Semantics of Types for Database Objects

This paper proposes a framework of denotational semantics of database type systems and constructs a type system for complex database objects. Starting with an abstract analysis of the relational model, we develop a mathematical theory for the structures of domains of database objects. Based on this framework, we construct a concrete database type system and its semantic domain. The type system allows arbitrarily complex structures that can be constructed using labeled records, labeled variants, finite sets and recursion. On the semantic domain, in addition to standard operations on records, variants and sets, a join and a projection are available as polymorphically typed computable functions on arbitrarily complex objects. We then show that both the type system and the semantic domain can be uniformly integrated in an ML-like programming language. This leads us to develop a database programming language that supports rich data structures and powerful operations for databases while enjoying desirable features of modern type systems of programming languages including strong static type-checking, static type inference and ML polymorphism.