Provably Fair Cooperative Scheduling

The context of this work is cooperative scheduling, a concurrency paradigm, where task execution is not arbitrarily preempted. Instead, language constructs exist that let a task voluntarily yield the right to execute to another task. The inquiry is the design of provably fair schedulers and suitable notions of fairness for cooperative scheduling languages. To the best of our knowledge, this problem has not been addressed so far. Our approach is to study fairness independently from syntactic constructs or environments, purely from the point of view of the semantics of programming languages, i.e., we consider fairness criteria using the formal definition of a program execution. We develop our concepts for classic structural operational semantics (SOS) as well as for the recent locally abstract, globally concrete (LAGC) semantics. The latter is a highly modular approach to semantics ensuring the separation of concerns between local statement evaluation and scheduling decisions. The new knowledge contributed by our work is threefold: first, we show that a new fairness notion, called quiescent fairness, is needed to characterize fairness adequately in the context of cooperative scheduling; second, we define a provably fair scheduler for cooperative scheduling languages; third, a qualitative comparison between the SOS and LAGC versions yields that the latter, while taking higher initial effort, is more amenable to proving fairness and scales better under language extensions than SOS. The grounding of our work is a detailed formal proof of quiescent fairness for the scheduler defined in LAGC semantics. The importance of our work is that it provides a formal foundation for the implementation of fair schedulers for cooperative scheduling languages, an increasingly popular paradigm (for example: akka/Scala, JavaScript, async Rust). Being based solely on semantics, our ideas are widely applicable. Further, our work makes clear that the standard notion of fairness in concurrent languages needs to be adapted for cooperative scheduling and, more generally, for any language that combines atomic execution sequences with some form of preemption.