A Case Study on Proving Transformations Correct: Data-Parallel Conversion

The issue of correctness in the context of a certain style of program transformation is investigated. This style is characterised by the fully automated application of large numbers of simple transformation rules to a representation of a functional program (serving as a specification) to produce an equivalent efficient imperative program. The simplicity of the transformation rules ensures that the proofs of their correctness are straightforward. A selection of transformations appropriate for use in a particular context are shown to preserve program meaning. The transformations convert array operations expressed as the application of a small number of general-purpose functions into applications of a large number of functions which are amenable to efficient implementation on an array processor.