The form of rules in combinatory categorial grammars (CCG) is constrained by three principles, called "adjacency", "consistency" and "inheritance". These principles have been claimed elsewhere to constrain the combinatory rules of composition and type raising in such a way as to make certain linguistic universals concerning word order under coordination follow immediately. The present paper shows that the three principles have an extremely natural expression in a unification-based interpretation of CCG in which directional information is an attribute of the arguments of functions grounded in string position. The aforementioned universals can thereby be derived as consequences of more elementary assumptions. Some desirable results follow, concerning type-raising and the parser.