From State- to Delta-Based Bidirectional Model Transformations: the Asymmetric Case

Existing bidirectional model transformation (BX) languages are mainly state-based: model alignment is hidden inside update propagating procedures, and model deltas are implicit. Weaving alignment with update propagation complicates the latter and makes it less predictable and less manageable. We propose to separate concerns and consider two distinct operations: delta discovery (alignment) and delta propagation. This architecture has several technological advantages, but requires a corresponding theoretical support. The goal of the paper is to develop a delta-based algebraic framework for the case of asymmetric BX, where one model is a view of the other. In this framework, model spaces are categories (nodes are models and arrows are composable deltas), and delta propagation procedures are mappings between them. We call the corresponding algebras delta lenses, prove their several basic properties, and explore their relationships with ordinary lenses - well-known algebraic models for state-based asymmetric BX.