research-article

Termination of rewriting under strategies

Authors:

Isabelle Gnaedig,

Hélène KirchnerAuthors Info & Claims

ACM Transactions on Computational Logic (TOCL), Volume 10, Issue 2

Article No.: 10, Pages 1 - 52

https://doi.org/10.1145/1462179.1462182

Published: 02 March 2009 Publication History

Abstract

A termination proof method for rewriting under strategies, based on an explicit induction on the termination property, is presented and instantiated for the innermost, outermost, and local strategies. Rewriting trees are simulated by proof trees generated with an abstraction mechanism, narrowing and constraints representing sets of ground terms. Abstraction introduces variables to represent normal forms without computing them and to control the narrowing mechanism, well known to easily diverge. The induction ordering is not given a priori, but defined with ordering constraints, incrementally set during the proof. It is established that termination under strategy is equivalent to the construction of finite proof trees schematizing terminating rewriting trees. Sufficient effective conditions to ensure finiteness are studied and the method is illustrated on several examples for each specific strategy.

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Gnaedig Appendix (a10-gnaedig-apndx.pdf)

Online appendix to termination of rewriting under strategies. The appendix supports the information on article 10.

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Lucas S(2021)Applications and extensions of context-sensitive rewritingJournal of Logical and Algebraic Methods in Programming10.1016/j.jlamp.2021.100680121(100680)Online publication date: Jun-2021
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Termination of rewriting under strategies

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cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 10, Issue 2

February 2009

275 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/1462179

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Copyright © 2009 ACM.

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Publication History

Published: 02 March 2009

Accepted: 01 September 2007

Revised: 01 August 2007

Received: 01 September 2006

Published in TOCL Volume 10, Issue 2

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Cited By

Lucas S(2021)Applications and extensions of context-sensitive rewritingJournal of Logical and Algebraic Methods in Programming10.1016/j.jlamp.2021.100680121(100680)Online publication date: Jun-2021
https://doi.org/10.1016/j.jlamp.2021.100680
Kirchner CKirchner Hde Oliveira A(2019)Analysis of Rewrite-Based Access Control PoliciesElectronic Notes in Theoretical Computer Science (ENTCS)10.1016/j.entcs.2009.02.072234(55-75)Online publication date: 5-Jan-2019
https://dl.acm.org/doi/10.1016/j.entcs.2009.02.072
Kirchner H(2015)Rewriting Strategies and Strategic Rewrite ProgramsLogic, Rewriting, and Concurrency10.1007/978-3-319-23165-5_18(380-403)Online publication date: 27-Aug-2015
https://doi.org/10.1007/978-3-319-23165-5_18
Kirchner CKirchner H(2014)Equational Logic and RewritingComputational Logic10.1016/B978-0-444-51624-4.50006-X(255-282)Online publication date: 2014
https://doi.org/10.1016/B978-0-444-51624-4.50006-X
Kirchner H(2013)A rewriting point of view on strategiesElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.112.15112(99-105)Online publication date: 1-Mar-2013
https://doi.org/10.4204/EPTCS.112.15
LäMmel RThompson SKaiser M(2013)Programming errors in traversal programs over structured dataScience of Computer Programming10.1016/j.scico.2011.11.00678:10(1770-1808)Online publication date: 1-Oct-2013
https://dl.acm.org/doi/10.1016/j.scico.2011.11.006
Meseguer J(2012)Twenty years of rewriting logicThe Journal of Logic and Algebraic Programming10.1016/j.jlap.2012.06.00381:7-8(721-781)Online publication date: Oct-2012
https://doi.org/10.1016/j.jlap.2012.06.003
Giesl JRaffelsieper MSchneider-Kamp PSwiderski SThiemann R(2011)Automated termination proofs for haskell by term rewritingACM Transactions on Programming Languages and Systems (TOPLAS)10.1145/1890028.189003033:2(1-39)Online publication date: 7-Feb-2011
https://dl.acm.org/doi/10.1145/1890028.1890030
Gnaedig IKirchner H(2011)Proving weak properties of rewritingTheoretical Computer Science10.1016/j.tcs.2011.04.028412:34(4405-4438)Online publication date: Aug-2011
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Bourdier TCirstea HDougherty DKirchner H(2010)Extensional and Intensional StrategiesElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.15.115(1-19)Online publication date: 26-Jan-2010
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