Confluence of Non-Left-Linear TRSs via Relative Termination

Klein, Dominik; Hirokawa, Nao

doi:10.1007/978-3-642-28717-6_21

Cited by 10 publications

(8 citation statements)

References 18 publications

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“…For reference in Table 2 we compare the power of the confluence provers participating in the Confluence Competition (CoCo), 9 i.e., ACP [4], CSI [30], and saigawa [11,13].…”

Section: Methodsmentioning

confidence: 99%

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Labelings for Decreasing Diagrams

2014

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This article is concerned with automating the decreasing diagrams technique of van Oostrom for establishing confluence of term rewrite systems. We study abstract criteria that allow to lexicographically combine labelings to show local diagrams decreasing. This approach has two immediate benefits. First, it allows to use labelings for linear rewrite systems also for left-linear ones, provided some mild conditions are satisfied. Second, it admits an incremental method for proving confluence which subsumes recent developments in automating decreasing diagrams. The techniques proposed in the article have been implemented and experimental results demonstrate how, e.g., the rule labeling benefits from our contributions.

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“…For reference in Table 2 we compare the power of the confluence provers participating in the Confluence Competition (CoCo), 9 i.e., ACP [4], CSI [30], and saigawa [11,13].…”

Section: Methodsmentioning

confidence: 99%

“…In addition it implements development closed critical pairs [19] and persistence [7]. Recently, the techniques introduced in [2] and [13] have also been integrated. -saigawa also heavily exploits relative termination, remarkably also to analyze confluence of non-left-linear systems [13].…”

Section: Methodsmentioning

confidence: 99%

Labelings for Decreasing Diagrams

2014

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“…A key idea in [2] is that AC rules are reversible. This idea was combined with the extended critical pair lemma of Jouannaud and Kirchner [13] in Saigawa [15] and more recently in CoLL [38], where the technique is extended to handle associative rules in the absence of commutation rules.…”

Section: Extensionsmentioning

confidence: 99%

CSI: New Evidence – A Progress Report

Nagele

Felgenhauer

Middeldorp

2017

Automated Deduction – CADE 26

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CSI is a strong automated confluence prover for rewrite systems which has been in development since 2010. In this paper we report on recent extensions that make CSI more powerful, secure, and useful. These extensions include improved confluence criteria but also support for uniqueness of normal forms. Most of the implemented techniques produce machine-readable proof output that can be independently verified by an external tool, thus increasing the trust in CSI. We also report on CSIˆho, a tool built on the same framework and similar ideas as CSI that automatically checks confluence of higher-order rewrite systems.

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“…Confluence of rewrite systems is an important property, which is intimately connected to uniqueness of normal forms, and hence to determinism of programs. In recent years there has been tremendous progress in establishing confluence or non-confluence of TRSs automatically, with a number of tools under active development, like ACP [2], Saigawa [8,11], CoLL [18], and our own tool, CSI [23].…”

Section: Introductionmentioning

confidence: 99%

Certification of Classical Confluence Results for Left-Linear Term Rewrite Systems

Nagele

Middeldorp

2016

Interactive Theorem Proving

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This paper presents the first formalization of three classic confluence criteria for first-order term rewrite systems by Huet and Toyama. We have formalized proofs, showing that (1) linear strongly closed systems, (2) left-linear parallel closed systems, and (3) left-linear almost parallel closed systems are confluent. The third result is extended to commutation. The proofs were carried out in the proof assistant Isabelle/HOL as part of the library IsaFoR and integrated into the certifier CeTA, significantly increasing the number of certifiable proofs produced by automatic confluence tools.

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Confluence of Non-Left-Linear TRSs via Relative Termination

Cited by 10 publications

References 18 publications

Labelings for Decreasing Diagrams

Labelings for Decreasing Diagrams

CSI: New Evidence – A Progress Report

Certification of Classical Confluence Results for Left-Linear Term Rewrite Systems

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