como, Italy
Duration: 1991 Apr 101991 Apr 12

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume488 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other4th International Conference on Rewriting Techniques and Applications, RTA-1991

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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