Technical Perspective for: MATLANG: Matrix Operations and Their Expressive Power

The main processing paradigm in data management is bulk processing. As introduced by Codd in the early 70's, under this paradigm relations are processed in bulk, one operator at a time. When applied to relations, this paradigm leads to relational algebra, and its variants, relational calculus, and SQL. Over the years, data management was faced with the challenge of extending bulk processing operators to new kinds of data, and/or new kinds of queries: nested relations, semistructured data, recursive queries. Each such extension requires significant systems development, which should be accompanied, in fact preceded, by a careful study of the expressive power of the new language. Is it as expressive, more expressive, or less expressive than relational algebra? The answer to this question has profound implications on the ability of data processing engines to optimize, compute, distribute, reuse queries in that language. For example, extending relational algebra with nested relations does not increase its expressive power, while extending it with fixpoint does, explaining why modern query engines have an easier time supporting JSON than recursion.