Re: Are there different programming languages that are compiled to the same intermediate language?

On 01/02/2023 08:07, Aharon Robbins wrote:> I've never understood this.
Isn't there a chicken and egg problem?
> How do we know that the theorem prover is correct and bug free?
A theorem prover generates a proof of the theorem (if it succeeds).
Checking the correctness of a proof is a much simpler task
than finding the proof in the first place and can be carried
out independently by different teams using different methods.
Appel and Haken's proof of the four colour theorem, for example,
involved a significant element of computer checking which was
independently double checked with different programs and computers.


> [It's a perfectly reasonable question. Alan Perlis, who was my thesis
> advisor, never saw any reason to believe that a thousand line proof
> was any more likely to be bug-free than a thousand line program.
> -John]


Mathematicians publish proofs all the time and only a tiny percentage
of published proofs turn out to have errors. Programmers release
programs all the time and a vanishingly small percentage of these
turn out to be free from all bugs. Alan Perlis may not have been able
to think of a reason why this should be the case, but it is,
nevetheless, the case.


--
Martin


Dr Martin Ward | Email: martin@gkc.org.uk | http://www.gkc.org.uk
G.K.Chesterton site: http://www.gkc.org.uk/gkc | Erdos number: 4
[Computer programs tend to be a lot longer than mathematical proofs. I
realize there are some 500 page proofs, but there are a whole lot of
500 page programs. It is my impression that in proofs, as in progams,
the longer and more complicated they are, the more likely they are to
have bugs. -John]

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