Safe Database Queries with External Functions

We consider the theory of database queries with functions on the complex value data model. The notion of a syntactic criteria, called “embedded allowed”, for queries which guarantee embedded domain independence, is generalized for this model. We show that all embedded allowed calculus (or fix-point) queries are external function-domain independent and continuous. We also develop an algorithm for translating embedded allowed queries into equivalent algebraic expressions as a basis for evaluating safe queries in all calculus-based query classes. In the second part of this paper, we compare the expressive power of various complex value query languages extended with functions and their certain restricted versions. If we assume polynomial time (space) complexity of external functions and type usage by the database, such as density, then strongly embedded allowed inflationary (partial) fix-point queries express precisely QPTIME (QPSPACE). Finally, we show the relationship between properties such as embedded domain independence, finiteness and embedded allowed in various calculus-based query languages.