A functional presentation of Pi calculus

Abstract

From the very beginning process algebra introduced the dichotomy between channels and processes. This dichotomy prevails in all present process calculi. The situation is in contrast to that with lambda calculus which has only one class of entities—the lambda terms. We introduce in this paper a process calculus called Lamp in which channels are process names. The language is more uniform than existing process calculi in two aspects: First it has a unified treatment of channels and processes. There is only one class of syntactical entities—processes. Second it has a unified presentation of both first order and higher order process calculi. The language is functional in the sense that lambda calculus is functional. Two bisimulation equivalences, barbed and closed bisimilarities, are proved to coincide. A natural translation from Pi calculus to Lamp is shown to preserve both operational and algebraic semantics. The relationship between lazy lambda calculus and Lamp is discussed.