Compositional semantics of dataflow networks with query-driven communication of exact values

We develop and study the concept of dataflow process networks as used for exampleby Kahn to suit exact computation over data types related to real numbers, such as continuous functions and geometrical solids. Furthermore, we consider communicating these exact objectsamong processes using protocols of a query-answer nature as introduced in our earlier work. This enables processes to provide valid approximations with certain accuracy and focusing on certainlocality as demanded by the receiving processes through queries. We define domain-theoretical denotational semantics of our networks in two ways: (1) directly, i. e. by viewing the whole network as a composite process and applying the process semantics introduced in our earlier work; and (2) compositionally, i. e. by a fixed-point construction similarto that used by Kahn from the denotational semantics of individual processes in the network. The direct semantics closely corresponds to the operational semantics of the network (i. e. it iscorrect) but very difficult to study for concrete networks. The compositional semantics enablescompositional analysis of concrete networks, assuming it is correct. We prove that the compositional semantics is a safe approximation of the direct semantics. Wealso provide a method that can be used in many cases to establish that the two semantics fully coincide, i. e. safety is not achieved through inactivity or meaningless answers. The results are extended to cover recursively-defined infinite networks as well as nested finitenetworks. A robust prototype implementation of our model is available.