Domain-independent queries on databases with external functions

AbstractWe study queries over databases with external functions, from a language-independent perspective. The input and output types of the external functions can be atomic values, flat relations, nested relations, etc. We propose a new notion of data-independence for queries on databases with external functions, which extends naturally the notion of generic queries on relational databases without external functions. In contrast to previous such notions, ours can also be applied to queries expressed in query languages with iterations. Next, we propose two natural notions of computability for queries over databases with external functions, and prove that they are equivalent, under reasonable assumptions. Thus, our definition of computability is robust. Finally, based on this equivalence result, we give examples of complete query languages with external functions. A byproduct of the equivalence result is the fact that Relational Machines (Abiteboul and V. Vianu, 1991; Abiteboul et al., 1992) are complete on nested relations: they are known not to be complete on flat relations

On Two Forms of Structural Recursion

. We investigate and compare two forms of recursion on sets for querying nested collections. The first one is called sri and it corresponds to sequential processing of data. The second one is called sru and it corresponds to data-parallel processing. A uniform first-order translation from sru into sri was known from previous work. The converse translation is by necessity more difficult and we have obtained three main results concerning it. First, we exhibit a uniform translation of sri queries into sru queries over the nested relational algebra. We observe that this translation maps PTIME algorithms into exponential-space queries. The second result proves that any uniform translation of sri queries into sru queries over the nested relational algebra must map some PTIME queries into exponential-space ones. In fact, in the presence of certain external functions, we provide a PTIME sri query for which any equivalent sru query requires exponential space. Thus, as a mechanism for implemen..