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Hyperlog is a declarative, graph-based language that supports database querying and update. It visualizes schema information, data, and query output as sets of nested graphs, which can be stored, browsed, and queried in a uniform way. Thus, the user need only be familiar with a very small set of syntactic constructs. Hyperlog queries consist of a set of graphs that are matched against the database. Database updates are supported by means of programs consisting of a set of rules. This paper discusses the formulation, evaluation, expressiveness, and optimization of Hyperlog queries and programs. We also describe a prototype implementation of the language and we compare and contrast our approach with work in a number of related areas, including visual database languages, graph-based data models, database update languages, and production rule systems.