Commutative Replicated Data Types (CRDTs) are a promising new class of data structures for large-scale shared mutable content in applications that only require eventual consistency. The WithOut Operational Transforms (WOOT) framework is the first CRDT for collaborative text editing introduced by Oster et al. (In: Conference on Computer Supported Cooperative Work (CSCW). ACM, New York, pp 259–268, 2006a). Its eventual consistency property was verified only for a bounded model to date. While the consistency of many other previously published CRDTs had been shown immediately with their publication, the property for WOOT remained open for 14 years. We use a novel approach identifying a previously unknown sort-key based protocol that simulates the WOOT framework to show its consistency. We formalize the proof using the Isabelle/HOL proof assistant to machine-check its correctness.

交换复制数据类型 (CRDT) 是一种很有前途的新型数据结构，适用于仅需要最终一致性的应用程序中的大规模共享可变内容。WithOut Operational Transforms (WOOT) 框架是 Oster 等人引入的第一个用于协作文本编辑的 CRDT。（在：计算机支持的合作工作会议 (CSCW)。ACM，纽约，第 259-268 页，2006a）。迄今为止，它的最终一致性属性仅针对有界模型进行了验证。虽然许多其他先前发布的 CRDT 的一致性在其发布时立即显示出来，但 WOOT 的财产仍然开放了 14 年。我们使用一种新颖的方法来识别以前未知的基于排序键的协议，该协议模拟 WOOT 框架以显示其一致性。