Name-free combinators for concurrency

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.