research-article

A proof system for separation logic with magic wand

Authors:

Sungwoo ParkAuthors Info & Claims

ACM SIGPLAN Notices, Volume 49, Issue 1

Pages 477 - 490

https://doi.org/10.1145/2578855.2535871

Published: 08 January 2014 Publication History

Abstract

Separation logic is an extension of Hoare logic which is acknowledged as an enabling technology for large-scale program verification. It features two new logical connectives, separating conjunction and separating implication, but most of the applications of separation logic have exploited only separating conjunction without considering separating implication. Nevertheless the power of separating implication has been well recognized and there is a growing interest in its use for program verification. This paper develops a proof system for full separation logic which supports not only separating conjunction but also separating implication. The proof system is developed in the style of sequent calculus and satisfies the admissibility of cut. The key challenge in the development is to devise a set of inference rules for manipulating heap structures that ensure the completeness of the proof system with respect to separation logic. We show that our proof of completeness directly translates to a proof search strategy.

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Cited By

Hóu ZClouston RGoré RTiu A(2018)Modular Labelled Sequent Calculi for Abstract Separation LogicsACM Transactions on Computational Logic10.1145/319738319:2(1-35)Online publication date: 28-Apr-2018
https://dl.acm.org/doi/10.1145/3197383
Mulder ICzajka ŁKrebbers R(2023)Beyond Backtracking: Connections in Fine-Grained Concurrent Separation LogicProceedings of the ACM on Programming Languages10.1145/35912757:PLDI(1340-1364)Online publication date: 6-Jun-2023
https://dl.acm.org/doi/10.1145/3591275
Mulder IKrebbers RGeuvers HJhala RDillig I(2022)Diaframe: automated verification of fine-grained concurrent programs in IrisProceedings of the 43rd ACM SIGPLAN International Conference on Programming Language Design and Implementation10.1145/3519939.3523432(809-824)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519939.3523432
Show More Cited By

Index Terms

A proof system for separation logic with magic wand
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Theorem proving algorithms
2. Theory of computation
  1. Logic
    1. Proof theory
  2. Models of computation
    1. Computability

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Published In

cover image ACM SIGPLAN Notices

ACM SIGPLAN Notices Volume 49, Issue 1

POPL '14

January 2014

661 pages

ISSN:0362-1340

EISSN:1558-1160

DOI:10.1145/2578855

Editor:
Mark W. Bailey
Hamilton College, Clinton, NY

Issue’s Table of Contents

POPL '14: Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
January 2014
702 pages
ISBN:9781450325448
DOI:10.1145/2535838
General Chair:
Suresh Jagannathan
Purdue University, USA
,
Program Chair:
Peter Sewell
University of Cambridge, UK

Copyright © 2014 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 08 January 2014

Published in SIGPLAN Volume 49, Issue 1

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Cited By

Hóu ZClouston RGoré RTiu A(2018)Modular Labelled Sequent Calculi for Abstract Separation LogicsACM Transactions on Computational Logic10.1145/319738319:2(1-35)Online publication date: 28-Apr-2018
https://dl.acm.org/doi/10.1145/3197383
Mulder ICzajka ŁKrebbers R(2023)Beyond Backtracking: Connections in Fine-Grained Concurrent Separation LogicProceedings of the ACM on Programming Languages10.1145/35912757:PLDI(1340-1364)Online publication date: 6-Jun-2023
https://dl.acm.org/doi/10.1145/3591275
Mulder IKrebbers RGeuvers HJhala RDillig I(2022)Diaframe: automated verification of fine-grained concurrent programs in IrisProceedings of the 43rd ACM SIGPLAN International Conference on Programming Language Design and Implementation10.1145/3519939.3523432(809-824)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519939.3523432
Jin ZZhang BCao TCao YWang H(2022)Reasoning About Block-Based Cloud Storage Systems via Separation LogicTheoretical Computer Science10.1016/j.tcs.2022.09.015Online publication date: Sep-2022
https://doi.org/10.1016/j.tcs.2022.09.015
Dardinier TParthasarathy GWeeks NMüller PSummers A(2022)Sound Automation of Magic WandsComputer Aided Verification10.1007/978-3-031-13188-2_7(130-151)Online publication date: 6-Aug-2022
https://doi.org/10.1007/978-3-031-13188-2_7
Sammler MLepigre RKrebbers RMemarian KDreyer DGarg DFreund SYahav E(2021)RefinedC: automating the foundational verification of C code with refined ownership typesProceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation10.1145/3453483.3454036(158-174)Online publication date: 19-Jun-2021
https://dl.acm.org/doi/10.1145/3453483.3454036
Jin ZZhang BZhang LCao YWang H(2021)An adaptation-complete proof system for local reasoning about cloud storage systemsTheoretical Computer Science10.1016/j.tcs.2021.12.018Online publication date: Dec-2021
https://doi.org/10.1016/j.tcs.2021.12.018
Hóu ZClouston RGoré RTiu A(2018)Modular Labelled Sequent Calculi for Abstract Separation LogicsACM Transactions on Computational Logic10.1145/319738319:2(1-35)Online publication date: 28-Apr-2018
https://dl.acm.org/doi/10.1145/3197383
Bannister CHöfner PKlein G(2018)Backwards and Forwards with Separation LogicInteractive Theorem Proving10.1007/978-3-319-94821-8_5(68-87)Online publication date: 4-Jul-2018
https://doi.org/10.1007/978-3-319-94821-8_5
Demri SDeters M(2016)Expressive Completeness of Separation Logic with Two Variables and No Separating ConjunctionACM Transactions on Computational Logic10.1145/283549017:2(1-44)Online publication date: 7-Jan-2016
https://dl.acm.org/doi/10.1145/2835490
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