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Distributed programs are often formulated in popular functional frameworkslike MapReduce, Spark and Thrill, but writing efficient algorithms for suchframeworks is usually a non-trivial task. As the costs of running faultyalgorithms at scale can be severe, it is highly desirable to verify theircorrectness.  We propose to employ existing imperative reference implementations asspecifications for MapReduce implementations. To this end, we present a novelverification approach in which equivalence between an imperative and aMapReduce implementation is established by a series of program transformations.  In this paper, we present how the equivalence framework can be used to proveequivalence between an imperative implementation of the PageRank algorithm andits MapReduce variant. The eight individual transformation steps areindividually presented and explained.

Proving Equivalence Between Imperative and MapReduce Implementations Using Program Transformations