The reflective higher-order calculus: Encodability, typability and separation

The ρ-calculus (Reflective Higher-Order Calculus) of Meredith and Radestock is a π-calculus-like language with unusual features, notably, structured names, runtime generation of free names, and the lack of a scoping operator. These features pose interesting difficulties for proofs of encodability, type system soundness and separation results. We describe two errors in a previous attempt to encode the π-calculus in the ρ-calculus by Meredith and Radestock. Then we give a new encoding and prove its correctness, using a set of encodability criteria close to those of Gorla, and discuss the adaptations necessary to work with a calculus with runtime generation of structured names. We create a simple type system for the ρ-calculus to show that the encoding is well-typed, and discuss the limitations that must be imposed when working with structured names. Lastly we prove a separation result, showing that the ρ-calculus cannot be encoded in the π-calculus.