On the Expressivity of a Weakest Precondition Calculus for a Simple Data-Parallel Programming Language

We present a weakest preconditions calculus `a la Dijkstra for a small common kernel of existing data-parallel languages. We use two-part assertions, where the current extent of parallelism is specified by a separate boolean vector expression. Our main contribution is concerned with the conditioning construct where which modifies the current extent of parallelism. We prove that the weakest (strict) preconditions of a where block is definable by an assertion as soon as its body is. We show that this is not the case with its weakest liberal preconditions. This sheds a new light on the deep semantic nature of the data-parallel conditioning construct