Simultaneous-Distributive Coordination and Context-Freeness

English is shown to be trans-context-free on the basis of coordinations of the respectively type that involve strictly syntactic cross-serial agreement. The agreement in question involves number in nouns and reflexive pronouns and is syntactic rather than semantic in nature because grammatical number in English, like grammatical gender in languages such as French, is partly arbitrary. The formal proof, which makes crucial use of the Interchange Lemma of Ogden et al., is so constructed as to be valid even if English is presumed to contain grammatical sentences in which respectively operates across a pair of coordinate phrases one of whose members has fewer conjuncts than the other; it thus goes through whatever the facts may be regarding constructions with unequal numbers of conjuncts in the scope of respectively, whereas other arguments have foundered on this problem.