Translating Canonical SQL to Imperative Code in Coq

TL;DR

This paper presents DBCert, the first mechanically verified compiler translating canonical SQL queries into imperative code in Coq, addressing bugs and divergence in SQL implementations for key features.

Contribution

It introduces a formal, verified translation pipeline from SQL to imperative code, including a complete SQL-to-Nested Relational Algebra translation and a mechanized algebra-to-Imp translation.

Findings

Verified correctness of SQL to imperative code translation

Supports SQL features like correlated queries and NULL semantics

Enables bug-free, reliable query compilation

Abstract

SQL is by far the most widely used and implemented query language. Yet, on some key features, such as correlated queries and NULL value semantics, many implementations diverge or contain bugs. We leverage recent advances in the formalization of SQL and query compilers to develop DBCert, the first mechanically verified compiler from SQL queries written in a canonical form to imperative code. Building DBCert required several new contributions which are described in this paper. First, we specify and mechanize a complete translation from SQL to the Nested Relational Algebra which can be used for query optimization. Second, we define Imp, a small imperative language sufficient to express SQL and which can target several execution languages including JavaScript. Finally, we develop a mechanized translation from the nested relational algebra to Imp, using the nested relational calculus as an intermediate step.