Types, Logic, and Semantics for Nested Databases

This work presents first steps towards a denotational semantics for relational databases. It is argued that such a semantics will increase the chances of successfully incorporating relational databases into typed programming languages. Database relations are seen as sets of data of a common structure. The main problem therefore is to model a type of sets. We propose the snack powerdomain for this purpose. Technically, the paper attempts to clarify two aspects of the domain theoretic background of this approach. We give a localic description of the snack powerdomain construction which reveals its logical simplicity. Second, we study a subdomain relation between Scott-domains on the denotational and the logical level. Again, the logical version is simple and intuitive. Such a relation is indispensable for introducing database operations such as `natural join'. 1 Introduction The theory of relational databases (see [16,11] for surveys) is highly developed and proves its usefulness in pra..