Performance-critical applications, including large-scale program analyses, graph analyses, and distributed system analyses, rely on fixed-point computations. The introduction of recursion using the WITH RECURSIVE keyword in SQL:1999 extended the ability of relational database systems to handle fixed-point computations, unlocking significant performance advantages by allowing computation to move closer to the data. Yet, with recursion, SQL becomes a Turing-complete programming language with new correctness and safety risks.

Full SQL lacks a fixed semantics, as the SQL specification is written in natural language and is full of ambiguities that database vendors resolve in divergent ways. As a result, reasoning about the correctness of recursive SQL programs must rely on isolated, composable properties of queries rather than wrestling a unified formal model out of a language with notoriously inconsistent implementations across systems. To address these challenges, we propose a calculus, $\lambda_{RQL}$, that derives properties from embedded recursive queries using the host-language type system and, depending on the database backend, rejects queries that may lead to the three classes of recursive query errors - runtime database exceptions, incorrect results, and non-termination. Queries that respect all properties are guaranteed to find the minimal fixed point in a finite number of steps.

We introduce TyQL, a practical implementation in Scala for safe, recursive language-integrated query. TyQL uses modern type system features of Scala 3, namely Named-Tuples and type-level pattern matching, to ensure query portability and safety. TyQL shows no performance penalty compared to SQL queries expressed as embedded strings while enabling a three-order-of-magnitude speedup over non-recursive SQL queries.