Uniqueness Analysis of Array Comprehensions

In this paper we introduce the uniqueness problem of array comprehensions. An array comprehension has the uniqueness property if it deenes each array element at most once. Uniqueness is a necessary condition for the correctness of single assignment languages such as Haskell, Id, and Sisal. The uniqueness problem can be stated as a data dependence problem, which in itself can be reformulated as an integer linear programming problem. We derive algorithms to solve this problem using the Omega test, an Integer Linear Programming tool.