“…Existing data-parallel languages, such as HPF, C , HyperC or MPL, include a similar core of data-parallel control structures. In previous papers, we have shown that it is possible to de ne a simple but representative data-parallel kernel language (the L language), to give it a formal operational 6] and denotational semantics 5], and to de ne a proof system for this language, in the style of the usual Hoare's logic approach 9,5]. The originality of our approach lies in the treatment of the extent of parallelism, that is, the subset of currently active indices at which a vector instruction is to be applied.…”