Odd-even sort in powerlists

The odd-even sort is studied, which can be considered a parallel version of bubble sort; it is simple to implement and to explain operationally, yet it is inefficient and somewhat tedious to prove correct. The algorithm consists of a sequence of phases, where each phase consists of an even step followed by an odd step. The odd-even sort is derived and its correctness is proven. In contrast to Batcher's (1968) networks, the odd-even sort is iterative in nature and does not have a simple definition in the powerlist notation. The derivation is somewhat surprising: from a simple characterization of what it means for a powerlist to be sorted, the algorithm emerges through a series of transformations.