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Programming geo-replicated distributed systems is challenging given the complexity of reasoning about different evolving states on different replicas. Existing approaches to this problem impose significant burden on application developers to consider the effect of how operations performed on one replica are witnessed and applied on others. To alleviate these challenges, we present a fundamentally different approach to programming in the presence of replicated state. Our insight is based on the use of invertible relational specifications of an inductively-defined data type as a mechanism to capture salient aspects of the data type relevant to how its different instances can be safely merged in a replicated environment. Importantly, because these specifications only address a data type's (static) structural properties, their formulation does not require exposing low-level system-level details concerning asynchrony, replication, visibility, etc. As a consequence, our framework enables the correct-by-construction synthesis of rich merge functions over arbitrarily complex (i.e., composable) data types. We show that the use of a rich relational specification language allows us to extract sufficient conditions to automatically derive merge functions that have meaningful non-trivial convergence properties. We incorporate these ideas in a tool called Quark, and demonstrate its utility via a detailed evaluation study on real-world benchmarks.