A Unified Treatment of Null Values Using Constraints

An important reality when studying relational databases is the fact that entries in relational tables may often be \missing" or only partially speciied. The study of such missing information has led to a rich body of work on \null values." It was recognized early on that there are many diierent types of null values, each of which reeects diierent intuitions about why a particular piece of information is missing. Diierent relations (or even the same relation) could contain diierent types of null values; yet, very little work has been done on providing a unifying model that reasons with diierent types of nulls. In this paper, we use constraints to provide a unifying framework for the most common types of nulls. We show how viewing tuples containing null values of these types can be viewed as constraints, and how this leads to an algebra for null values. In particular, this algebra contains a unique operator (called the \compaction" operator) used to remove redundancies from null valued relations. We have studied various properties of this algebra. We have built a prototype implementation based on the null valued operators described here and conducted various experiments using this testbed.