Authors: Robert Soule, Martin Hirzel, Bugra Gedik, Robert Grimm Title: From a Calculus to an Execution Environment for Stream Processing Abstract At one level, this paper is about River, a virtual execution environment for stream processing. Stream processing is a paradigm well-suited for many modern data processing systems that ingest high-volume data streams from the real world, such as audio/video streaming, high-frequency trading, and security monitoring. One attractive property of stream processing is that it lends itself to parallelization on multi-cores, and even to distribution on clusters when extreme scale is required. Stream processing has been co-evolved by several communities, leading to diverse languages with similar core concepts. Providing a common execution environment reduces language development effort and increases portability. We designed River as a practical realization of Brooklet, a calculus for stream processing. So at another level, this paper is about a journey from theory (the calculus) to practice (the execution environment). The challenge is that, by definition, a calculus abstracts away all but the most central concepts. Hence, there are several research questions in concretizing the missing parts, not to mention a significant engineering effort in implementing them. But the effort is well worth it, because the benefit of using a calculus as a foundation is that it yields clear semantics and proven correctness results.