Data structure synthesis is the task of generating data structure implementations from high-level specifications. Recent work in this area has shown potential to save programmer time and reduce the risk of defects. Existing techniques focus on data structures for manipulating subsets of a single collection, but real-world programs often track multiple related collections and aggregate properties such as sums, counts, minimums, and maximums.

This paper shows how to synthesize data structures that track subsets and aggregations of multiple related collections. Our technique decomposes the synthesis task into alternating steps of query synthesis and incrementalization. The query synthesis step implements pure operations over the data structure state by leveraging existing enumerative synthesis techniques, specialized to the data structures domain. The incrementalization step implements imperative state modifications by re-framing them as fresh queries that determine what to change, coupled with a small amount of code to apply the change. As an added benefit of this approach over previous work, the synthesized data structure is optimized for not only the queries in the specification but also the required update operations. We have evaluated our approach in four large case studies, demonstrating that these extensions are broadly applicable.