We present a formal framework for a recently introduced approach to Automated Round-trip Software Engineering (ARE) in source-level aspect weaving systems. Along with the formalization we improve the original method and suggest a new concept of weaving transactions in Aspect-oriented Programming (AOP). As the major contribution we formally show how, given a tree-shaped intermediate representation of a program and an ancillary transposition tree, manual edits in statically woven code can consistently be mapped back to their proper source of origin, which is either in the application core or in an element in the aspect space. The presented formalism is constructive. It frames AOP by generalizing static aspect weaving to classical tree transformations.