Parallelization via context preservation

Abstract program schemes, such as scan or homomorphism, can capture a wide range of data parallel programs. While versatile, these schemes are of limited practical use on their own. A key problem is that the more natural sequential specifications may not have associative combine operators required by these schemes. As a result, they often fail to be immediately identified. To resolve this problem, the authors propose a method to systematically derive parallel programs from sequential definitions. This method is special in that it can automatically invent auxiliary functions needed by associative combine operators. Apart from a formalisation, they also provide new theorems, based on the notion of context preservation, to guarantee parallelization for a precise class of sequential programs