Jennifer Lundelius Welch, Leslie Lamport, and Nancy Lynch

Highly-optimized concurrent algorithms are often hard to prove correct because they have no natural decomposition into separately provable parts. This paper presents a proof technique for the modular verification of such non-modular algorithms. It generalizes existing verification techniques based on a totally-ordered hierarchy of refinements to allow a partially-ordered hierarchy -- that is, a lattice of different views of the algorithm. The technique is applied to the well-known distributed minimum spanning tree algorithm of Gallager, Humblet and Spira, which has until recently lacked a rigorous proof.