[maxiepoo]

The use of the term "witness" here comes from constructive logic, where proofs of propositions have actual computational content. There "witness" means the same thing as "proof" but is more evocative that the proof is data that can actually be manipulated.

You might like this article if you're interested to learn more: http://jozefg.bitbucket.org/posts/2015-01-09-constructivism....