The actor theory framework is a general semantic framework, based on the actor computation model, for specifying and reasoning about components of open distributed systems. It can be used to define both operational and trace-like interaction semantics for actor programming languages and specification notations. It can also be used to directly specify actor system components. The framework allows descriptions of system components written using different notations or at different levels of abstraction to be related: translations between actor programming languages can be shown to preserve interaction semantics, notions of satisfaction and refinement for specification notations can be defined and, using actor theory transformations, different descriptions of a component can be shown to be equivalent. In this paper we define the notion of an equationally presented actor theory and a mapping of equational presentations to theories in rewriting logic. We show that this mapping gives a correct representation of actor theory semantics by defining a correspondence between finite actor theory computations and rewrite theory proofs. To treat infinite computations and admissibility we extend the rewriting logic initial model construction to include infinite proofs, extend the mapping to infinite computations, and show that the correspondence preserves interaction semantics.
Keywords: actor theory, interaction semantics, rewriting logic, composability