A theory of memory models

Abstract

A memory model for a concurrent imperative programming language specifies which writes to shared variables may be seen by reads performed by other threads. We present a simple mathematical framework for relaxed memory models for programming languages. To instantiate this framework for a specific language, the designer must choose the notion of atomic steps supported by the language (e.g. 32-bit reads and writes) and specify how a composite step may be broken into a sequence of atomic steps (the decomposition rule). This rule determines which sequence of intermediate writes (if any) are visible to concurrent reads by other threads. Different choices of the rule lead to models which permit a read to return any value if there is a concurrent write (race), or models which satisfy a "No Thin Air Read" property. The former is suitable for languages such as C++ (programs with races have undefined behavior), and the latter for Java. Other intermediate models are possible, useful and interesting.We establish that all models in the framework satisfy the Fundamental Property of relaxed memory models: programs whose sequentially consistent (SC) executions have no races must have have only SC executions. We show how to define synchronization constructs (such as volatiles of various kinds) in the framework, and discuss the causality test cases from the Java Memory Model.

A Better x86 Memory Model: x86-TSO

“…They argue that the additional intensional detail increases the effectiveness of simulation-based verification. Saraswat et al [18] also define memory models in terms of local reordering, and prove a DRF theorem, but focus on high-level languages. Several groups have used proof tools to tame the intricacies of these models, including Yang et al [22], using Prolog and SAT solvers to explore an axiomatic Itanium model, and Aspinall anď Sevčík [5], who formalised and identified problems with the Java Memory Model using Isabelle/HOL.…”

Parameterized Memory Models and Concurrent Separation Logic

“…LI is an inter-thread transformation. It is unclear how it relates to our subsumption relation, but the examples [26] involving LI (e.g., the cross-over example) can be supported following the pattern with which we reproduce the prescient-write example in Sect. 4.…”

“…The RAO model by Saraswat et al [26] consists of a family of transformations (IM, CO, AU, LI, PR and DX). Unlike our subsumption relation which gives only an abstract and extensional formulation of semantics preservation between sequential threads, each of them defines a very specific class of transformations.…”

“…well-synchronized programs) behave in a sequentially consistent manner. The DRF-guarantee is also known as the fundamental property [26] of a memory model. It is desirable because it frees the programmer from reasoning about idiosyncrasies of memory models when the program is well-synchronized.…”

A Theory of Speculative Computation

“…By considering parallel composition of speculations, we also include relaxed memory models [1] into this picture -though not those that try to capture compiler optimizations, that transform the code on the basis of semantical reasoning (see [4,20,24]). …”