A Rigorous Correctness Proof for Pastry

Peer-to-peer protocols for maintaining distributed hash tables, such as Pastry or Chord, have become popular for a class of Internet applications. While such protocols promise certain properties concerning correctness and performance, verification attempts using formal methods invariably discover border cases that violate some of those guarantees. Tianxiang Lu reported correctness problems in published versions of Pastry and also developed a model, which he called LuPastry, for which he provided a partial proof of correct delivery assuming no node departures, mechanized in the TLA$$^+$$+ Proof System. Lu's proof is based on certain assumptions that were left unproven. We found counter-examples to several of these assumptions. In this paper, we present a revised model and rigorous proof of correct delivery, which we call LuPastry$$^+$$+. Aside from being the first complete proof, LuPastry$$^+$$+ also improves upon Lu's work by reformulating parts of the specification in such a way that the reasoning complexity is confined to a small part of the proof.