An Extensional Treatment of Dataflow Deadlock

We discuss deadlock in reference to a simple equational dataflow language, and devise a test (the cycle sum test) which is applied to the dependency graph of a program. We use Kahn’s extensional semantics of dataflow and give a purely extensional (non-operational) proof that no program passing the cycle sum test can ever deadlock. The proof is based on the notions of size (length) and completeness in the domain of histories, and should extend to a much wider context.