arXiv subjects

Germán Andrés Delbianco

Publications and source records attributed to Germán Andrés Delbianco.

4 recordsLinked to original sources

arXiv2021

On Algebraic Abstractions for Concurrent Separation Logics

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.

cs.PL↗

arXiv2019

Specifying Concurrent Programs in Separation Logic: Morphisms and Simulations

In addition to pre- and postconditions, program specifications in recent separation logics for concurrency have employed an algebraic structure of resources---a form of state transition system---to describe the state-based program invariants that must be preserved, and to record the permissible atomic changes to program state. In this paper we introduce a novel notion of resource morphism, i.e. structure-preserving function on resources, and show how to effectively integrate it into separation logic, using an associated notion of morphism-specific simulation. We apply morphisms and simulations to programs verified under one resource, to compositionally adapt them to operate under another resource, thus facilitating proof reuse.

cs.PL↗

arXiv2017

Subjective Simulation as a Notion of Morphism for Composing Concurrent Resources

Recent approaches to verifying programs in separation logics for concurrency have used state transition systems (STSs) to specify the atomic operations of programs. A key challenge in the setting has been to compose such STSs into larger ones, while enabling programs specified under one STS to be linked to a larger one, without reverification. This paper develops a notion of morphism between two STSs which permits such lifting. The morphisms are a constructive form of simulation between the STSs, and lead to a general and concise proof system. We illustrate the concept and its generality on several disparate examples, including staged construction of a readers/writers lock and its proof, and of proofs about quiescence when concurrent programs are executed without external interference.

cs.PL↗

arXiv2017

Concurrent Data Structures Linked in Time

Arguments about correctness of a concurrent data structure are typically carried out by using the notion of linearizability and specifying the linearization points of the data structure's procedures. Such arguments are often cumbersome as the linearization points' position in time can be dynamic (depend on the interference, run-time values and events from the past, or even future), non-local (appear in procedures other than the one considered), and whose position in the execution trace may only be determined after the considered procedure has already terminated. In this paper we propose a new method, based on a separation-style logic, for reasoning about concurrent objects with such linearization points. We embrace the dynamic nature of linearization points, and encode it as part of the data structure's auxiliary state, so that it can be dynamically modified in place by auxiliary code, as needed when some appropriate run-time event occurs. We name the idea linking-in-time, because it reduces temporal reasoning to spatial reasoning. For example, modifying a temporal position of a linearization point can be modeled similarly to a pointer update in separation logic. Furthermore, the auxiliary state provides a convenient way to concisely express the properties essential for reasoning about clients of such concurrent objects. We illustrate the method by verifying (mechanically in Coq) an intricate optimal snapshot algorithm due to Jayanti, as well as some clients.

cs.LO↗