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.

中文翻译：

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具有修正和 K-Putput 的多 delta 透镜的多模型同步

多个（超过 2 个）模型同步对于 MDE 来说无处不在且很重要，但其理论基础得到的关注远少于二元情况。具体来说，bx 社区在更新传播的代数模型框架中对后者进行了广泛研究，称为镜片. 我们迈出了恢复平衡的一步，并提出了多元 delta 透镜的概念。除了多重性，我们的镜头还具有反光的更新，当一致性恢复需要对违反一致性的更新进行一些修改时，以及合理的放放法对于精确指定的受限类可组合更新对，这需要更新传播与更新组合的兼容性。我们强调了各种镜头合成方式对框架实际应用的重要性，并证明了几种合成结果。