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With the growth in transistor counts in modern hardware, heterogeneous systems are becoming commonplace. Core counts are increasing such that GPU and CPU designs are reaching deep into the tens of cores. For performance reasons, different cores in a heterogeneous platform follow different design choices. Based on throughput computing goals, GPU cores tend to support wide vectors and substantial register files. Current designs optimize CPU cores for latency, dedicating logic to caches and out-of-order dependence control. Heterogeneous parallel primitives (HPP) addresses two major shortcomings in current GPGPU programming models: it supports full composability by defining abstractions and increases flexibility in execution by introducing braided parallelism. Heterogeneous parallel primitives is an object-oriented, C++11-based programming model that addresses these shortcomings on both CPUs and massively multithreaded GPUs: it supports full composability by defining abstractions using distributed arrays and barrier objects, and it increases flexibility in execution by introducing braided parallelism. This paper implemented a feature-complete version of HPP, including all syntactic constructs, that runs on top of a task-parallel runtime executing on the CPU. They continue to develop and improve the model, including reducing overhead due to channel management, and plan to make a public version available sometime in the future.