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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. 

High-level data types are often associated with semantic invariants that must be preserved by any correct implementation. While having implementations enforce strong guarantees such as linearizability or serializability can often be used to prevent invariant violations in concurrent settings, such mechanisms are impractical in geo-distributed replicated environments, the platform of choice for many scalable Web services. To achieve high-availability essential to this domain, these environments admit various forms of weak consistency that do not guarantee all replicas have a consistent view of an application's state. Consequently, they often admit difficult-to-understand anomalous behaviors that violate a data type's invariants, but which are extremely challenging, even for experts, to understand and debug. In this paper, we propose a novel programming framework for replicated data types (RDTs) equipped with an automatic (bounded) verification technique that discovers and fixes weak consistency anomalies. Our approach, implemented in a tool called Q9, involves systematically exploring the state space of an application executing on top of an eventually consistent data store, under an unrestricted consistency model but with a finite concurrency bound. Q9 uncovers anomalies (i.e., invariant violations) that manifest as finite counterexamples, and automatically generates repairs for such anamolies by selectively strengthening consistency guarantees for specific operations. Using Q9, we have uncovered a range of subtle anomalies in implementations of well-known benchmarks, and have been able to apply the repairs it mandates to effectively eliminate them. Notably, these benchmarks were written adopting best practices suggested to manage distributed replicated state (e.g., they are composed of provably convergent RDTs (CRDTs), avoid mutable state, etc.). While the safety guarantees offered by our technique are constrained by the concurrency bound, we show that in practice, proving bounded safety guarantees typically generalize to the unbounded case. 

Serializability is a well-understood correctness criterion that simplifies reasoning about the behavior of concurrent transactions by ensuring they are isolated from each other while they execute. However, enforcing serializable isolation comes at a steep cost in performance because it necessarily restricts opportunities to exploit concurrency even when such opportunities would not violate application-specific invariants. As a result, database systems in practice support, and often encourage, developers to implement transactions using weaker alternatives. These alternatives break the strong isolation guarantees offered by serializable transactions to permit greater concurrency. Unfortunately, the semantics of weak isolation is poorly understood, and usually explained only informally in terms of low-level implementation artifacts. Consequently, verifying high-level correctness properties in such environments remains a challenging problem. To address this issue, we present a novel program logic that enables compositional reasoning about the behavior of concurrently executing weakly-isolated transactions. Recognizing that the proof burden necessary to use this logic may dissuade application developers, we also describe an inference procedure based on this foundation that ascertains the weakest isolation level that still guarantees the safety of high-level consistency assertions associated with such transactions. The key to effective inference is the observation that weakly-isolated transactions can be viewed as functional (monadic) computations over an abstract database state, allowing us to treat their operations as state transformers over the database. This interpretation enables automated verification using off-the-shelf SMT solvers. Our development is parametric over a transaction’s specific isolation semantics, allowing it to be applicable over a range of concurrency control mechanisms. Case studies and experiments on real-world applications (written in an embedded DSL in OCaml) demonstrate the utility of our approach, and provide strong evidence that automated verification of weakly-isolated transactions can be placed on the same formal footing as their strongly-isolated serializable counterparts.