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 \emph{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 \emph{delta lenses}, prove their several basic
properties, and explore their relationships with ordinary lenses ---
well-known algebraic models for state-based asymmetric BX.