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 Readproperty. 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.