"blah happened before bleh [but we missed that]" is caused by using variables, 100% of the time. Also, if you do not use variables, there cannot possibly be such a thing.
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Sure, you could write proofs that passwords don't get logged. That'd be great. That's a way weaker claim than not using variables automatically makes it impossible to accidentally log passwords (it doesn't).
No, I could (have, long ago) write a proof that this kind of bug cannot co-exist in the absence of variables.
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Dude, I can write a proof by contradiction in a tweet: do { request <- getRequest print request handle request } There's no mutable variables there.
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That's not a negative proof of the claim :)
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