The algebraic hierarchy of the FTA Project (2002)
| Venue: | Journal of Symbolic Computation, Special Issue on the Integration of Automated Reasoning and Computer Algebra Systems |
| Citations: | 14 - 7 self |
BibTeX
@INPROCEEDINGS{Geuvers02thealgebraic,
author = {Herman Geuvers and Y Pollack and Freek Wiedijk and Jan Zwanenburg},
title = {The algebraic hierarchy of the FTA Project},
booktitle = {Journal of Symbolic Computation, Special Issue on the Integration of Automated Reasoning and Computer Algebra Systems},
year = {2002},
pages = {271--286},
publisher = {Elsevier}
}
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Abstract
Abstract. We describe a framework for algebraic expressions for the proof assistant Coq. This framework has been developed as part of the FTA project in Nijmegen, in which a complete proof of the fundamental theorem of algebra has been formalized in Coq. The algebraic framework that is described here is both abstract and structured. We apply a combination of record types, coercive subtyping and implicit arguments. The algebraic framework contains a full development of the real and complex numbers and of the rings of polynomials over these fields. The framework is constructive. It does not use anything apart from the Coq logic. The framework has been successfully used to formalize non-trivial mathematics as part of the FTA project.
