We study how program analysis can be used to: Automatically prove partial correctness of correct programs. Discover, locate, and diagnose bugs in incorrect programs. Specifically, we present an algorithm that analyzes sorting programs that manipulate linked lists. A prototype of the algorithm has been implemented. We show that the algorithm is sufficiently precise to discover that (correct versions) of bubble-sort and insertion-sort procedures do, in fact, produce correctly sorted lists as outputs, and that the invariant "is-sorted" is maintained by list-manipulation operations such as element-insertion, element-deletion, and even destructive list reversal and merging of two sorted lists. When we run the algorithm on erroneous versions of bubble-sort and insertion-sort procedures, it is able to discover and sometimes even locate and diagnose the error.