An operational semantics for pure dataflow

Abstract

In this paper 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.

Our proof of the Kahn Principle makes use of two player infinite games of perfect information. Infinite games turn out to be an extremely useful tool for defining and proving results about operational semantics.