The Name-Passing Calculus

Name-passing calculi are foundational models for mobile computing. Research into these models has produced a wealth of results ranging from relative expressiveness to programming pragmatics. The diversity of these results call for clarification and reorganization. This paper applies a model independent approach to the study of the namepassing calculi, leading to a uniform treatment and simplification. The technical tools and the results presented in the paper form the foundation for a theory of name-passing calculus. 1 Mobility in Practice and in Theory Mobile calculi feature the ability to pass around objects that contain channel names. Higher order CCS [91, 92, 93, 94] for instance, is a calculus with a certain degree of mobility. In a mobile calculus, a process that receives an object may well make use of the names which appear in the object to engage in further interactions. It is in this sense that the communication topology is dynamic. It was soon realized that the communication mechanism that restricts the contents of communications to the channel names gives rise to a simple yet versatile model that is more powerful than the process-passing calculi [79, 80, 82, 81]. This is the π-calculus of Milner, Parrow and Walker [60]. See [71] for a gentle introduction to the model and the history of the name-passing calculus and [87] for a broader coverage. A seemingly innocent design decision of the π-calculus is to admit a uniform treatment of the names. This decision is however not supported by the semantics of the mobile calculi. From a process term T one could construct the input prefix term a(x).T (1) and the localization term (x)T. (2) According to the definition of the π-calculus, the semantics of x which appears in (1) is far different from that of x in (2). In the former x is a name variable, or a dummy name, that can be instantiated by an arbitrary name when the prefix engages in an interaction. In the latter x is a local name that can never be confused with another name. The input prefix forces the unbound name x in T to be a name variable, whereas the localization operator forces the unbound name x in T to be a constant name. This apparent contradiction is behind all the semantic complications of the π-calculus. And nothing has been gained by these complications. In what follows we take a look at some of the issues caused by the confusion. To begin with, the standard operational semantics of the π-calculus has not been very smooth. An extremely useful command in both practice and theory is the two leg if-statement if φ then S else T . In mobile calculi this can be defined by introducing the conditional terms [x=y]T and [x,y]T . The semantics of these terms have been defined respectively by the match rule T λ −→ T ′ [x=x]T λ −→ T ′ (3) and the mismatch rule T λ −→ T ′ [x,y]T λ −→ T ′ x , y. (4)