By Kensuke Kozima and Atsushi Igarashi. In Proceedings of the Asian Symposium on Programming Languages and Systems (APLAS2013), volume 8301 of Lecture Notes in Computer Science, pages 58-73, Melbourne, Australia, December 2013. Springer-Verlag.
We study a Hoare Logic to reason about GPU kernels, which are parallel programs executed on GPUs. We consider the SIMT (Single Instruction Multiple Threads) execution model, in which multiple threads execute in lockstep (that is, execute the same instruction at a time). When control branches both branches are executed sequentially but during the execution of each branch only those threads that take it are enabled; after the control converges, all threads are enabled and execute in lockstep again. In this paper we adapt Hoare Logic to the SIMT setting, by adding an extra component representing the set of enabled threads to the usual Hoare triples. It turns out that soundness and relative completeness do not hold for all programs; a difficulty arises from the fact that one thread can invalidate the loop termination condition of another thread through shared memory. We overcome this difficulty by identifying an appropriate class of programs for which soundness and relative completeness hold.