Summary: We describe an event-style (or poset) semantics for conflict-free rewrite systems, such as the \(\lambda\)-calculus, and other stable transition systems with a residual relation. Our interpretation is based on considering redex-families as events. It treats permutation-equivalent reductions as representing the same concurrent computation. Due to erasure of redexes, event structures are inadequate for such an interpretation. We therefore extend the prime event structure model by axiomatizing permutation-equivalence on finite configurations in two different ways, for the conflict-free case, and show that these extended models are equivalent to known stable transition models with axiomatized residual and family relations.
For the entire collection see [Zbl 0920.00047].