Queries on Databases With User-Defined Functions

The notion of a database query is generalized for databases with user-defined functions. Then, we can prove that the computable queries coincide with those expressible by an extension of the relational machine, with oracles ([4]). This implies that any complete query language, extended with user-defined function symbols in a "reasonable" way, is still complete. We give an example of a complete query language with user-defined functions, and discuss its connections with object inventions.