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Checking query equivalence is of great significance in database systems. Prior work in automated query equivalence checking sets the first steps in formally modeling and reasoning about query optimization rules, but only supports a limited number of query features. In this paper, we present Qed, a new framework for query equivalence checking based on bag semantics. Qed uses a new formalism called Q-expressions that models queries using different normal forms for efficient equivalence checking, and models features such as integrity constraints and NULLs in a principled way unlike prior work. Our formalism also allows us to define a new query fragment that encompasses many real-world queries with a complete equivalence checking algorithm, assuming a complete first-order theory solver. Empirically, Qed can verify 299 out of 444 query pairs extracted from the Calcite framework and 979 out of 1287 query pairs extracted from CockroachDB, which is more than 2× the number of cases proven by prior state-of-the-art solver. 

Exploiting the relationships among data is a classical query optimization technique. As persistent data is increasingly being created and maintained programmatically, prior work that infers data relationships from data statistics misses an important opportunity. We present Coco, the first tool that identifies data relationships by analyzing database-backed applications. Once identified, Coco leverages the constraints to optimize the application's physical design and query execution. Instead of developing a fixed set of predefined rewriting rules, Coco employs an enumerate-test-verify technique to automatically exploit the discovered data constraints to improve query execution. Each resulting rewrite is provably equivalent to the original query. Using 14 real-world web applications, our experiments show that Coco can discover numerous data constraints from code analysis and improve real-world application performance significantly.