@InProceedings{jung95, author = {A. Jung and H. Puhlmann}, title = {Types, Logic, and Semantics for Nested Databases}, editor = {M. Main and S. Brookes}, volume = 1, series = {Electronic Notes in Theoretical Computer Science}, booktitle = {11th Conference on Mathematical Foundations of Programming Semantics}, year = 1995, publisher = {Elsevier Science Publishers {B.V.}}, abstract = {This work presents first steps towards a denotational semantics for relational data\-ba\-ses. 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 {\em 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'.} }