The equivalence of an operational and a denotational semantics for pure dataflow
In this thesis we prove the equivalence of an operational and a denotational semantics for pure dataflow. The term pure dataflow refers to dataflow nets in which the nodes are functional (i.e., the output history is a function of the input history only) and the arcs are unbounded fifo queues. Gilles Kahn gave a method for the representation of a pure dataflow net as a set of equations; one equation for each arc in the net. Kahn stated, and we prove, that the operational behaviour of a pure dataflow net is exactly described by the least fixed point solution to the net’s associated set of equations. In our model we do not require that nodes be sequential nor deterministic, not even the functional nodes. As a consequence our model has a claim of being completely general. In particular our nets have what we call the elcapsulation property in that any subnet can be replaced in any pure dataflow context by a node having exactly the same input/output behaviour. Our model is also complete in the sense that our nodes have what we call the universality property, that is, for any continuous history function there exists a node that will compute it. The proof of the Kahn principle given in this thesis makes use of infinite games of perfect information. Infinite games turn out to be an extremely useful tool for defining and proving results about operational semantics. We use infinite games to give for the first time a completely general definition of subnet functionality. In addition their use in certain proofs is effective in reducing notational complexity. Finally we look at possible ways of extending Kahn’s denotational model by the introduction of pause objects called hiatons. Finally we describe interesting ways of refining our operational model.