To adapt to a changing world, we must be able to switch between rules already learned and, at other times, learn rules anew. Often we must do both at the same time, switching between known rules while also constantly re-estimating them. Here, we show these two processes, rule switching and rule learning, rely on distinct but intertwined computations, namely fast inference and slower incremental learning. To this end, we studied how monkeys switched between three rules. Each rule was compositional, requiring the animal to discriminate one of two features of a stimulus and then respond with an associated eye movement along one of two different response axes. By modeling behavior, we found the animals learned the axis of response using fast inference (rule switching) while continuously re-estimating the stimulus–response associations within an axis (rule learning). Our results shed light on the computational interactions between rule switching and rule learning, and make testable neural predictions for these interactions.