Linearizability with Ownership Transfer

TL;DR

This paper extends the classical notion of linearizability to account for ownership transfer via shared heap, enabling correct reasoning about concurrent libraries that interact through shared data structures.

Contribution

It introduces a new definition of linearizability with ownership transfer and proves an Abstraction Theorem for reasoning about client correctness with shared memory.

Findings

Linearizability with ownership transfer can be derived from classical linearizability under certain conditions.

The new definition allows sound abstraction of library implementations in shared memory environments.

The Abstraction Theorem facilitates reasoning about clients without detailed library knowledge.

Abstract

Linearizability is a commonly accepted notion of correctness for libraries of concurrent algorithms. Unfortunately, it assumes a complete isolation between a library and its client, with interactions limited to passing values of a given data type. This is inappropriate for common programming languages, where libraries and their clients can communicate via the heap, transferring the ownership of data structures, and can even run in a shared address space without any memory protection. In this paper, we present the first definition of linearizability that lifts this limitation and establish an Abstraction Theorem: while proving a property of a client of a concurrent library, we can soundly replace the library by its abstract implementation related to the original one by our generalisation of linearizability. This allows abstracting from the details of the library implementation while reasoning about the client. We also prove that linearizability with ownership transfer can be derived from the classical one if the library does not access some of data structures transferred to it by the client.