Overlay networks are used today in a variety of distributed systems ranging from file-sharing and storage systems to communication infrastructures. However, designing, building and adapting these overlays to the intended application and the target environment is a difficult and time consuming process. To ease the development and the deployment of such overlay networks we have implemented P2, a system that uses a declarative logic language to express overlay networks in a highly compact and reusable form. P2 can express a Narada-style mesh network in 16 rules, and the Chord structured overlay in only 47 rules. P2 directly parses and executes such specifications using a dataflow architecture to construct and maintain overlay networks. We describe the P2 approach, how our implementation works, and show by experiment the feasibility of our approach. This is joint work with Tyson Condie, Joe Hellerstein, Petros Maniatis, Timothy Roscoe and Ion Stoica. This work will also appear in SOSP 2005.