A central but unresolved aspect of problem-solving in AI is the capability to introduce and use abstractions, something humans excel at. Work in cognitive science has demonstrated that humans tend towards higher levels of abstraction when engaged in collaborative task-oriented communication, enabling gradually shorter and more information-efficient utterances. Several computational methods have attempted to replicate this phenomenon, but all make unrealistic simplifying assumptions about how abstractions are introduced and learned. Our method, Procedural Abstractions for Communicating Efficiently (PACE), overcomes these limitations through a neuro-symbolic approach. On the symbolic side, we draw on work from library learning for proposing abstractions. We combine this with neural methods for communication and reinforcement learning, via a novel use of bandit algorithms for controlling the exploration and exploitation trade-off in introducing new abstractions. PACE exhibits similar tendencies to humans on a collaborative construction task from the cognitive science literature, where one agent (the architect) instructs the other (the builder) to reconstruct a scene of block-buildings. PACE results in the emergence of an efficient language as a by-product of collaborative communication. Beyond providing mechanistic insights into human communication, our work serves as a first step to providing conversational agents with the ability for human-like communicative abstractions.