Incremental View Maintenance for Nested-Relational Databases.

Incremental view maintenance is an essential tool for speeding up the processing of large, locally changing workloads. Its fundamental challenge is to ensure that changes are propagated from input to output more efficiently than via recomputation. We formalize this requirement for positive nested relational algebra (NRA+) on bags and we propose a transformation deriving deltas for any expression in the language. The main difficulty in maintaining nested queries lies in the inability to express within NRA+ the efficient updating of inner bags, i.e., without completely replacing the tuples that contain them. To address this problem, we first show how to efficiently incrementalize IncNRA+, a large fragment of NRA+ whose deltas never generate inner bag updates. We then provide a semantics-preserving transformation that takes any nested query into a collection of IncNRA+ queries. This constitutes the first static solution for the efficient incremental processing of languages with nested collections. Furthermore, we show that the state-of-the-art technique of recursive IVM, originally developed for positive relational algebra with aggregation, also extends to nested queries. Finally, we generalize our static approach for the efficient incrementalization of NRA+ to a family of simply-typed lambda calculi, given that its primitives are themselves efficiently incrementalizable.