Data-stream processing has continuously risen in importance as the amount of available data has been steadily increas- ing over the last decade. Besides traditional domains such as data-center monitoring and click analytics, there is an increasing number of network-enabled production machines that generate continuous streams of data. Due to their continuous nature, queries on data-streams can be more complex, and distinctly harder to understand then database queries. As users have to consider operational details, maintenance and debugging become challenging. Current approaches model data-streams as sequences, be- cause this is the way they are physically received. These models result in an implementation-focused perspective. We explore an alternate way of modeling data-streams by focusing on time-slicing semantics. This focus results in a model based on functions, which is better suited for reasoning about query semantics. By adapting the definitions of relevant concepts in stream processing to our model, we illustrate the practical useful- ness of our approach. Thereby, we link data-streams and query primitives to concepts in functional programming and mathematics. Most noteworthy, we prove that data-streams are monads, and show how to derive monad definitions for current data-stream models. We provide an abstract, yet practical perspective on data- stream related subjects based on a sound, consistent query model. Our work can serve as solid foundation for future data-stream query-languages.
In our earlier work @cite_8 , we focused on a generic set of operations for continuous queries. We motivated the necessity for pattern matching and more powerful window constructs, and showed that equality may be proven. However, we could not provide a formal proof, as our model relied on conventions, and a sequential perspective is less convenient for proofs than a functional one. This is one of the main motivations for this paper.
@cite_8
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Many interesting applications of continuous-query processing are concerned with pattern matching or complex temporal aggregation of events. Real-world queries that rely on these operations are difficult to implement in current stream-processing systems. The reason seems to be a gap between two types of existing query languages: Some languages (e. g. CQL) offer a small set of simple operators that can be combined in order to create complex queries. While these languages provide sound and comprehensible semantics, they lack the expressiveness required for many real-world applications. Other approaches (e. g. Aurora) provide powerful operators but lack semantic strictness, which is required for reasoning about query results. Such reasoning is a prerequisite for safe query optimization. We try to bridge this gap by integrating operators for pattern matching and time-aware aggregates into a general-purpose stream model featuring stream partitioning. These operators can answer several questions that we have found to be relevant in a real-world object-tracking scenario. Moreover, they are formally defined, allowing expressive and efficient queries to be written in CQL-like languages, while remaining understandable and easy to use.