  Grammar-based sentence generation has been thoroughly explored for
Context-Free Grammars (CFGs), but remains unsolved for recognition-based
approaches such as Parsing Expression Grammars (PEGs). Lacking tool support,
language designers using PEGs have difficulty predicting the behaviour of their
parsers. In this paper, we extend the idea of derivatives, originally
formulated for regular expressions, to PEGs. We then present a novel technique
for sentence generation based on derivatives, applicable to any grammatical
formalism for which the derivative can be defined--now including PEGs. Finally,
we propose applying derivatives more generally to other problems facing
language designers and implementers.
