Event Structures for the Reversible Early Internal [Formula: see text]-Calculus

The [Formula: see text]-calculus is a widely used process calculus, which models communications between processes and allows the passing of communication links. Various operational semantics of the [Formula: see text]-calculus have been proposed, which can be classified according to whether transitions are unlabelled (so-called reductions) or labelled. With labelled transitions, we can distinguish early and late semantics. The early version allows a process to receive names it already knows from the environment, while the late semantics and reduction semantics do not. All existing reversible versions of the [Formula: see text]-calculus use reduction or late semantics, despite the early semantics of the (forward-only) [Formula: see text]-calculus being more widely used than the late. We define [Formula: see text]IH, the first reversible early [Formula: see text]-calculus, and give it a denotational semantics in terms of reversible bundle event structures. The new calculus is a reversible form of the internal [Formula: see text]-calculus, which is a subset of the [Formula: see text]-calculus where every link sent by an output is private, yielding greater symmetry between inputs and outputs.