Verifying the Correctness and Amortized Complexity of a Union-Find Implementation in Separation Logic with Time Credits.
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| Title: | Verifying the Correctness and Amortized Complexity of a Union-Find Implementation in Separation Logic with Time Credits. |
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| Authors: | Charguéraud, Arthur1,2 Arthur.Chargueraud@inria.fr, Pottier, François1 Francois.Pottier@inria.fr |
| Source: | Journal of Automated Reasoning. Mar2019, Vol. 62 Issue 3, p331-365. 35p. |
| Abstract: | Union-Find is a famous example of a simple data structure whose amortized asymptotic time complexity analysis is nontrivial. We present a Coq formalization of this analysis, following Alstrup et al.'s recent proof. Moreover, we implement Union-Find as an OCaml library and formally endow it with a modular specification that offers a full functional correctness guarantee as well as an amortized complexity bound. In order to reason in Coq about imperative OCaml code, we use the CFML tool, which implements Separation Logic for a subset of OCaml, and which we extend with time credits. Although it was known in principle that amortized analysis can be explained in terms of time credits and that time credits can be viewed as resources in Separation Logic, we believe our work is the first practical demonstration of this approach. Finally, in order to explain the meta-theoretical foundations of our approach, we define a Separation Logic with time credits for an untyped call-by-value λ-calculus, and formally verify its soundness. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Automated Reasoning is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 134695881 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Verifying the Correctness and Amortized Complexity of a Union-Find Implementation in Separation Logic with Time Credits. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Charguéraud%2C+Arthur%22">Charguéraud, Arthur</searchLink><relatesTo>1,2</relatesTo><i> Arthur.Chargueraud@inria.fr</i><br /><searchLink fieldCode="AR" term="%22Pottier%2C+François%22">Pottier, François</searchLink><relatesTo>1</relatesTo><i> Francois.Pottier@inria.fr</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Automated+Reasoning%22">Journal of Automated Reasoning</searchLink>. Mar2019, Vol. 62 Issue 3, p331-365. 35p. – Name: Abstract Label: Abstract Group: Ab Data: Union-Find is a famous example of a simple data structure whose amortized asymptotic time complexity analysis is nontrivial. We present a Coq formalization of this analysis, following Alstrup et al.'s recent proof. Moreover, we implement Union-Find as an OCaml library and formally endow it with a modular specification that offers a full functional correctness guarantee as well as an amortized complexity bound. In order to reason in Coq about imperative OCaml code, we use the CFML tool, which implements Separation Logic for a subset of OCaml, and which we extend with time credits. Although it was known in principle that amortized analysis can be explained in terms of time credits and that time credits can be viewed as resources in Separation Logic, we believe our work is the first practical demonstration of this approach. Finally, in order to explain the meta-theoretical foundations of our approach, we define a Separation Logic with time credits for an untyped call-by-value λ-calculus, and formally verify its soundness. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Automated Reasoning is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10817-017-9431-7 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 35 StartPage: 331 Titles: – TitleFull: Verifying the Correctness and Amortized Complexity of a Union-Find Implementation in Separation Logic with Time Credits. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Charguéraud, Arthur – PersonEntity: Name: NameFull: Pottier, François IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2019 Type: published Y: 2019 Identifiers: – Type: issn-print Value: 01687433 Numbering: – Type: volume Value: 62 – Type: issue Value: 3 Titles: – TitleFull: Journal of Automated Reasoning Type: main |
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