Data never ends, but decisions cannot wait. Every fraud alert, monitoring dashboard, and real-time AI agent is a program that runs forever over unbounded data and must keep producing answers worth acting on. Two decades of research and industrial practice have made stream pro-cessing mature. However, the simple question: what is a stream? Has different answers by dif-ferent communities: a time-varying relation, a partially ordered set of events, a plain sequence.

Such a fragmentation runs deeper than notation. Streaming applications rely on a wide range of programming interfaces, from asynchronous programming using actors to streaming SQL. Alt-hough empirical, in the informal stack of stream processing languages, users face a progression of abstraction levels, from explicit control of state and parallelism to more declarative functional and relational interfaces. What remains missing is a principled account of how these layers re-late, what guarantees they expose, and where their semantics diverge.

Clarification is urgent. A coherent foundation for streaming computation must synthesize princi-ples shared by the data management and programming languages communities. This Dagstuhl Seminar aims to bring the two together on equal footing to build a shared framework for compar-ison of streaming computation.

Three working axes will run through the week:

Abstractions and Interfaces compares models of streams, time, and state, and asks which guar-antees must cross abstraction boundaries.

Programming Models and Languages spans declarative dialects, functional designs, and the calculi and intermediate representations that connect them, asking which differences between languages are fundamental and which are accidents of tradition.

Execution Models and Runtime Contracts make explicit what runtimes actually promise (sched-uling, state management, recovery, consistency, optimization boundaries) and which of those contracts the layers above can rely on. Questions we will discuss include:

• What is a stream, formally, and when can one model be mapped onto another without changing what programs mean?
• Which concepts, such as windowing, ordering, and progress, are fundamental, and which are artefacts of a particular language or engine?
• When are translations among dataflow, functional, and relational formalisms semantically faithful, and where do they become lossy?
• How much of the unbounded past must a computation retain for its answers to be justified, and can that scope be derived from reliability contracts instead of hand-set windows?
• Which runtime guarantees, from state and recovery to backpressure and consistency, must remain explicit for streaming programs to be portable across engines?
• When programs over streams are written by AI models rather than programmers, where should their semantics live?

The week is organized into working groups that will draft a taxonomy and glossary of streaming abstractions, a map of the semantic mismatches between layers, languages, and systems, and a research roadmap toward convergence where it is technically feasible: the seed of the Dagstuhl Report and a joint outlook paper.

Keywords: stream processing · unbounded data · programming languages · dataflow program-ming · semantics · windowing · state management · runtime contracts