From Lenses to Tiles: Model Synchronization via Double Categories

The paper describes a novel mathematical framework for model
synchronization. It is based on diagram operations and can be
considered an essential generalization of \emph{lenses}---a popular
algebraic approach to the view update problem. A distinctive feature
of the framework is that both view and update mappings are first
class citizens and explicitly occur in arity shapes of the operations
of update translation. We show that lenses augmented with mappings
give rise to double categories and discuss the benefits of this
formalism.