Name-free combinators for concurrency

TL;DR

This paper introduces a name-free combinator calculus for concurrency by replacing bound name operators with reflective operators, enabling a faithful embedding of the asynchronous pi calculus without bound names.

Contribution

It presents the first combinator calculus for concurrency that eliminates bound names using reflective operators, extending Yoshida's work.

Findings

Successful embedding of asynchronous pi calculus into the new combinator calculus

Demonstration that multisorted Lawvere theories capture the calculus's semantics

First name-free combinator calculus for concurrency

Abstract

Yoshida demonstrated how to eliminate the bound names coming from the input prefix in the asynchronous pi calculus, but her combinators still depend on the "new" operator to bind names. We modify Yoshida's combinators by replacing "new" and replication with reflective operators to provide the first combinator calculus with no bound names into which the asynchronous pi calculus has a faithful embedding. We also show that multisorted Lawvere theories enriched over graphs suffice to capture the operational semantics of the calculus.