On algebraic abstractions for concurrent separation logics

Abstract

Concurrent separation logic is distinguished by transfer of state ownership upon parallel composition and framing. The algebraic structure that underpins ownership transfer is that of partial commutative monoids (PCMs). Extant research considers ownership transfer primarily from the logical perspective while comparatively less attention is drawn to the algebraic considerations. This paper provides an algebraic formalization of ownership transfer in concurrent separation logic by means of structure-preserving partial functions (i.e., morphisms) between PCMs, and an associated notion of separating relations. Morphisms of structures are a standard concept in algebra and category theory, but haven't seen ubiquitous use in separation logic before. Separating relations. are binary relations that generalize disjointness and characterize the inputs on which morphisms preserve structure. The two abstractions facilitate verification by enabling concise ways of writing specs, by providing abstract views of threads' states that are preserved under ownership transfer, and by enabling user-level construction of new PCMs out of existing ones.

Decision Problems in a Logic for Reasoning About Reconfigurable Distributed Systems

“…Local reasoning about concurrent programs has been traditionally the focus of Concurrent Separation Logic (CSL), based on a parallel composition rule [36], initially with a non-interfering (race-free) semantics [8] and later combining ideas of assumeand rely-guarantee [28,38] with local reasoning [22,42] and abstract notions of framing [15,16,21]. However, the body of work on CSL deals almost entirely with sharedmemory multithreading programs, instead of distributed systems, which is the aim of our work.…”

Reasoning about Reconfigurations of Distributed Systems

“…Local reasoning about parallel programs has been traditionally within the scope of Concurrent Separation Logic (CSL), that introduced a parallel composition rule [36], with a non-interfering (race-free) semantics of shared-memory parallelism [8]. Considering interference in CSL requires more general proof rules, combining ideas of assume-and rely-guarantee [39,29] with local reasoning [26,46] and abstract notions of framing [17,16,25]. These rules generalize from both standard CSL parallel composition and rely-guarantee rules, allowing even to reason about properties of concurrent objects, such as (non-)linearizability [43].…”

Verification of Component-based Systems with Recursive Architectures

“…In combination with the proof system reported in [4], the verification method presented in this paper can automatically prove the correctness of a distributed system after the reconfiguration of its coordinating architecture. Since various dialects of (Concurrent) Separation Logic are being commonly used to specify and reason about concurrent systems [5,6,7], we expect this new logic to be easily accepted by the research and development community. The contribution of this paper is three-fold:…”