 Since there are no restrictions on what m assigns to members of E, the formal statement captures both compositionality of reference and compositionality of meaning. As stated, the principle captures local distributive language-bound compositionality: it requires that each application of each syntactic rule within a language be matched by an application of an appropriate semantic function. To capture cross-linguistic compositionality is easy: all we need to say is that the expressions within E are the expressions of all possible human languages. (Of course, if we allow the syntactic algebra to contain expressions of different languages, we may want to insist that syntactic operations map expressions of a language onto complex expressions of the same language and that they remain undefined for cases when their argument positions are filled by expressions from different  languages.[14])  