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. © 2022 American Physical Society.