Humans flexibly solve new problems that differ from those previously practiced. This ability to flexibly generalize is supported by learned concepts that represent useful structure common across different problems. Here we develop a naturalistic drawing task to study how humans rapidly acquire structured prior knowledge. The task requires drawing visual figures that share underlying structure, based on a set of composable geometric rules and simple objects. We show that people spontaneously learn abstract drawing procedures that support generalization, and propose a model of how learners can discover these reusable drawing procedures. Trained in the same setting as humans, and constrained to produce efficient motor actions, this model discovers new drawing program subroutines that generalize to test figures and resemble learned features of human behavior. These results suggest that two principles guiding motor program induction in the model - abstraction (programs can reflect high-level structure that ignores figure-specific details) and compositionality (new programs are discovered by recombining previously learned programs) - are key for explaining how humans learn structured internal representations that guide flexible reasoning and learning.