Efficient computations in formal proofs
Date: July 17th (Wednesday)
Time: ??.??
Abstract
Formal proofs in mathematics and computer science are being studied
because these objects can be verified by a very simple computer
program. An important open problem is whether these formal proofs can
be generated with an effort not much greater than writing a
mathematical paper in, say, (La)TeX. Modern systems for
proof-development make the formalization of reasoning relatively
easy. Formalizing computations such that the results can be used in
formal proofs is not immediate. In this paper it is shown how to
obtain formal proofs of statements
like Prime(n) in the context of Peano arithmetic or
in the context of rings.
It is hoped that the
method will help bridge the gap between systems of computer algebra
and systems of proof-development.
