Abstract. The principle of compositionality, as standardly dened, re-gards grammars as compositional that are not compositional in an intu-itive sense of the word. There is, for example, no notion of a part of a string or structure involved in the formal denition. We shall therefore propose here a stricter version of compositionality. It consists in a con-junction of principles which assure among other that complex signs are in a literal sense made from simpler signs, with the meaning and syntac-tic type being computed in tandem. We shall argue that given this strict principle, quite powerful string handling mechanisms must be assumed. Linear Context Free Rewrite Systems (see [13]) are not enough to gener-ate human languages, but most likel...