The TELA structure – a set of layered and linked lattices – the notion of similarity between TELA structures based on the notion of Edit Distance, and the MSSM algorithm based on dynamic programming techniques are all introduced in order to formalize Translation Memories (TMs). The paper shows how this approach leads to a real gain in recall and precision, and allows the extension of TM towards rudimentary, yet useful Example-Based Machine Translation (EBMT) called ‘Shallow Translation’.