Dataflow analysis of array and scalar references

Given a program written in a simple imperative language (assignment statements,for loops, affine indices and loop limits), this paper presents an algorithm for analyzing the patterns along which values flow as the execution proceeds. For each array or scalar reference, the result is the name and iteration vector of the source statement as a function of the iteration vector of the referencing statement. The paper discusses several applications of the method: conversion of a program to a set of recurrence equations, array and scalar expansion, program verification and parallel program construction.