Closed Action Calculi

Action calculi provide a framework for capturing many kinds of interactive behaviour by focussing on the primitive notion of names. We introduce a name-free account of action calculi, called the closed action calculi, and show that there is a strong correspondence between the original presentation and the name-free presentation. We also add free names plus natural axioms to the closed world, and show that the abstraction operator can be constructed as a derived operator. Our results show that in some sense names are inessential. However, the purpose of action calculi is to understand formalisms which mimic the behaviour of interactive systems. Perhaps more significantly therefore, these results highlight the important presentational role that names play.

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