Three approaches to partiality in the sketch data model

Partial information is common in real-world databases. Yet the theoretical foundations of data models are not designed to support references to missing data (often termed nulls). Instead, we usually analyse a clean data model based on assumptions about complete information, and later retrofit support for nulls. The sketch data model is a recently developed approach to database speci£cation based on category theory. The sketch data model is general enough to support references to missing information within itself (rather than by retro£tting). In this paper we explore three approaches to incorporating partial information in the sketch data model. The approaches, while fundamentally different, are closely related, and we show that under certain fairly strong hypotheses they are Morita equivalent (that is they have the same categories of models, up to equivalence). Despite this equivalence, the query languages arising from the three approaches are subtly different, and we explore some of these differences.