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

Abstract

Flow networks are inductively defined, assembled from small network modules to produce arbitrarily large ones, with interchangeable and expanding functionally-equivalent parts. We carry out this induction formally using a domain-specific language (DSL). Associated with our DSL is a typing system (or static semantics), a system of formal annotations that enforce desirable properties of flow networks as invariants across their interfaces. A prerequisite for a type theory is a formal semantics, i.e., a rigorous definition of the entities that qualify as feasible flows through the networks, possibly restricted to satisfy additional efficiency or safety requirements. We carry out this via a denotational semantics.