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Layer Systems for Proving Confluence

Authors:

Bertram Felgenhauer,

Aart Middeldorp,

Vincent Van OostromAuthors Info & Claims

ACM Transactions on Computational Logic (TOCL), Volume 16, Issue 2

Article No.: 14, Pages 1 - 32

https://doi.org/10.1145/2710017

Published: 09 March 2015 Publication History

Abstract

We introduce layer systems for proving generalizations of the modularity of confluence for first-order rewrite systems. Layer systems specify how terms can be divided into layers. We establish structural conditions on those systems that imply confluence. Our abstract framework covers known results like modularity, many-sorted persistence, layer-preservation, and currying. We present a counterexample to an extension of persistence to order-sorted rewriting and derive new sufficient conditions for the extension to hold. All our proofs are constructive.

References

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Cited By

Jouannaud JOrejas F(2023)Unification of drags and confluence of drag rewritingJournal of Logical and Algebraic Methods in Programming10.1016/j.jlamp.2022.100845131(100845)Online publication date: Feb-2023
https://doi.org/10.1016/j.jlamp.2022.100845
Dowek GFérey GJouannaud JLiu J(2022)Confluence of left-linear higher-order rewrite theories by checking their nested critical pairsMathematical Structures in Computer Science10.1017/S0960129522000044(1-36)Online publication date: 17-Mar-2022
https://doi.org/10.1017/S0960129522000044
Hirokawa NNagele Jvan Oostrom VOyamaguchi M(2019)Confluence by Critical Pair Analysis RevisitedAutomated Deduction – CADE 2710.1007/978-3-030-29436-6_19(319-336)Online publication date: 27-Aug-2019
https://dl.acm.org/doi/10.1007/978-3-030-29436-6_19
Show More Cited By

Index Terms

Layer Systems for Proving Confluence
1. Theory of computation
  1. Logic
  2. Models of computation
    1. Computability

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Published In

cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 16, Issue 2

March 2015

260 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/2737801

Editor:
Dale Miller
INRIA Saclay, France

Issue’s Table of Contents

Copyright © 2015 Owner/Author.

Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 09 March 2015

Accepted: 01 December 2014

Revised: 01 October 2014

Received: 01 April 2014

Published in TOCL Volume 16, Issue 2

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Cited By

Jouannaud JOrejas F(2023)Unification of drags and confluence of drag rewritingJournal of Logical and Algebraic Methods in Programming10.1016/j.jlamp.2022.100845131(100845)Online publication date: Feb-2023
https://doi.org/10.1016/j.jlamp.2022.100845
Dowek GFérey GJouannaud JLiu J(2022)Confluence of left-linear higher-order rewrite theories by checking their nested critical pairsMathematical Structures in Computer Science10.1017/S0960129522000044(1-36)Online publication date: 17-Mar-2022
https://doi.org/10.1017/S0960129522000044
Hirokawa NNagele Jvan Oostrom VOyamaguchi M(2019)Confluence by Critical Pair Analysis RevisitedAutomated Deduction – CADE 2710.1007/978-3-030-29436-6_19(319-336)Online publication date: 27-Aug-2019
https://dl.acm.org/doi/10.1007/978-3-030-29436-6_19
Felgenhauer BRapp F(2018)Layer Systems for Confluence—FormalizedTheoretical Aspects of Computing – ICTAC 201810.1007/978-3-030-02508-3_10(173-190)Online publication date: 15-Oct-2018
https://doi.org/10.1007/978-3-030-02508-3_10
Nagele JFelgenhauer BMiddeldorp A(2017)CSI: New Evidence – A Progress ReportAutomated Deduction – CADE 2610.1007/978-3-319-63046-5_24(385-397)Online publication date: 11-Jul-2017
https://doi.org/10.1007/978-3-319-63046-5_24

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