Functional Programming Formalisms for OODBMS Methods

Two well-studied functional formalisms in the theory of programming languages are (1) applicative program schemas and (2) typed lambda calculi. We relate these programming formalisms to object-oriented databases (OODBs) and in particular to the description of methods. The language of method schemas (MS) is a programming formalism based on applicative program schemas with additional key object-oriented features such as classes, methods, inheritance, name overloading, and late binding. From [AKRW92], we present its syntax and semantics and survey the state-of-the-art of consistency checking or signature inference for this language, a problem which can be used in studyingbase schema evolution. We then relate MS with more conventional database query languages by showing that its expressive power over finite ordered databases is PTIME. Despite its simplicity and applicability, MS does not directly model the tuple, set, and list complex structures that are quite common in databases. Also, it does not treat functions as objects, i.e., methods are different from objects. It is possible to achieve these two capabilities using the typed lambda calculus with equality as a database query language, even without any object-oriented features. From [HKM93], we illustrate how this pure functional language subsumes most conventional database query languages including the relational calculus/algebra, Datalog (with or without negation), and the complex object calculus/algebra (with or without powerset). In conclusion, we argue that the appropriate programming formalism for OODBs must be a functional language that combines the object-oriented MS with the expressive $TLC^=$ and facilitates operations on sets of objects.