Parallelization via Context

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 spec-iications may not have associative combine operators required by these schemes. As a result, they often fail to be immediately identiied. To resolve this problem, we propose a method to systematically derive parallel programs from sequential deenitions. This method is special in that it can automatically invent auxiliary functions needed by associa-tive combine operators. Apart from a formalisation, we also provide new theorems, based on the notion of context preservation , to guarantee parallelization for a precise class of sequential programs.