Uniqueness and Completeness Analysis of Array Comprehensions

In this paper we introduce the uniqueness and completeness problems of array comprehensions. An array comprehension has the uniqueness property if it defines each array element at most once. Uniqueness is a necessary condition for correctness in 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 uniqueness using the Omega Test, an Integer Linear Programming tool. An array comprehension has the completeness property if all its elements are defined. Completeness is a necessary condition for strict arrays. We present an algorithm that tests for completeness and describe an implementation of the algorithm based on multivariate polynomials