Turing-completeness of additive transformations in the ETS formalism

We represent strings over a finite alphabet by the data structures, called string structs, introduced in the evolving transformation system (ETS) model, which was proposed as a general model for structural object representation and classification and has been formalized recently. Then we describe string languages as classes of structs generated by a finite set of context-sensitive transformations. The transformations are assumed to be additive, or non-deleting, in order to maintain the explicitness of representation of the constructive history of objects from a class, postulated in the ETS formalism. In case of strings, additive transformations are context-sensitive insertions; however, in case of structs they are more general. We prove that any recursive language can be represented as a class of string structs generated by additive transforms.