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We introduce partially-stateful data-flow, a new streaming data-flow model that supports eviction and reconstruction of data-flow state on demand. By avoiding state explosion and supporting live changes to the data-flow graph, this model makes data-flow viable for building long-lived, low-latency applications, such as web applications. Our implementation, Noria, simplifies the back-end infrastructure for read-heavy web applications while improving their performance. A Noria application supplies a relational schema and a set of parameterized queries, which Noria compiles into a data-flow program that pre-computes results for reads and incrementally applies writes. Noria makes it easy to write high-performance applications without manual performance tuning or complex-to-maintain caching layers. Partial statefulness helps Noria limit its in-memory state without prior data-flow systems' restriction to windowed state, and helps Noria adapt its data-flow to schema and query changes while on-line. Unlike prior data-flow systems, Noria also shares state and computation across related queries, eliminating duplicate work. On a real web application's queries, our prototype scales to 5x higher load than a hand-optimized MySQL baseline. Noria also outperforms a typical MySQL/memcached stack and the materialized views of a commercial database. It scales to tens of millions of reads and millions of writes per second over multiple servers, outperforming a state-of-the-art streaming data-flow system.