Swarm protocols are a recently introduced formalism for specifying, implementing, and verifying peer-to-peer systems called swarms. A swarm consists of distributed agents called machines that communicate by asynchronous event propagation. Following a local-first model, each machine can progress without requiring continuous connectivity to other machines. Existing models of swarms are not compositional, making the modular development of large and complex swarm applications as well as the reuse of code difficult. We address these issues by presenting novel theory and techniques for the compositional specification, verification, and implementation of swarms. These results enable the correct compositional reuse of pre-existing swarm protocols and machine implementations. We implement these contributions in a companion software artifact which enables the automatic integration of independently designed and verified swarm components.