On Encoding the Pi-calculus in Higher-Order Calculi

The connection between first-order calculi and higher-order calculi have been examined in many setting within the area of process calculi. In this paper we examine two existing encodings of the pi-calculus in higher-order calculi: the encoding in HOpi-calculus by Sangiorgi and Walker and the encoding in Plain CHOCS by Thomsen. We propose a new encoding of the synchronous pi-calculus in the calculus of Higher-Order Mobile Embedded Resources (Homer) inspired by the aforementioned encodings. Homer is a pure higher-order calculus with mobile processes in nested locations, defined as a simple, conservative extension of the core process-passing subset of Thomsen's Plain CHOCS. Our encoding demonstrates that non-linear higher-order process-passing together with mobile resources in, possibly local, named locations are sufficient to express pi-calculus name-passing.