Functional Collection Programming with Semi-Ring Dictionaries

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 develop SDQL, a statically typed language centered around semi-ring dictionaries, that can encode expressions in relational algebra with aggregations, functional collections, and linear algebra. Furthermore, thanks to the semi-ring algebraic structures behind these dictionaries, SDQL unifies a wide range of optimizations commonly used in databases and linear algebra. As a result, SDQL enables efficient processing of hybrid database and linear algebra workloads, by putting together optimizations that are otherwise confined to either database systems or linear algebra frameworks. Through experimental results, we show that a handful of relational and linear algebra workloads can take advantage of the SDQL language and optimizations. Overall, we observe that SDQL achieves competitive performance to Typer and Tectorwise, which are state-of-the-art in-memory systems for (flat, not nested) relational data, and achieves an average 2x speedup over SciPy for linear algebra workloads. Finally, for hybrid workloads involving linear algebra processing over nested biomedical data, SDQL can give up to one order of magnitude speedup over Trance, a state-of-the-art nested relational engine.