Previous efforts to formally verify code written for GPUs have focused solely on kernels written within the traditional data-parallel GPU programming model. No previous work has considered the higher performance, but more complex, {\em warp-specialized} kernels based on producer-consumer {\em named barriers} available on current hardware. In this work we present the first formal operational semantics for named barriers and define what it means for a warp-specialized kernel to be correct. We give algorithms for verifying the correctness of warp-specialized kernels and prove that they are both sound and complete for the most common class of warp-specialized programs. We also present WEFT, a verification tool for checking warp-specialized code. Using WEFT, we discover several non-trivial bugs in production warp-specialized kernels.