Formal Verification of Relational Algebra Transformations in Fiat2 Using Coq

Abstract

Data-intensive applications often involve operations over structured datasets, such as filtering, joining, and projecting records. Relational database systems generally use query planners to optimize high-level SQL queries into efficient execution plans. While these systems apply well-established query transformations, they typically assume the correctness of these transformations rather than formally proving them. The absence of formal guarantees can be a significant limitation for systems with strict correctness requirements. This thesis contributes to Fiat2, a Python-like high-level programming language for data-intensive workloads that integrates formal verification via the Coq proof assistant. We focus on proving the correctness of several rewrite-based query optimizations commonly used in database engines. Specifically, we formalize and prove the correctness of algebraic rewrites involving combinations of filters, joins, and projections, as well as join-reordering rewrites. All rewrites are proven in Coq to preserve the semantics of the original program under list semantics, meaning that the output lists are fully equivalent (or permutations, in the case of join reordering). These verified rewrites serve as a foundation for future optimization in Fiat2, enabling significant optimizations while preserving the semantics of the original queries with correctness guarantees. The results demonstrate the feasibility of integrating formally verified query optimizations into a practical high-level programming language.