Multiple model synchronization with multiary delta lenses with amendment and K-Putput

Multiple (more than 2) model synchronization is ubiquitous and important for MDE, but its theoretical underpinning gained much less attention than the binary case. Specifically, the latter was extensively studied by the bx community in the framework of algebraic models for update propagation called lenses. We make a step to restore the balance and propose a notion of multiary delta lens. Besides multiarity, our lenses feature reflective updates, when consistency restoration requires some amendment of the update that violated consistency, and a reasonable Put Put law that requires compatibility of update propagation with update composition for a precisely specified restricted class of composable update pairs. We emphasize the importance of various ways of lens composition for practical applications of the framework, and prove several composition results.