A universal process of a process calculus is one that, given the Gödel index of a process of a certain type, produces a process equivalent to the encoded process. This paper demonstrates how universal processes can be formally defined and how a universal process of the value-passing calculus can be constructed. The existence of such a universal process in a process model can be explored to implement higher order communications, security protocols, and programming languages in the process model. A process version of the S-m-n theorem is stated to showcase how to embed the recursion theory in a process calculus.

• 03D20 - Recursive functions and relations, subrecursive hierarchies
• 68Q85 - Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)