Causal Trees, Finally

Causal trees are one of the earliest pioneering contributions of Pierpaolo Degano, in joint work with Philippe Darondeau. The idea is to record causality dependencies in processes and in their actions. As such, causal trees sit between interleaving models and truly concurrent ones and they originate an abstract, event-based bisimulation semantics for causal processes, where, intuitively, minimal causal trees represent the semantic domain. In the paper we substantiate this feeling, by first defining a nominal, compositional operational semantics based on History-Dependent automata and then we apply categorical techniques, based on named-sets, showing that causal trees form the final coalgebra semantics of a suitable coalgebraic representation of causal behaviour.