Julia GraphBLAS with Nonblocking Execution

From the beginning, the GraphBLAS were designed for "nonblocking execution"; i.e., calls to GraphBLAS methods return as soon as the arguments to the methods are validated and define a directed acyclic graph (DAG) of GraphBLAS operations. This lets GraphBLAS implementations fuse functions, elide unneeded objects, exploit parallelism, plus any additional DAG-preserving transformations. GraphBLAS implementations exist that utilize nonblocking execution but with limited scope. In this paper, we describe our work to implement GraphBLAS with support for aggressive nonblocking execution. We show how features of the Julia programming language greatly simplify implementation of nonblocking execution. This is work-in-progress sufficient to show the potential for nonblocking execution and is limited to GraphBLAS methods required to support PageRank.