We present Hedgehog, a general-purpose library for taking advantage of powerful compute nodes, multicore CPUs, and multiple GPUs. The novel aspects of Hedgehog are: (1) its explicit representation of a program as a dataflow graph, (2) its pure dataflow-driven scheduling, (3) its maintenance of a computation's localized state via state managers, and (4) its fine control of memory via memory managers. This dataflow approach results in extremely low overhead for task executions (< 1 microsecond) and no-cost profiling at the task level. This allows us to prototype operations that compare favorably with leading libraries such as cuBLAS-XT.