Update algorithms for the sketch data model

The authors have developed a new approach to database interoperability using the sketch data model. That technique has now been used in a number of applications, but an important question remains: What are the algorithms that support updates in the sketch data model? The question has significant content since the sketch data model uses EA-sketches to specify data structures, and these include constraint and other information not normally supported by relational database management systems. In this paper we answer the question by using the framework of EA sketches to give a detailed mathematical treatment of database updates, providing a formal definition of insert update together with an algorithm which provably achieves updates. The algorithm is new as it is the first to treat data and constraints on an equal categorical footing. We also note that further exactness properties (limits and colimits) can aid specification, and we provide algorithms for updates of EA sketched databases with finite limits. These are the first update algorithms for such databases. The sketch data model is being used in industry for designing interoperations for computer supported cooperative work and computer assisted software engineering (CASE) tools are under development. The paper is predominantly theoretical, and provides an important link needed for CASE tool development.