Adhesive High-Level Replacement Systems with Negative Application Conditions

The goal of this paper is the generalization of basic results for adhesive High-Level Replacement (HLR) systems to adhesive HLR systems with negative application conditions. These conditions restrict the application of a rule by expressing that a specific structure should not be present before or after applying the rule to a certain context. Such a condition influences thus each rule application or transformation and therefore changes significantly the properties of the replacement system. The effect of negative application conditions on the replacement system is described in the generalization of the following results, formulated already for adhesive HLR systems without negative application conditions: Local Church-Rosser Theorem, Parallelism Theorem, Completeness Theorem for Critical Pairs, Concurrency Theorem, Embedding and Extension Theorem and Local Confluence Theorem or Critical Pair Lemma. These important generalized results will support the development of formal analysis techniques for adhesive HLR replacement systems with negative application conditions