This content originally appeared on DEV Community and was authored by SQLFlash
Introduction
In today’s information-driven society, database systems have become the backbone of modern information infrastructure. As the standard query language for relational databases, SQL (Structured Query Language) has drawn increasing attention from both academia and industry, particularly in the area of performance optimization. Among various optimization techniques, SQL query equivalence verification plays a foundational role—supporting critical tasks such as query rewriting and execution plan selection—while also ensuring the correctness of query results.
As database technologies continue to evolve, SQL equivalence checking has become increasingly important in scenarios such as automated optimizers, SQL rewriting tools, and formal verification frameworks. However, it is essential to recognize that verifying SQL equivalence is a fundamentally complex problem. This complexity stems from three primary factors: the intricate syntax and semantics of SQL itself, diverse semantic boundary conditions (e.g., null handling, sets vs. multisets), and implementation differences across database platforms. As a result, SQL equivalence checking is far more challenging than equivalence checking in traditional logic.
To address this challenge, researchers and practitioners have developed a variety of formal modeling techniques, proof strategies, and verification tools. These approaches span a wide spectrum, from algebraic transformations and semantic mappings to automated theorem proving and symbolic execution. This article aims to provide a comprehensive survey of major methodologies and application scenarios in SQL equivalence verification, summarizing the current state of research while analyzing the applicability, advantages, limitations, and future trends of each approach. Our goal is to offer a clear knowledge map for researchers and engineers, supporting ongoing innovation in SQL optimization and verification technologies.
Verification Approaches
Result-Based Verification
Result-based verification is the most intuitive method for validating SQL equivalence. It determines semantic equivalence by comparing the output result sets of two queries. This approach is straightforward and widely used in practice. For instance, prominent datasets like WikiSQL and Spider in the NL2SQL (Natural Language to SQL) domain rely on result-based validation to assess equivalence between generated SQL and reference answers.
However, this method has notable limitations. As highlighted in [1], equivalence under a limited dataset—referred to as instance equivalence—does not guarantee semantic equivalence in general cases. This can lead to false conclusions in real-world applications.
Example:
-- Query 1
SELECT name FROM users WHERE age > 18;
-- Query 2
SELECT name FROM users WHERE age > 30;
If the current database contains no records where age is between 19 and 30, both queries will return identical results. However, this does not prove their equivalence across all possible datasets.
Algebraic Equivalence
Algebraic methods, grounded in relational algebra, offer the most theoretically sound approach to SQL equivalence verification. This approach involves translating SQL queries into algebraic expressions—using operations such as selection, projection, joins, aggregation, and nesting—and then applying axioms and heuristics to prove equivalence.
Several tools have been developed using this approach. Cosette 2 is a notable example: an automated SQL equivalence prover that formalizes large subsets of SQL in the Coq proof assistant and the Rosette symbolic virtual machine. For any given pair of queries, Cosette either produces a formal proof of equivalence or a counterexample.
Another significant tool is EQUITAS 3, which follows a two-stage process: SQL queries are first translated from their Abstract Syntax Tree (AST) representation into symbolic representations (SR) using first-order logic (FOL). Then, SMT (Satisfiability Modulo Theories) solvers are used to determine containment between the symbolic forms.
VeriEQL 4 further contributes by proposing a bounded SQL equivalence verification framework under integrity constraints. It formalizes SQL semantics using list operations and higher-order functions.
Despite their rigor, these tools face several common challenges:
- Heavy reliance on specific SQL parsers, limiting the scope of supported queries.
- Many algorithms are exhaustive and lack general applicability across diverse SQL dialects.
- Tool development and maintenance require significant investment, causing many projects to be discontinued.
Large Language Model (LLM)-Based Methods
The rise of large language models (LLMs) has introduced promising heuristic approaches to SQL equivalence verification. Recent studies demonstrate the potential of LLMs in this domain.
For example, LLM-SQL-Solver 5 confirms through systematic experiments that LLMs exhibit impressive accuracy in SQL equivalence tasks. Similarly, SQLEquiQuest 6 finds that modern LLMs outperform traditional tools like Cosette and VeriEQL.
Notably, SQLEquiQuest also introduced a benchmark dataset [7] for evaluating SQL equivalence tools, providing a valuable resource for future research. In parallel, Actiontech released a similar dataset [8], enriching the benchmarking infrastructure for this field.
Despite their promise, LLM-based methods face the following challenges:
- Lack of formal theoretical guarantees; outputs may be unreliable.
- A known bias toward incorrectly labeling non-equivalent queries as equivalent.
- While often aligned with human judgment, their results still require manual verification in critical applications.
Summary and Future Outlook
his survey has outlined the evolution of SQL equivalence verification methods—from simple result-based approaches to rigorous algebraic techniques, and more recently, to LLM-driven heuristics. Each method presents unique strengths and challenges, making them suitable for different use cases.
Particularly promising is the future of LLM-based methods. Although current models lack the theoretical rigor of formal approaches, their ability to handle complex queries and diverse SQL dialects signals great potential. Future research is likely to explore hybrid methods that combine the reasoning capabilities of LLMs with the formal guarantees of traditional approaches—leading to more powerful and reliable SQL equivalence verification tools.
References
- [1]https://ar5iv.labs.arxiv.org/html/2010.02840
- [2]https://www.cs.cmu.edu/~15811/papers/db.pdf
- [3]https://ar5iv.labs.arxiv.org/html/2004.00481
- [4]https://ar5iv.labs.arxiv.org/html/2403.03193
- [5]https://arxiv.org/html/2312.10321
- [6]https://arxiv.org/html/2412.05561
- [7]https://github.com/rajatb115/LLMs-for-SQL-Equivalence-Checking
- [8]https://github.com/actiontech/sql-llm-benchmark
This content originally appeared on DEV Community and was authored by SQLFlash