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We present an algorithm for generating strings from logical form encodings that improves upon previous algorithms in that it places fewer restrictions on the class of grammars to which it is applicable. In particular, unlike a previous bottom-up generator, it allows use of semlantically nonmonotonic grammars, yet unlike top-down methods, it also permits left-recursion. The enabling design feature of the algorithm is its implicit traversal of the analysis tree for the string being generated in a semantic-head-driven fashion.