From State- to Delta-based Bidirectional Model Transformations: the Symmetric Case

Algebraic frameworks are important for building semantic foundations
of bidirectional model transformations (BX). Symmetric BX are those
for which neither model in a pair of synchronized models fully
determines the other. We build two algebraic frameworks for symmetric
BXs, with one correctly implementing the other, and both being
delta-based generalizations of previous state-based frameworks. We
also identify two new algebraic laws---weak undoability and weak
invertibility, which are important for both state- and delta-based
setting.