I Contents 1 Introduction 1 2 Monolithic Arrays 1 3 from Macs to Double Loops: an Example 4 4 Problem Formulation and Solution Strategy 6

Unimodular transformation has been proposed as a powerful techniques for loop parallelization in imperative language programs. In this paper, we propose to apply unimodular transformation to functional language programs. In particular, we propose a method of applying unimodular transformation to monolithic arrays such as Haskell array comprehensions. Using our method, a compiler can deduce a safe and parallel order of evaluation for a given monolithic array. We formulate the problem of unimodular transformation under the context of functional programming. Instead of solving the result integer programming problem using expensive general solution techniques, we developed an e cient solution scheme by making use of the dependence direction and distance information in guiding the search of optimal solutions. We report an implementation of the algorithms in our experimental testbed. i