{ rjmh, pareto, sabry We have designed and implemented a type-based analysis for proving some baaic properties of reactive systems. The analysis manipulates rich type expressions that contain in-formation about the sizes of recursively defined data struc-tures. Sized types are useful for detecting deadlocks, non-termination, and other errors in embedded programs. To establish the soundness of the analysis we have developed an appropriate semantic model of sized types. 1 Embedded Functional Programs In a reactive system, the control software must continu-ously react to inputs from the environment. We distin-guish a class of systems where the embedded programs can be naturally expressed as functional programs manipulat-ing streams. This class of programs appears to be large enough for many purposes [2] and is the core of more ex-pressive formalisms that accommodate asynchronous events, non-determinism, etc. The fundamental criterion for the correctness of pro-grams embedded in reactive systems is Jwene.ss. Indeed, before considering the properties of the output, we must en-sure that there is some output in the first place: the program must continuous] y react to the input streams by producing elements on the output streams. This latter property may fail in various ways: e the computation of a stream element may depend on itself creating a “black hole, ” or e the computation of one of the output streams may demand elements from some input stream at different rates, which requires unbounded buffering, or o the computation of a stream element may exhaust the physical resources of the machine or even diverge.