Subobject Transformation Systems

Subobject transformation systems (sts) are proposed as a novel formal framework for the analysis of derivations of transformation systems based on the algebraic, double-pushout (dpo) approach. They can be considered as a simplified variant of dpo rewriting, acting in the distributive lattice of subobjects of a given object of an adhesive category. This setting allows for a direct analysis of all possible notions of causality between any two productions without requiring an explicit match. In particular several equivalent characterizations of independence of productions are proposed, as well as a local Church-Rosser theorem in the setting of sts. Finally, we show how any derivation tree in an ordinary dpo grammar leads to an sts via a process-like construction and show that relational reasoning in the resulting sts is sound and complete with respect to the independence in the original derivation tree.