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SQL is one of the most popular tools for data analysis, and it is now used byan increasing number of users without having expertise in databases. Severalstudies have proposed programming-by-example approaches to help suchnon-experts to write correct SQL queries. While existing methods support avariety of SQL features such as aggregation and nested query, they suffer asignificant increase in computational cost as the scale of example tablesincreases. In this paper, we propose an efficient algorithm utilizingproperties known in relational algebra to synthesize SQL queries from input andoutput tables. Our key insight is that a projection operator in a programsketch can be lifted above other operators by applying transformation rules inrelational algebra, while preserving the semantics of the program. This enablesa quick inference of appropriate columns in the projection operator, which isan essential component in synthesis but causes combinatorial explosions inprior work. We also introduce a novel form of constraints and its top-downpropagation mechanism for efficient sketch completion. We implemented thisalgorithm in our tool PATSQL and evaluated it on 226 queries from priorbenchmarks and Kaggle's tutorials. As a result, PATSQL solved 68% of thebenchmarks and found 89% of the solutions within a second. Our tool isavailable at https://naist-se.github.io/patsql/.

PATSQL: Efficient Synthesis of SQL Queries from Example Tables with Quick Inference of Projected Columns