Parallelism and Concurrency Theorems for Rules with Nested Application Conditions

Abstract

We present Local Church-Rosser, Parallelism, and Concurrency Theorems for rules with nested application conditions in the framework of weak adhesive HLR categories including different kinds of graphs. The proofs of the statements are based on the corresponding statements for rules without application conditions and two Shift-Lemmas, saying that nested application conditions can be shifted over morphisms and rules.