dsimcha:
> overflow

Good provers take in account integral overflows too.


> rounding error

Interval (floating point) arithmetic can be used to face a large part of this 
problem. I hope to see a good Interval arithmetic lib for D in few years.


> compiler bugs
> OS bugs

Those software too can be proven :-) Microsoft is working on provable OS kernel.


> hardware bugs

You can use RAM with error correction, redundancy, etc.

Proofs are one useful tool for high-reliability systems. They are not enough, 
of course.

"Beware of bugs in the above code; I have only proved it correct, not tried 
it.''
-- Knuth

Bye,
bearophile

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