GSDLAB TECHNICAL REPORT An algebraic semantics for bidirectional model synchronization

The goal of the present document is to support the taxonomy for bidirectional model synchronization developed in [1] with a formal semantics. The taxonomy is 3D so that each synchronization type is characterized by a triple of coordinates (x, y, z), in which x classifies the organizational symmetry of the case, y is for the informational symmetry, and z is for incrementality of the update propagation operations. Different types of delta lenses (algebraic structures modeling bx) can be classified by points on the YZ-plane. As for the x-coordinate, it says, roughly, whether update propagation is unior bi-directional, but as it was shown in [1], there are several important refinements of the twovalued uni, bi-classification so that actually axis X has four rather than two points. A formal semantics for the enriched X-classification seems to be an entirely novel aspect for the (delta) lens literature. There are also several contributions for the very delta lens framework within the plane YZ. First of all, we build a product line of delta lenses so that each concrete delta lens structure is characterizes by two parameters. To this end, we will build a framework in which an asymmetric delta lens appears as a special case of the symmetric one, which is in a sense dual to the Johnson and Rosebrugh construction, in which a symmetric lens is presented as a span of asymmetric lenses [2]. The second novelty is more essential: we present lax versions of major lens laws of compositionality (the infamous PutPut), and invertibility.