A Coq mechanised formal semantics for realistic SQL queries : Formally reconciling SQL and (extended) relational algebra.

In this article, we provide a Coq mechanised, executable, formal semantics for realistic SQL queries consisting of select [distinct] from where group by having queries with NULL values, functions, aggregates, quantifiers and nested, potentially correlated, sub-queries. We then relate this fragment to a Coq formalised (extended) relational algebra that enjoys a bag semantics. Doing so we provide the first formally mechanised proof of the equivalence of SQL and extended relational algebra and, from a compilation perspective, thanks to the Coq extraction mechanism to Ocaml, a Coq certified semantic analyser for a SQL compiler.