Hyperstream Processing Systems Nonstandard Modeling of Continuous-Time Signals
We exploit the apparent similarity between (discrete-time) stream processing and (continuous-time) signal processing and transfer a deductive verification framework from the former to the latter. Our development is based on rigorous semantics that relies on nonstandard analysis (NSA). Specifically, we start with a discrete framework consisting of a Lustre-like stream processing language, its Kahn-style fixed point semantics, and a program logic (in the form of a type system) for partial correctness guarantees. This stream framework is transferred as it is to one for hyperstreams-streams of streams, that typically arise from sampling (continuous-time) signals with progressively smaller intervals-via the logical infrastructure of NSA. Under a certain continuity assumption we identify hyperstreams with signals; our final outcome thus obtained is a deductive verification framework of signals. In it one verifies properties of signals using the (conventionally discrete) proof principles, like fixed point induction.
stream processing signal processing nonstandard analysis type system hybrid system