[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85328-en":3,"doc-seo-85328-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},85328,1099514068365,"Aurelia","https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?_k=1776742907772140068",8,"Research & Report","Completeness of Logical Atomicity for Linearizability in Concurrent Separation Logic","Linearizability is a core correctness condition for concurrent data structures, but using it as a specification for clients can be difficult within concurrent separation logic. Prior work introduced logical atomicity, a specification style that internalizes operation atomicity using separation-logic reasoning rules and supports easier compositional verification. This paper proves a completeness theorem for Iris: every linearizable data structure admits a corresponding logically atomic specification. It embeds multiple linearizability proof techniques and derives results for queue implementations, mechanized in Rocq Prover.","arXiv :2607 . 1 1435v 1 [ cs .LO] 13 Jul 2026  \nCompleteness of Logical Atomicity for Linearizability in Concurrent Separation Logic  \nZICHEN ZHANG, New York University, USA  \nSIMON ODDERSHEDE GREGERSEN, CISPA Helmholtz Center for Information Security, Germany JOSEPH TASSAROTTI∗ , New York University, USA  \nLinearizability is a standard correctness condition for concurrent data structures. It guarantees that operations behave as if they took effect at some atomic instant between their call and return points. Despite the central role linearizability plays, in the context of concurrent separation logics, prior work has argued for instead using a style of specification that internalizes the atomicity of operations in terms of the logic’s reasoning rules, known as logical atomicity. These logically atomic specifications are intended to be easier to compose inside of the logic than linearizability. Prior work has shown that in the Iris separation logic framework, a certain form of logically atomic specifications implies that a data structure is linearizable, which can be understood as a soundness theorem. However, the converse remained an open question: for every linearizable data structure, is it always possible to derive a corresponding logically atomic specification?  \nThis paper resolves this question in the affirmative. We prove a completeness theorem for Iris that derives a logically atomic specification for any linearizable data structure. As a consequence, we are able to embed a variety of linearizability proof techniques into Iris and use them to derive logically atomic specifications. We apply this to three linearizability proof methods: aspect-oriented linearizability proofs, forward simulations with commit points, and meta-configuration tracking. Using these embeddings, we derive logically atomic specifications for the Herlihy-Wing queue and the Baskets Queue. We furthermore establish a connection between logical atomicity and an encoding of refinement in Iris that has been used in prior logical relations models. This result allows us to transport logically atomic specifications across refinements, which we apply to the Folly MPMC queue implementation. All of the results in this paper have been mechanized in the Rocq Prover.  \nAdditional KeyWords and Phrases: Iris, Separation Logic, Linearizability, Logical Atomicity, Prophecy Variables, Contextual Refinement  \n1 Introduction  \nLinearizability is a standard correctness condition for concurrent data structures [32, 33, 62] . It ensures that concurrent operations behave as if they took effect atomically in a way that is compatible with a sequential specification of the data structure. Because linearizability is such a widely used correctness condition for concurrent data structures, a vast array of formal methods techniques related to linearizability have been developed. These include various proof techniques [1, 6, 11, 20, 21, 30, 39, 56], program logics [28, 47, 69, 70], automated verifiers [50, 51, 72, 79], and tools for checking for linearizability violations [7, 10, 19, 27, 35, 44, 59] . Alongside this, researchers have developed various adaptations of linearizability, including relaxations for weak memory [8, 14, 16], more compositional formulations [74], restrictions that guarantee stronger properties [13, 25], and variants for durable or persistent memory [2, 3, 37] .  \nLogical Atomicity. Yet despite the central role linearizability plays, a number of researchers have argued that linearizability, as formally defined, is not so easy to use to verify clients of a linearizable data structure. In particular, while concurrent separation logic (CSL) has been successfully used to verify a range of concurrent programs, and there are even ways to use CSL to prove that a  \n∗ Also affiliated with Amazon Web Services. This paper does not reflect the views of Amazon Web Services.  \nAuthors’ Contact Information: Zichen Zhang, [zichenzhang@nyu.edu](zichenzhang@nyu.edu), New York","cbCaiuEWaIlp2wgb","https://ap.wps.com/l/cbCaiuEWaIlp2wgb","pdf",795809,2,1,38,"English","en",105,"# Introduction\n## Linearizability\n## Logical Atomicity","[{\"question\":\"What problem does the paper address about linearizability in concurrent separation logic?\",\"answer\":\"It addresses that, although linearizability is standard and can be proved for internal data structures, it can be hard to use in pre/post-condition style reasoning for clients in concurrent separation logic.\"},{\"question\":\"What is the main contribution of the paper regarding logical atomicity?\",\"answer\":\"It proves a completeness theorem for Iris showing that for every linearizable data structure, a corresponding logically atomic specification can be derived.\"},{\"question\":\"How does the completeness result enable further work in Iris?\",\"answer\":\"It allows embedding several linearizability proof techniques into Iris to derive logically atomic specifications, including results for specific queue implementations and the transport of specifications across refinements.\"}]",1784202518,96,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"completeness-of-logical-atomicity-for-linearizability-in-concurrent-separation-logic","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/completeness-of-logical-atomicity-for-linearizability-in-concurrent-separation-logic/85328/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-23","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the paper address about linearizability in concurrent separation logic?","Question",{"text":75,"@type":76},"It addresses that, although linearizability is standard and can be proved for internal data structures, it can be hard to use in pre/post-condition style reasoning for clients in concurrent separation logic.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the main contribution of the paper regarding logical atomicity?",{"text":80,"@type":76},"It proves a completeness theorem for Iris showing that for every linearizable data structure, a corresponding logically atomic specification can be derived.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the completeness result enable further work in Iris?",{"text":84,"@type":76},"It allows embedding several linearizability proof techniques into Iris to derive logically atomic specifications, including results for specific queue implementations and the transport of specifications across 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