Abstract. This work discusses the CROQUE approach to the maintenance problem for materialized views. In a CROQUE database, application-speci ed collections (type extents or classes) themselves need not be materialized. In exchange, the system maintains (redundant) views of the application data that help to minimize query response time. We understand views as functions of database objects and examine algebraic properties of these functions, in particular linearity, to derive incremental update plans. It turns out that it is feasible to employ ODMG OQL as a view de nition language { instead of inventing a specialized one { in such an environment, since the majority of its clauses represent linear functions.