Separation of Concerning Things: A Simpler Basis for Defining and Programming with the C/C++ Memory Model

Abstract

The C/C++ memory model provides a range of mechanisms that programmers of concurrent code can use to control accesses to shared variables. The C standard describes the memory model in terms of cross-thread relationships between events, making thread-local, compositional reasoning difficult. In this paper we define the C memory model as a relationship between instructions, straightforwardly based on fundamental properties of data dependencies or artificially injected ordering constraints. Reasoning comprises program transformation with respect to potential instruction reorderings. In the best case one can then reuse an existing result from standard imperative techniques, or failing that employ standard techniques to the transformed program. Other formalisations typically involve complex semantic models, requiring the development of specialised inference systems and assertion languages. A key aspect of our work is that the memory model definition is kept separate to other considerations of a rich programming language such as C. The formal framework is especially suitable for concise code targeting x86, Arm, and RISC-V architectures.

A Syntax and Semantics Definitions

Functions over the Syntax. Write and read variables can be extracted from instructions (11) as follows.

We set . The fences of an instruction $\alpha$, $|\!\alpha \!|$, underpinning relation ${{ \textsc {fnc}}}$, are given by , , and . Memory order constraints from instructions and expressions, underpinning relation ${{ \textsc {ocs}}}$, are extracted as follows.

Any of the functions ($\textsf{fn}(.)$) defined above can be straightforwardly lifted to commands in the following generic pattern.

Operational Semantics. The main rules of the operational semantics for the language in (6) are below [5]. An action $\alpha$ executes as a single step and terminates, i.e., . The composite commands execute as follows, where $\tau$ is a silent (unobservable) step and $c^{n}_{{{ \textsc {m}}}}$ is n-fold iteration of $c$ wrt. ${{ \textsc {m}}}$.

These rules are standard, except for the rule for that allows an action $\beta$ of $c_2$ to proceed before $c_1$ provided $\beta$ can be reordered with $c_1$ according to ${{ \textsc {m}}}$.