A Coq Mechanised Formal Semantics for Realistic SQL Queries

Véronique Benzaken (1) , Évelyne Contejean (2)

1 VALS - LRI - Vérification d'Algorithmes, Langages et Systèmes (LRI)
2 LRI - Laboratoire de Recherche en Informatique

In this article, we provide a Coq mechanised, executable, formal semantics for a realistic fragment of SQL consisting of select [distinct] from where group by having queries with NULL values, functions, aggregates, quantifiers and nested potentially correlated sub-queries. Relying on the Coq extraction mechanism to Ocaml, we further produce a Coq certified semantic analyser for a SQL compiler. We then relate this fragment to a Coq formalised (extended) relational algebra that enjoys a bag semantics hence recovering all well-known algebraic equivalences upon which are based most of compilation optimisations. By doing so, we provide the first formally mechanised proof of the equivalence of SQL and extended relational algebra.

Mots clés: Coq; • Theory of computation → Pro-gram semantics; Formal Semantics; SQL; CCS Concepts • Information systems → Relational data-base query languages

Domaines: Logique en informatique [cs.LO]; Langage de programmation [cs.PL]; Base de données [cs.DB]

Véronique Benzaken, Évelyne Contejean. A Coq Mechanised Formal Semantics for Realistic SQL Queries: Formally Reconciling SQL and Bag Relational Algebra. CPP 19, ACM, Jan 2019, Cascais, Portugal. pp.249-261, ⟨10.1145/3293880.3294107⟩. ⟨hal-01955433⟩