On the completeness of a proof system for a simple data-parallel programming language (extended abstract)

Proving Data-Parallel Programs: A Unifying Approach

“…Although some partial results have been proved ( 3]), completeness of the initial proof system is not easy to establish.…”

“…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.…”

A design of a parallel dictionary using skip lists

“…Assuming that we are given an ordered array of k keys, the algorithm routes a set of packets containing the keys along the skip list, until the packets stop at appropriate places. We apply stepwise development techniques along the lines suggested in the work by Gabarrb and Gavalda [lo] and Bough et al [4]. This is fundamental to be able to implement these algorithms on real machines.…”