(I'm going to do a lazy permute on your stream of consciousness; hope it terminates :-). I think the Rubicon here is the step from one to many -- one function/procedure to many, one thread to many, one processor to many, ... . Our favorite pure functions are like the Hoare triples and Dijkstra weakest preconditions of the formal methods folks in that the latter abstract from the body of a procedure to the input-output relation it computes; both the function and the abstracted procedure are atomic and outside of time. After all, aren't "referential transparency" and "copy rule" all about replacing a function body with its results? Well, as soon as there are two or more functions/procedures in the same environment, the prospect of interaction and interference arises, and our nice, clean, *comprehensible* atemporal semantics get replaced by temporal logic, path expressions, trace specifications, what have you. Some notion of process is inevitable, since now each computation must be treated as an activity over time in order to relate events that occur doing the execution of one computation with the events of another. Functional programming gives us the possibility of using algebra to simplify the task of reasoning about single programs. Of course, non-functional procedures can also be reasoned about algebraically, since a procedure P(args) that hammers on state can be adequately described by a pure function f_P :: Args -> State -> State. The problem is, of course, that the state can be large. But the functional paradigm offers some hope for containing the complexity in the world of many as it does in the world of one. I think combining formalisms like Hoare's CSP or Milner's CCS with computations gives us the possibility of doing algebra on the temporal event sequences corresponding to their interactions; the hope is that this is simpler than doing proofs in dynamic or temporal logic. Using functional programs simplifies the algebraic task by reducing the size of the set of events over which the algebra operates -- you consider only the explicitly shared parameters and results, not the implicitly shared memory that can couple non-functional procedures. It is conceivable that you can get your compositionality here as well. Suppose we package computations with input-output parameter specifications and CSP-like specifications of the pattern of event sequences produced when the computation executes. It may be possible to reason about the interactions of the event sequences of groups of packages, determine the event sequences over non-hidden events provided by the composite system, etc. As far as Bulat's comment goes, I'm mostly in agreement. My dataflow view was really driven by the intuition that a functional program can be described by a network of subfunctions linking outputs to inputs; cross your eyes a little and voila! A dataflow network. And if we're smart enough to make a compiler do that, why bother the programmer? But you're not talking about analyzing a function into a parallel/concurrent/distributed implementation; rather, you're interested in synthesizing a temporal process out of interacting computations. The temporal aspect won't go away. And that's the problem. -- Bill Wood