A Reactive Operational Semantics for a Lambda-Calculus with Time Warps

This work is supported by the Emergence project “ReaLiSe” funded by the city of Paris. Abstract Many computer systems are reactive : they execute in continuous interaction with their environment. From the perspective of functional programming, reactive systems can be modeled and programmed as stream functions. Several lines of research have exploited this point of view. Works based on Nakano’s guarded recursion use type-theoretical modalities to guarantee productivity. Works based on synchronous programming use more specialized methods but guarantee incremental processing of stream fragments. In this paper, we contribute to a recent synthesis between the two approaches by describing how a language with a family of type-theoretical modalities can be given an incremental semantics in the synchronous style. We prove that this semantics coincides with a more usual big-step semantics.