$\mathcal{M}$-adhesive transformation systems with nested application conditions. Part 1: parallelism, concurrency and amalgamation. (26th June 2014) - EHRIG, HARTMUT; GOLAS, ULRIKE; HABEL, ANNEGRET; LAMBERS, LEEN; OREJAS, FERNANDO
<x content-type="archive" xml:space="preserve">Abstract</x> Nested application conditions generalise the well-known negative application conditions and are important for several application domains. In this paper, we present Local Church–Rosser, Parallelism, Concurrency and Amalgamation Theorems for rules with nested application conditions in the framework of <alternatives><inline-graphic xlink:href="ark:/27927/pghmrxd3sr" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /> <![CDATA[$\mathcal{M}$]]> </alternatives>-adhesive categories, where <alternatives><inline-graphic xlink:href="ark:/27927/pghmrxd3sr" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /> <![CDATA[$\mathcal{M}$]]> </alternatives>-adhesive categories are slightly more general than weak adhesive high-level replacement categories. Most of the proofs are based on the corresponding statements for rules without application conditions and two shift lemmas stating that nested application conditions can be shifted over morphisms and rules.