In this paper we consider simple language extensions given by a pair of transducers. When these transducers are viewed as trees transformers, one of this transducer provides an embedding of the original language into its extension while the other, a left-inverse to the embedding, allows every expression of the extended language to be expanded into an expression of the original language. This is of course the easy case and the work presented here should be considered as a work in progress where we have reach only a very preliminary stage. The purpose of this report is to introduce our approach to the extension of domain specific languages, fix the notations and definitions and illustrate the case, of what might be termed the class of the split extensions, where the embedding of the language into its extension has a left-inverse. We shall, in the next future, investigate the general case of language extensions where the embedding doesn't necessarily have a left-inverse.