Abstract
We prove the completeness of an assertional proof system for a simple loop-free data-parallel language. This proof system is based on two-part assertions, where the predicate on the current value of variables is separated from the specification of the current extent of parallelism. The proof is based on a Weakest Precondition (WP) calculus. In contrast with the case of usual scalar languages, not all WP can be defined by an assertion. Yet, partial definability suffices to prove the completeness thanks to the introduction of hidden variables in assertions. The case of data-parallel programs with loops is briefly discussed in the conclusion.KeywordsConcurrent ProgrammingSpecifying and Verifying and Reasoning about ProgramsSemantics of Programming LanguagesData-Parallel LanguagesProof SystemHoare LogicWeakest Preconditions
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