Safety and translation of calculus queries with scalar functions

An important research goal for the 90’s is the development of programming languages which support database functionalities. One approach, illustrated by PASCAL/R [Sch77], is to extend an imperative language (here PASCAL) to incorporate access to a particular database model (here relational). In this approach, it is desirable to permit ae much communication as possible between the underlying programming language and the database access language. In particular, it is essential that scalar functions (i.e., interpreted functions that use only atomic values as inputs and outputs), both system-defined or user-defined, can be used inside database queries. While it is relatively straightforward to provide this in the context of the relational algebra, supporting this in the relational calculus is significantly more difficult. Indeed, the calculus sublanguage of PASCAL/R does not permit the use of scalar functions. We present here the theoretical component for a comprehensive framework for supporting the flexible use of (total) scalar functions in relational calculus queries. Our framework generalizes previous work on the relational calculus to this context. We use the notion of embedded domain independent (called “bounded depth domain independent” in [AB88] ), and generalize the notion of allowed [Top87] to embedded allowed (emallowed). In the full paper it is shown that each emallowed query is embedded domain independent. This is demonstrated using a non-trivial extension of the van Gelder-Topor algorithm [GT91] for translating allowed calculus queries into the relational algebra. In order to

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