The modern world runs on software. From smartphones and automobiles to medical devices and power plants, executable code drives insight and automation. However, there is a catch: computer code often contains programming errors—some small, some large. These glitches can lead to unexpected results—and systematic failures.
"In many cases, software flaws don't make any difference. In other cases, they can cause massive problems," says Kathleen Fisher, professor and chair of the computer science department at Tufts University and a former official of the U.S. Defense Advanced Research Projects Agency (DARPA).
The specification "For all values j and k such that 0 <= j < k < N, it must be the case that B[i] < B[j]." defines indexes j and k, yet uses indexes i and j. It also is problematic if the initial array contains elements of equal value. These are not just incompleteness issues.
The inventor of TLA+ is Leslie Lamport, 2013 ACM Turing Award winner:
"For fundamental contributions to the theory and practice of distributed and concurrent systems, notably the invention of concepts such as causality and logical clocks, safety and liveness, replicated state machines, and sequential consistency." Lamport's web site, lamport.org, discusses TLA+ and some of its industrial applications.
Thanks, J. Paul and Lawrence for your comments. I appreciate you pointing out these things, especially Leslie Lamport's contributions.
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