cient Compilation of High - Level Data Parallel

We present a high-level parallel calculus for nested sequences, NSC, ooered as a possible theoretical \core" of an entire class of collection-oriented parallel languages. NSC is based on while-loops as opposed to general recursion. A formal, machine independent deenition of the parallel time complexity and the work complexity of programs in NSC is given. Our main results are: (1) We give a translation method for a particular form of recursion, called map-recursion, into NSC, that preserves the time complexity and adds an arbitrarily small overhead to the work complexity, and (2) We give a compilation method for NSC into a very simple vector parallel machine, which preserves the time complexity and again adds an arbitrarily small overhead to the work complexity.