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"A generator is a parser of randomness." This perspective on generators forrandom data structures is well established as folklore in the programminglanguages community, but it has apparently never been formalized, nor have itsconsequences been deeply explored.  We present free generators, which unify parsing and generation using a commonstructure that makes the relationship between the two concepts precise. Freegenerators lead naturally to a proof that a large class of generators can befactored into a parser plus a distribution over choice sequences. Further, freegenerators support a notion of derivative, analogous to familiar Brzozowskiderivatives of formal languages, that allows analysis tools to "preview" theeffect of a particular generator choice. This, in turn, gives rise to a novelalgorithm for generating data structures satisfying user-specifiedpreconditions.

Parsing Randomness: Unifying and Differentiating Parsers and Random Generators