How humans grow and maintain abstract knowledge from the sparse, streaming noisy data of experience is a longstanding challenge in cognitive science. Any computational account must satisfy at least three desiderata: It must be (1) data-efficient and compute-efficient, (2) capture gradations of uncertainty to support intelligent inquiry and information gathering, and (3) be flexible enough to mentally represent the endless range of concepts people can learn and think about. Here we introduce a computational model that captures these three properties, by encoding symbolic knowledge as mental programs that combine natural language with source code, and sequentially inferring mental programs using LLM-guided Bayesian learning algorithms. Across a range of behavioral studies this model successfully reproduces quantitative signatures of human inductive learning and active inquiry, such as anchoring, garden-pathing, and other effects. In contrast, pure LLMs and classic Bayesian models either fail at the underlying task, or do not reproduce human behavior, or succeed only at exorbitant computational cost. These results suggest that one way humans continually grow their knowledge is by mentally representing many hypotheses spanning language-like and program-like representations, then revising those hypotheses to approximate Bayesian updates, while a bottom-up neural mechanism (an LLM) makes inference both tractable and learnable.

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