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C/C++/OpenCL-based high-level synthesis (HLS) becomes more and more popular for field-programmable gate array (FPGA) accelerators in many application domains in recent years, thanks to its competitive quality of results (QoR) and short development cycles compared with the traditional register-transfer level design approach. Yet, limited by the sequential C semantics, it remains challenging to adopt the same highly productive high-level programming approach in many other application domains, where coarse-grained tasks run in parallel and communicate with each other at a fine-grained level. While current HLS tools do support task-parallel programs, the productivity is greatly limited (1) in the code development cycle due to the poor programmability, (2) in the correctness verification cycle due to restricted software simulation, and (3) in the QoR tuning cycle due to slow code generation. Such limited productivity often defeats the purpose of HLS and hinder programmers from adopting HLS for task-parallel FPGA accelerators. In this paper, we extend the HLS C++ language and present a fully automated framework with programmer-friendly interfaces, unconstrained software simulation, and fast hierarchical code generation to overcome these limitations and demonstrate how task-parallel programs can be productively supported in HLS. Experimental results based on a wide range of real-world task-parallel programs show that, on average, the lines of kernel and host code are reduced by 22% and 51%, respectively, which considerably improves the programmability. The correctness verification and the iterative QoR tuning cycles are both greatly shortened by 3.2x and 6.8x, respectively. Our work is open-source at https://github.com/UCLA-VAST/tapa/.