Combinatory formulations of concurrent languages

We design a system with six <italic>Basic Combinators</italic> and prove that it is powerful enough to embed the full asynchronous π-calculus, including replication. Our theory for constructing <italic>Combinatory Versions</italic> of concurrent languages is based on a method, used by Quine and Bernays, for the general elimination of variables in linguistic formalisms. Our combinators are designed to eliminate the requirement of <italic>names</italic> that are <italic>bound</italic> by an<italic>input prefix</italic>. They also eliminate the need for input prefix, output prefix, and the accompanying mechanism of <italic>substitution</italic>. We define a notion of <italic>bisimulation</italic> for the combinatory version and show that the combinatory version preserves the semantics of the original calculus. One of the distinctive features of the approach is that it can be used to rework several process algebras in order to derive equivalent combinatory versions.

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