1 The Semantics of Transactions and Weak Memory in x 86 , Power , ARMv 8 , and C + +

Weak memory models trade programmability for performance, while transactional memory (TM) aims for ease of programming, sometimes at a performance cost. The semantics of both have been studied in detail, but their combined semantics is not well understood. This is problematic because TM is currently available, either natively or via extensions, in widely-used architectures and languages such as x86, Power, and C++, all of which have weak memory models. Our work aims to provide an formal understanding of the interplay between weak memory and TM, without which, programmers cannot robustly reason about programs that use both of these important concurrent programming constructs. Our first research contribution is the definition of axiomatic models that capture the combination of TM and weak memory as it exists in x86, Power, and C++, and one way that the ARMv8 memory model could be extended to support TM. Our second contribution is the systematic methodology we use to validate our models. This methodology is based around a new tool that is able to synthesise – automatically and exhaustively – exactly the minimal test programs that distinguish any two axiomatic models. This enables us to validate our models by comparing them against both an upper-bound model (transactional sequential consistency) and a lower-bound model (the non-transactional version of each model), and then checking that the outcomes of all the generated programs on existing hardware (where available) are consistent with our models. We further validate our models by checking compilation schemes from C++ transactions to hardware transactions.