Kahn's Networks of Processes as discrete analogues of Picard's Systems of Differential Equations

Anyone who has studied parallel programming with Kahn's networks of processes and also systems theory or control theory has noticed a strong similarity between the two. For one thing, both use similar diagrams, often with feedback, to express computations formed as compositions of incremental transforms. What is a mathematical basis for reconciling the two? Picard's theorem is a classical result in the theory of differential equations and integral equations. Kahn's theorem has similar renown in the theory of parallel programming, networks of processes, and stream processing. In this paper we clarify how these results are related, and show that Kahn's theorem and Picard's theorem are both special cases of a more general result. That we can do this may be surprising, since the foundations of the two theorems are quite different: metric function spaces and the fixed point theorem for contraction mappings in Picard's case, and complete partially ordered sets and the fixed point theorem for..