Proving equivalence between imperative and MapReduce implementations using program transformations

Distributed programs are often formulated in popular functional frameworks like MapReduce,
Spark and Thrill, but writing efficient algorithms for such frameworks is usually a non-trivial
task. As the costs of running faulty algorithms at scale can be severe, it is highly desirable
to verify their correctness.
We propose to employ existing imperative reference implementations as specifications
for MapReduce implementations. To this end, we present a novel verification approach in
which equivalence between an imperative and a MapReduce implementation is established
by a series of program transformations.
In this paper, we present how the equivalence framework can be used to prove equivalence
between an imperative implementation of the PageRank algorithm and its MapReduce
variant. The eight individual transformation steps are individually presented and explained.