"Using lightweight modeling to understand Chord" (Pamela Zave; ACM SIGCOMM Computer Communication Review, 42(2):50-57, April 2012) summarizes the results of modeling and analyzing the Chord ring-maintenance protocol with Alloy. The paper shows that no published version of Chord is correct, even when obvious bugs are fixed. Not one of the seven claimed invariants is actually an invariant.
A correct version of Chord is documented in "How to make Chord correct" (Pamela Zave; submitted for publication, 2015). This paper also includes examples explaining why original Chord is incorrect, a necessary and sufficient inductive invariant, and a detailed presentation of the proof of correctness.
The following Alloy models include the formal specification of correct Chord, the invariant, and all proof steps.
"Experiences with protocol description" (Pamela Zave; 1st International Workshop on Rigorous Protocol Engineering, Vancouver, Canada, October 2011) explains the nature of some of the flaws in the prior reasoning about Chord. Such flaws are typical when there is no formal specification or automated checking of a protocol.
This work has also led to "A practical comparison of Alloy and Spin" (Pamela Zave; Formal Aspects of Computing 27: 239-253, 2015).
For those interested in the comparison, chordfull.als is the model of the original Chord protocol used in the first paper.
For those who wish to see and compare Promela models (for the Spin model-checker) of various versions: