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Developing applications is becoming increasingly difficult due to recent growth in machine complexity along many dimensions, especially that of parallelism. We are studying data types that can be used to represent data parallel operations. Developing parallel programs with these data types have numerous advantages and such a strategy should facilitate parallel programming and enable portability across machine classes and machine generations without significant performance degradation. In this paper, we discuss our vision of data parallel programming with powerful abstractions. We first discuss earlier work on data parallel programming and list some of its limitations. Then, we introduce several dimensions along which is possible to develop more powerful data parallel programming abstractions. Finally, we present two simple examples of data parallel programs that make use of operators developed as part of our studies.