Computer-Assisted Mathematics at Work -- The Hahn-Banach Theorem in Isabelle/Isar (2000)
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| Venue: | TYPES FOR PROOFS AND PROGRAMS: TYPES’99, LNCS |
| Citations: | 8 - 5 self |
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@INPROCEEDINGS{Bauer00computer-assistedmathematics,
author = {Gertrud Bauer and Markus Wenzel},
title = {Computer-Assisted Mathematics at Work -- The Hahn-Banach Theorem in Isabelle/Isar},
booktitle = {TYPES FOR PROOFS AND PROGRAMS: TYPES’99, LNCS},
year = {2000},
publisher = {}
}
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Abstract
We present a complete formalization of the Hahn-Banach theorem in the simply-typed set-theory of Isabelle/HOL, such that both the modeling of the underlying mathematical notions and the full proofs are intelligible to human readers. This is achieved by means of the Isar environment, which provides a framework for high-level reasoning based on natural deduction. The final result is presented as a readable formal proof document, following usual presentations in mathematical textbooks quite closely. Our case study demonstrates that Isabelle/Isar is capable to support this kind of application of formal logic very well, while being open for an even larger scope.
