Reasoning about arrays
John Reynolds · Communications of the ACM · 1979
A variety of concepts, laws, and notations are presented which facilitate reasoning about arrays. The basic concepts include intervals and their partitions, functional restriction, images, pointwise extension of relations, ordering, single-point variation of functions, various equivalence relations for array values, and concatenation. The effectiveness of these ideas is illustrated by informal descriptions of algorithms for binary search and merging, and by a short formal proof.