Parallel programming with data structures and higher order functions

Abstract

Linear lists, which are the standard data structure in functional programming languages, have proved to be useful for many applications. Yet for several reasons it seems that there is a need for additional applicative data structures: Firstly, functional programming languages are well suited for parallel execution, because programs written in these languages cannot have side effects, and expressions can be evaluated independently. But parallel execution of functional programs is often hampered by the linear structure of lists, which supports only one element at a time algorithms. Secondly, lists lack the expressive power that we need in general purpose languages. For example, there is a need for array-like data structures. Thirdly, many functions on lists have to be defined recursively. No matter how efficiently recursion may be implemented, it will always fall short of the efficiency that can be obtained with imperative implementations. We propose a choice of data structures and corresponding higher order functions that enable programmers to write concise and (almost) recursion-free functional programs which have a higher degree of potential parallelism. Possible implementation techniques are discussed, and the major complexity result is that, under parallel evaluation, many functions on our data structures need only logarithmic time, whereas using lists results in linear time complexity.