Logical relations for fine-grained concurrency

Turon, Aaron; Thamsborg, Jacob; Ahmed, Amal; Birkedal, Lars; Dreyer, Derek

doi:10.1145/2429069.2429111

Cited by 60 publications

(42 citation statements)

References 49 publications

(64 reference statements)

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“…However, much work still remains as this reasoning method cannot handle all algorithms. Some logics have introduced speculative linearization points to increase their applicability [25,18]; our approach to helping is closely related to this, and we hope could be extended to speculation. But there are still examples beyond this form of reasoning: for instance there are no proofs of the Herlihy-Wing queue [14] using linearization points (with helping and/or speculation).…”

Section: Related Workmentioning

confidence: 99%

A Generic Logic for Proving Linearizability

Khyzha

Gotsman

Parkinson

2016

FM 2016: Formal Methods

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Linearizability is a commonly accepted notion of correctness for libraries of concurrent algorithms, and recent years have seen a number of proposals of program logics for proving it. Although these logics differ in technical details, they embody similar reasoning principles. To explicate these principles, we propose a logic for proving linearizability that is generic: it can be instantiated with different means of compositional reasoning about concurrency, such as separation logic or rely-guarantee. To this end, we generalise the Views framework for reasoning about concurrency to handle relations between programs, required for proving linearizability. We present sample instantiations of our generic logic and show that it is powerful enough to handle concurrent algorithms with challenging features, such as helping.

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Section: Related Workmentioning

confidence: 99%

A Generic Logic for Proving Linearizability

Khyzha

Gotsman

Parkinson

2016

FM 2016: Formal Methods

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“…Instead of resorting to prophecy variables, we follow the speculation idea [31]. For the concrete step at a potential LP (e.g., line 5 of readPair), we execute the abstract operation speculatively and keep both the result and the original abstract configuration.…”

Section: Try-commit Commands For Future-dependent Lpsmentioning

confidence: 99%

“…Conditional compare-and-swap (CCAS) [31] is a simplified version of the RDCSS algorithm [12]. It involves both the helping mechanism and future-dependent LPs.…”

Section: Conditional Casmentioning

confidence: 99%

“…Recently, Turon et al [31] propose logical relations to verify fine-grained concurrency, which establish contextual refinement between the library and the specification. Underlying the model a similar simulation is defined.…”

Section: Related Work and Conclusionmentioning

confidence: 99%

“…Given the equivalence between linearizability and refinement, we would expect the simulations to justify the soundness of the LP method and to serve as the meta-theory of our logic. However, existing thread-local simulations do not support non-fixed LPs (except the recent work [31], which we will discuss in Sec. 7).…”

Section: Introductionmentioning

confidence: 99%

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Modular verification of linearizability with non-fixed linearization points

Liang

Feng

2013

Proceedings of the 34th ACM SIGPLAN Conference on Programming Language Design and Implementation

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Locating linearization points (LPs) is an intuitive approach for proving linearizability, but it is difficult to apply the idea in Hoarestyle logic for formal program verification, especially for verifying algorithms whose LPs cannot be statically located in the code. In this paper, we propose a program logic with a lightweight instrumentation mechanism which can verify algorithms with nonfixed LPs, including the most challenging ones that use the helping mechanism to achieve lock-freedom (as in HSY eliminationbased stack), or have LPs depending on unpredictable future executions (as in the lazy set algorithm), or involve both features. We also develop a thread-local simulation as the meta-theory of our logic, and show it implies contextual refinement, which is equivalent to linearizability. Using our logic we have successfully verified various classic algorithms, some of which are used in the java.util.concurrent package.

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On the Versatility of Open Logical Relations

Barthe

Crubillé

Lago

et al. 2020

Lecture Notes in Computer Science

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Logical relations are one among the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be immediately proved by means of logical relations, for instance program continuity and differentiability in higher-order languages extended with real-valued functions. Informally, the problem stems from the fact that these properties are naturally expressed on terms of non-ground type (or, equivalently, on open terms of base type), and there is no apparent good definition for a base case (i.e. for closed terms of ground types). To overcome this issue, we study a generalization of the concept of a logical relation, called open logical relation, and prove that it can be fruitfully applied in several contexts in which the property of interest is about expressions of first-order type. Our setting is a simply-typed λ-calculus enriched with real numbers and real-valued first-order functions from a given set, such as the one of continuous or differentiable functions. We first prove a containment theorem stating that for any collection of real-valued firstorder functions including projection functions and closed under function composition, any well-typed term of first-order type denotes a function belonging to that collection. Then, we show by way of open logical relations the correctness of the core of a recently published algorithm for forward automatic differentiation. Finally, we define a refinement-based type system for local continuity in an extension of our calculus with conditionals, and prove the soundness of the type system using open logical relations.

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Logical relations for fine-grained concurrency

Cited by 60 publications

References 49 publications

A Generic Logic for Proving Linearizability

A Generic Logic for Proving Linearizability

Modular verification of linearizability with non-fixed linearization points

On the Versatility of Open Logical Relations

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