Definition
Plain language
Mathematically proving that a piece of software does exactly what it's supposed to, for every possible input — not just testing it on examples.
As stated in the literature
The use of machine-checked mathematical proof to establish that a system satisfies a formal specification across all inputs, message orderings, and failures; contrasted with testing, which only samples behaviors. Underlies verified systems like seL4, CompCert, and Chapar.
Also called: formally verified
Why it matters: It provides certainty that ordinary testing cannot, catching bugs that only appear in rare input combinations that no test suite would ever happen to try.
For example, instead of testing a banking program on a few transactions, formal verification proves it never loses money for any sequence of transactions at all.
Heard on the show
“" The deeper finding is that AI plus formal verification has an auditing function on the human side of the work.”Episode 067 — An AI Just Solved a 1996 Erdős Problem—and the Simplest Agent Won