Intensional and Extensional Semantics of Dataflow Programs

Abstract.

We compare two semantic models of dataflow programs: a synchronous version of the classical Kahn semantics, and a new semantics in a category of synchronous processes. We consider the Kahn semantics to be extensional, as it describes the functions computed by dataflow nodes, and the categorical semantics to be intensional, as it describes the step-by-step production of output tokens from input tokens. Assuming that programs satisfy Wadge’s cycle sum condition and are therefore deadlock-free, we prove that the two semantics are equivalent. This equivalence result amounts to a proof that function composition in the extensional semantics is faithfully modelled by the detailed interactions of the intensional semantics, and provides further insight into the nature of dataflow computation.