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Serverless computing with cloud functions is quickly gaining adoption, but constrains programmers with its limited support for state management. We introduce a shared file system for cloud functions. It offers familiar POSIX semantics while taking advantage of distinctive aspects of cloud functions to achieve scalability and performance beyond what traditional shared file systems can offer. We take advantage of the function-grained fault tolerance model of cloud functions to proceed optimistically using local state, safe in the knowledge that we can restart if cache reads or lock activity cannot be reconciled upon commit. The boundaries of cloud functions provide implicit commit and rollback points, giving us the flexibility to use transaction processing techniques without changing the programming model or API. This allows a variety of stateful sever-based applications to benefit from the simplicity and scalability of serverless computing, often with little or no modification.