From diagrammatic confluence to modularity

Authors:
Jean-Pierre Jouannaud;Jiaxiang Liu
Affiliations:
INRIA-LIAMA, Beijing, China and Software Chair, Tsinghua University, Beijing, China;INRIA-LIAMA, Beijing, China and School of Software, Tsinghua University, Beijing, China and Tsinghua National Laboratory for Information Science and Technology (TNList), Beijing, China and Key Lab ...
Venue:
Theoretical Computer Science
Year:
2012

Citing 17
Cited 0

On the Church-Rosser property for the direct sum of term rewriting systems

Journal of the ACM (JACM)
Completion of a set of rules modulo a set of equations

SIAM Journal on Computing
On word problems in equational theories

14th International Colloquium on Automata, languages and programming
Rewrite systems

Handbook of theoretical computer science (vol. B)
Proving refutational completeness of theorem-proving strategies: the transfinite semantic tree method

Journal of the ACM (JACM)
Modularity of confluence: a simplified proof

Information Processing Letters
Confluence by decreasing diagrams

Theoretical Computer Science
On the modularity of termination of term rewriting systems

Theoretical Computer Science
Tree-Manipulating Systems and Church-Rosser Theorems

Journal of the ACM (JACM)
Complete Sets of Reductions for Some Equational Theories

Journal of the ACM (JACM)
Deciding Combinations of Theories

Proceedings of the 6th Conference on Automated Deduction
Church-Rosser Theorems for Abstract Reduction Modulo an Equivalence Relation

RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
Abstract canonical inference

ACM Transactions on Computational Logic (TOCL)
Confluence by Decreasing Diagrams

RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Modularity of Confluence

IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Diagrammatic Confluence and Completion

ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Modular church-rosser modulo

RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications

Quantified Score

Hi-index	5.23

Visualization

Abstract

This paper builds on a fundamental notion of rewriting theory that characterizes confluence of a (binary) rewriting relation, Klop's cofinal derivations. Cofinal derivations were used by van Oostrom to obtain another characterization of confluence of a rewriting relation via the existence of decreasing diagrams for all local peaks. In this paper, we show that cofinal derivations can be used to give a new, concise proof of Toyama's celebrated modularity theorem and its recent extensions to rewriting modulo in the case of strongly-coherent systems, an assumption discussed in depth here. This is done by generalizing cofinal derivations to cofinal streams, allowing us in turn to generalize van Oostrom's result to the modulo case.