Abstract. The principle of compositionality, as standardly defined, regards grammars as compositional that are not compositional in an intuitive sense of the word. There is, for example, no notion of a part of a string or structure involved in the formal definition. We shall therefore propose here a stricter version of compositionality. It consists in a conjunction of principles which assure among other that complex signs are in a literal sense made from simpler signs, with the meaning and syntactic 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 generate human languages, but most likely Literal Movement Grammars will do. A grammar is compositional if the meaning of a (complex) expression is determined from the meaning of its (immediate) parts together with their mode of combination. A language is compositional if there is a composi...