An abstract categorical semantics for functional reactive programming with processes

Abstract

Linear-time temporal logic and functional reactive programming (FRP) are related via a Curry-Howard correspondence. Thereby proofs of "always," "eventually," and "until" propositions correspond to behaviors, events, and processes, respectively. Processes in the FRP sense combine continuous and discrete aspects and generalize behaviors and events. In this paper, we develop a class of axiomatically defined categorical models of FRP with processes. We call these models abstract process categories (APCs). We relate APCs to other categorical models of FRP, namely temporal categories and concrete process categories.