The syntax and semantics of a domain-specific language for flow-network design

Abstract

Flow networks are inductively defined, assembled from small components to produce arbitrarily large ones, with interchangeable functionally-equivalent parts. We carry out this induction formally using a domain-specific language (DSL). Associated with our DSL are a semantics and a typing theory. The latter gives rise to a system of formal annotations that enforce desirable properties of flow networks as invariants across their interfaces. A prerequisite for a typing theory is a formal semantics, i.e., a rigorous characterization of flows that are safe for the network (limited to the notion of feasible flows in this paper, unfeasible flows being considered unsafe). We give a detailed presentation of a denotational semantics only, but also point out the elements that an equivalent operational semantics must include.