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## Paper: *Generic parallel functional programming* To appear at ICFP 2017 [PDF and BibTeX](http://conal.net/papers/generic-parallel-functional/) ### Abstract Parallel programming, whether imperative or functional, has long focused on arrays as the central data type. Meanwhile, typed functional programming has explored a variety of data types, including lists and various forms of trees. *Generic* functional programming decomposes these data types into a small set of fundamental building blocks: sum, product, composition, and their associated identities. Definitions over these few fundamental type constructions then automatically assemble into algorithms for an infinite variety of data types---some familiar and some new. This paper presents generic functional formulations for two important and well-known classes of parallel algorithms: parallel scan (generalized prefix sum) and fast Fourier transform (FFT). Notably, arrays play no role in these formulations. Consequent benefits include a simpler and more compositional style, much use of common algebraic patterns and freedom from possibility of run-time indexing errors. The functional generic style also clearly reveals deep commonality among what otherwise appears to be quite different algorithms. Instantiating the generic formulations, two well-known algorithms for each of parallel scan and FFT naturally emerge, as well as two possibly new algorithms.

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