Serverless computing and stream processing represent two dominant paradigms for event-driven data processing, yet both make assumptions that render them inefficient for short-running, lightweight, and unpredictable streams that require stateful processing. We propose stream functions as a novel extension of the Function-as-a-Serivce model that treat short streams as the unit of execution, state, and scaling. Stream functions process streams via an iterator-based interface, enabling seamless inter-event logic while retaining the elasticity and scale-to-zero capabilities offered by serverless platforms. Our evaluation shows that stream functions reduce the processing overhead by ~99 % compared to a mature stream process- ing engine in a video-processing use case. By providing comparable performance to serverless functions with stream semantics, stream functions provide an effective and efficient abstractions for a class of workloads underserved by existing models.