A Reflective Higher-order Calculus

Abstract

The π-calculus is not a closed theory, but rather a theory dependent upon some theory of names. Taking an operational view, one may think of the π-calculus as a procedure that when handed a theory of names provides a theory of processes that communicate over those names. This openness of the theory has been exploited in π-calculus implementations, where ancillary mechanisms provide a means of interpreting of names, e.g. as tcp/ip ports. But, foundationally, one might ask if there is a closed theory of processes, i.e. one in which the theory of names arises from and is wholly determined by the theory of processes.Here we present such a theory in the form of an asynchronous message-passing calculus built on a notion of quoting. Names are quoted processes, and as such represent the code of a process, a reification of the syntactic structure of the process as an object for process manipulation. Name- passing in this setting becomes a way of passing the code of a process as a message. In the presence of a dequote operation, turning the code of a process into a running instance, this machinery yields higher-order characteristics without the introduction of process variables.As is standard with higher-order calculi, replication and/or recursion is no longer required as a primitive operation. Somewhat more interestingly, the introduction of a process constructor to dynamically convert a process into its code is essential to obtain computational completeness, and simultaneously supplants the function of the ν operator. In fact, one may give a compositional encoding of the ν operator into a calculus featuring dynamic quote as well as dequote.