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Non-termination Proving at Scale

Authors:

Julien Vanegue,

Peter O’HearnAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 8, Issue OOPSLA2

Article No.: 280, Pages 246 - 274

https://doi.org/10.1145/3689720

Published: 08 October 2024 Publication History

Abstract

Program termination is a classic non-safety property whose falsification cannot in general be witnessed by a finite trace. This makes testing for non-termination challenging, and also a natural target for symbolic proof. Several works in the literature apply non-termination proving to small, self-contained benchmarks, but it has not been developed for large, real-world projects; as such, despite its allure, non-termination proving has had limited practical impact. We develop a compositional theory for non-termination proving, paving the way for its scalable application to large codebases. Discovering non-termination is an under-approximate problem, and we present UNTer, a sound and complete under-approximate logic for proving non-termination. We then extend UNTer with separation logic and develop UNTer^SL for heap-manipulating programs, yielding a compositional proof method amenable to automation via under-approximation and bi-abduction. We extend the Pulse analyser from Meta and develop Pulse^∞, an automated, compositional prover for non-termination based on UNTer^SL. We have run Pulse^∞ on large codebases and libraries, each comprising hundreds of thousands of lines of code, including OpenSSL, libxml2, libxpm and CryptoPP; it discovered several previously-unknown non-termination bugs and have reported them to developers of these libraries.

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Cited By

Verscht LKaminski B(2025)A Taxonomy of Hoare-Like Logics: Towards a Holistic View using Predicate Transformers and Kleene Algebras with Top and TestsProceedings of the ACM on Programming Languages10.1145/37048969:POPL(1782-1811)Online publication date: 9-Jan-2025
https://dl.acm.org/doi/10.1145/3704896
Zhang LZilberstein NKaminski BSilva A(2024)Quantitative Weakest Hyper Pre: Unifying Correctness and Incorrectness Hyperproperties via Predicate TransformersProceedings of the ACM on Programming Languages10.1145/36897408:OOPSLA2(817-845)Online publication date: 8-Oct-2024
https://doi.org/10.1145/3689740
Zilberstein NSridharan M(2024)Unified Analysis Techniques for Programs with OutcomesCompanion Proceedings of the 2024 ACM SIGPLAN International Conference on Systems, Programming, Languages, and Applications: Software for Humanity10.1145/3689491.3691814(4-6)Online publication date: 20-Oct-2024
https://dl.acm.org/doi/10.1145/3689491.3691814

Index Terms

Non-termination Proving at Scale
1. Software and its engineering
  1. Software notations and tools
    1. General programming languages
2. Theory of computation
  1. Logic
  2. Semantics and reasoning
    1. Program reasoning
      1. Program analysis
      2. Program verification

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cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 8, Issue OOPSLA2

October 2024

2691 pages

EISSN:2475-1421

DOI:10.1145/3554319

Editor:
Michael Hicks
Amazon, USA

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This work is licensed under a Creative Commons Attribution International 4.0 License.

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Association for Computing Machinery

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Published: 08 October 2024

Published in PACMPL Volume 8, Issue OOPSLA2

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Cited By

Verscht LKaminski B(2025)A Taxonomy of Hoare-Like Logics: Towards a Holistic View using Predicate Transformers and Kleene Algebras with Top and TestsProceedings of the ACM on Programming Languages10.1145/37048969:POPL(1782-1811)Online publication date: 9-Jan-2025
https://dl.acm.org/doi/10.1145/3704896
Zhang LZilberstein NKaminski BSilva A(2024)Quantitative Weakest Hyper Pre: Unifying Correctness and Incorrectness Hyperproperties via Predicate TransformersProceedings of the ACM on Programming Languages10.1145/36897408:OOPSLA2(817-845)Online publication date: 8-Oct-2024
https://doi.org/10.1145/3689740
Zilberstein NSridharan M(2024)Unified Analysis Techniques for Programs with OutcomesCompanion Proceedings of the 2024 ACM SIGPLAN International Conference on Systems, Programming, Languages, and Applications: Software for Humanity10.1145/3689491.3691814(4-6)Online publication date: 20-Oct-2024
https://dl.acm.org/doi/10.1145/3689491.3691814

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