Many data parallel algorithms – Fast Fourier Transform, Batcher’s sorting schemes and prefixsum – exhibit recursive structure. We propose a data structure, powerlist, that permits succinct descriptions of such algorithms, highlighting the roles of both parallelism and recursion. Simple algebraic properties of this data structure can be exploited to derive properties of these algorithms and establish equivalence of different algorithms that solve the same problem.

Nested data parallelism has been shown to be an important feature of parallel languages, allowing the concise expression of algorithms that operate on irregular data structures such as graphs and sparse matrices. However, previous nested dataparallel languages have relied on a vector PRAM implementation layer that cannot be efficiently mapped to MPPs with high inter-processor latency. This thesis shows that by restricting the problem set to that of data-parallel divide-and-conquer algorithms I can maintain the expressibility of full nested data-parallel languages while achieving good efficiency on current distributed-memory machines. Specifically, I define

“He who loves practice without theory is like the sailor who boards ship without a rudder and compass and never knows where he may be cast.” Leonardo da Vinci (1452–1519) Computer programming has been, largely, an intuitive activity. Programmers are taught to understand programming in operational terms, i.e., how a computer executes a program. As the field has matured, we see many effective theories for designing and reasoning about computer programs in specific domains. Such theories reduce the mental effort, and the amount of experimentation needed to design a product. They are as indispensable for their domains as calculus is for solving scientific and engineering problems. I am attracted to effective theories primarily because they save labor (for the human and the computer), and secondarily because they give us better assurance about the properties of programs. The original inspiration to design a computer science course which illustrates the applications of effective theories in practice came from Elaine Rich and J