A Coq mechanised formal semantics for realistic SQL queries - formally reconciling SQL and bag relational algebra.
CPP '19: 8th ACM SIGPLAN International Conference on Certified Programs and Proofs Cascais Portugal January, 2019(2019)
Abstract
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.
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Key words
SQL, Formal Semantics, Coq
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