Queries with External Predicates

Real-life query languages feature external predicates such as user-defined functions or built-in arithmetic and string operations. These predicates are often infinite, potentially leading to unsafe or non-computable queries. To overcome this, traditional languages such as SQL, put significant syntactic restrictions on the use of external predicates. These restrictions have been relaxed in a number of modern query languages, each doing it in their own way. Our goal therefore is to provide a theoretical basis for querying with external predicates. To this end, we formalize queries with external predicates based on the notion of access patterns. We develop a suitable evaluation model, based on Turing machines with oracles, and tailor the classical notion of query safety to it. Since query safety is undecidable in general, we can only produce sufficient conditions for guaranteeing safety. We do so by developing an inference system to derive safety and computability for relational algebra, first-order logic, as well as for a language that combines them both.