Elements for Parallel Array Computations

Parallel high performance array programming in functional languages is usually performed with a fixed set of carefully chosen high-level combinators. Problems that fall outside the design scope for the combinators usually result in programs that are too slow and programmers resort to implementing them in low-level imperative languages without safety guarantees. We present element sets that allow us to keep the safety of functional high-level combinators but relaxes the specification order for array elements. The cost of the flexibility is two proof obligations for the compiler or library writer and the return is safety guarantees with zero performance overhead for all programs. We implemented element sets in a compiler and measured to see that that scalability and performance remained competitive with our solution.