An approach to the study of program testing is introduced in which program testing is treated as a special kind of equivalence problem. In this approach, classes of programs P * and associated classes of test sets T * are defined which have the property that if two programs P and Q in P * agree on a set of tests from T *, then P and Q are computationally equivalent. The properties of a class P * and the associated class T * can be thought of as defining a set of assumptions about a hypothetical correct version Q of a program P in P *. If the assumptions are valid then it is possible to prove the correctness of P by testing. The main result of the paper is an equivalence theorem for classes of programs which carry out sequences of computations involving the elements of arrays.