This paper introduces semi-ring dictionaries, a powerful class of compositional and purely functional collections that subsume other collection types such as sets, multisets, arrays, vectors, and matrices. We developed SDQL, a statically typed language that can express relational algebra with aggregations, linear algebra, and functional collections over data such as relations and matrices using semi-ring dictionaries. Furthermore, thanks to the algebraic structure behind these dictionaries, SDQL unifies a wide range of optimizations commonly used in databases (DB) and linear algebra (LA). As a result, SDQL enables efficient processing of hybrid DB and LA workloads, by putting together optimizations that are otherwise confined to either DB systems or LA frameworks. We show experimentally that a handful of DB and LA workloads can take advantage of the SDQL language and optimizations. Overall, we observe that SDQL achieves competitive performance relative to Typer and Tectorwise, which are state-of-the-art in-memory DB systems for (flat, not nested) relational data, and achieves an average 2x speedup over SciPy for LA workloads. For hybrid workloads involving LA processing, SDQL achieves up to one order of magnitude speedup over Trance, a state-of-the-art nested relational engine for nested biomedical data, and gives an average 40% speedup over LMFAO, a state-of-the-art in-DB machine learning engine for two (flat) relational real-world retail datasets.
View on arXiv