Class diagrams are among the most popular modeling lan-guages in industrial use. In a model-driven development process, class diagrams evolve, so it is important to be able to assess differences between revisions, as well as to propagate differences using suitable merge operations. Existing differencing and merging methods are mainly syntactic, concentrating on edit operations applied to model elements, or they are based on sampling: enumerating some examples of instances which characterize the difference between two diagrams. This paper presents the first known (to the best of our knowledge) automatic model merging and differencing operators supported by a formal semantic theory guaranteeing that they are semantically sound. All instances of the merge of a model and its difference with another model are automatically instances of the second model. The differences we synthesize are represented using class diagram notation (not edits, or instances), which allows creation of a simple yet flexible algebra for diffing and merging. It also allows presenting changes comprehensively, in a notation already known to users.