  We implement a divide-and-concur iterative projection approach to
context-free grammar inference. Unlike most state-of-the-art models of natural
language processing, our method requires a relatively small number of discrete
parameters, making the inferred grammar directly interpretable -- one can read
off from a solution how to construct grammatically valid sentences. Another
advantage of our approach is the ability to infer meaningful grammatical rules
from just a few sentences, compared to the hundreds of gigabytes of training
data many other models employ. We demonstrate several ways of applying our
approach: classifying words and inferring a grammar from scratch, taking an
existing grammar and refining its categories and rules, and taking an existing
grammar and expanding its lexicon as it encounters new words in new data.
