In sections 2 and 3 we have sketched an analysis of cross-serial dependency constructions and its interaction with the position and scope of adjuncts. The rules given there are actually part of a larger fragment that covers the syntax of Dutch verb clusters in more detail. The fragment accounts for cross-serial dependencies and extraposition constructions (including cases of `partial' extraposition), infinitivus-pro-participio, modal and participle inversion, the position of particles in verb clusters, clitic climbing, partial VP-topicalization, and verb second. In the larger fragment, additional recursive constraints are introduced, but the syntax is still restricted to application only.
The result of Carpenter  emphasizes the importance of lexical rules. There is a tendency in both CG and HPSG to rely more and more on mechanisms (such as inheritance and lexical rules or recursive constraints) that operate in the lexicon. The unrestricted generative capacity of recursive lexical rules implies that the remaining role of syntax can be extremely simple. In the examples above we have stressed this by giving an account for the syntax of cross-serial dependencies (a construction that is, given some additional assumptions, not context-free) using application only. In general, such an approach seems promising, as it locates the sources of complexity for a given grammar in one place, namely the lexicon.