A memory consistency model specifies the allowed behaviors of shared memory concurrent programs. At the language level, these models are known to have a non-trivial impact on the safety of program optimizations. This limits the ability to rearrange/refactor code without introducing new behaviors. Existing programming language memory models try to address this by permitting more ( relaxed/weak ) concurrent behaviors, but are still unable to allow all the desired optimizations. A core problem is that weaker consistency models may also render optimizations unsafe, a conclusion that goes against the intuition of them allowing more behaviors. This exposes an open problem of the compositional interaction between memory consistency semantics and optimizations; which parts of the semantics correspond to allowing/disallowing which set of optimizations is unclear. In this work, we establish a formal foundation suitable enough to understand this compositional nature. We decompose optimizations into a finite set of elementary effects , over which aspects of safety can be assessed. We use this decomposition to identify a desirable compositional property ( complete ) that would guarantee the safety of optimizations from one memory model to another. We showcase its practicality by proving such a property between Sequential Consistency (SC) and SC RR , the latter allowing independent read-read reordering over SC . Our work potentially paves way to a new design methodology of programming-language memory models, one that places emphasis on the optimizations desired to be performed.

Memory consistency models traditionally specify the behavior of shared memory concurrent hardware. Hardware behavior drifts away from traditional sequential reasoning, thus exhibiting behaviors that are termed as "weak". Weaker consistency models allow for more concurrent behaviors, thus justifying hardware optimizations such as read/write buffers. In parallel, weaker memory models for software allow more compiler optimizations (transformations). However, this "more" may not be strict: certain safe optimizations in stronger models are rendered unsafe in ones weaker than them. We identify properties that must hold among a pair of weak and strong memory models to guarantee this. We propose a framework using which we could build such models, showcasing our results in allowing Read Read reordering over Sequential Consistency (SC). We also show how to partially retain our desired property for a pair of models, placing constraints on the set of transformations or equivalently, on program structure. Lastly, we discuss the potential advantage of designing models satisfying such properties.