While the generative view of language processing builds bigger units out of smaller ones by means of rewriting steps, the axiomatic view eliminates invalid linguistic structures out of a set of possible structures by means of wellformedness principles. We present a generator based on the axiomatic view and argue that when combined with a TAG-like grammar and a flat semantics, this axiomatic view permits avoiding drawbacks known to hold either of top-down or of bottom-up generators.