Fibrational Semantics of Dataflow Networks

Beginning with the category Dom of Scott domains and continuous maps, we introduce a syntax for dataaow networks as \systems of inequalities," and provide an associated operational semantics. We observe that, under this semantics, a system of inequalities determines a two-sided bration in Dom. This leads to the introduction of a certain class of cartesian arrows of spans as a notion of morphism for systems. The resulting structure Sys, consisting of domains, systems, and mor-phisms, forms a bicategory that embeds Dom up to equivalence and is suitable as a semantic model for nondeterministic networks. Isomorphism in Sys amounts to a notion of system equivalence \up to deterministic internal computations."