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From: guttman@linus.mitre.org
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To: info-hol@clover.ucdavis.edu
Subject: HOL for mathematics?

I am curious about the suitability of HOL for doing non-trivial mathematics in
a rigorous context.

Maybe I can put it this way:  Suppose a latter-day Russell wanted to develop
completely rigorous versions of the foundations of various portions of
mathematics.  Assuming he wanted to work within simple type theory, then HOL
would suggest itself as an "assistant".

Do you have a sense of how difficult it would be to develop, within HOL, proofs
of typical theorems, say, chosen from the beginnings of analysis?  I have in
mind facts about continuous functions, derivatives, etc; examples might
include:

 1. the intermediate value theorem;
 2. a continuous function on a compact set is uniformly continuous;
 3. the chain rule for differentiation.

Do you think that the goal would be tractable?  Has anyone worked on this sort
of thing?  The only related effort that I am aware of is Elsa Gunter's "Doing
Algebra..." which Mike Gordon kindly pointed out to me.

Thanks for your interest.

        Josh

