Distributed Exact Real Computation via Extra-Lazy Dataflow Networks

We adapt the concept of dataflow process network to suit computation with real numbers and other data types that require approximation, providing a framework for com-positional distributed exact computation with these data types. Our processes communicate approximations with each other in a lazy request-response manner, which is ad-vantageous for geometrical objects and functions where the locality of approximations can be directed by requests. We do not provide a process calculus, instead, starting at the level of event traces, we derive a domain-theoretical semantics. Thanks to such generality, many different data types and representations fit into the framework. Our domain-theoretical semantics is an abstraction of the request-response behaviour, combining a denotational semantics at the data type level with a generalised concept of convergence rate. We show that a safe estimate of this semantics can be derived compositionally without referring to the event trace level except for atomic processes.