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  The algebraic hierarchy of the FTA Project (2002) [19 citations — 8 self]

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by Herman Geuvers, Y Pollack, Freek Wiedijk, Jan Zwanenburg
Journal of Symbolic Computation, Special Issue on the Integration of Automated Reasoning and Computer Algebra Systems
http://www.cs.kun.nl/~freek/pubs/alghier.ps.gz
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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 elds. The framework is constructive. It does not use anything apart from the Coq logic. The framework has been successfully used to formalize non-trivial

Citations

248 Vulnerabilities Analysis – Bishop - 1999
52 PVS: A prototype veri system – Owre, Rushby, et al. - 1992
44 Enhancing the NuPRL proof development system and applying it to computational abstract algebra – Jackson - 1995
30 Coercive subtyping – Luo - 1999
27 The Machine-Checked Literate Formalisation Of Algebra In Type Theory – Bailey - 1998
19 A constructive proof of the fundamental theorem of algebra without using the rationals – Geuvers, Wiedijk, et al. - 2001
14 AXIOM: The Scienti Computation System – Jenks, Sutor - 1992
12 Fundamental Theorem of Algebra – Milewski - 2001
12 Dependently Typed Records for Representing Mathematical Structure – Pollack - 2000
10 Equational reasoning via partial re – Geuvers, Wiedijk, et al. - 2000
9 et al. The Coq Proof Assistant Reference – Barras - 1998
9 Field: une procédure de décision pour les nombres réels en Coq – Delahaye, Mayero - 2001
9 Mizar: An impression – Wiedijk - 1999
7 Erganzung zu einer Arbeit von Hellmuth Kneser uber den Fundamentalsatz der Algebra – Kneser - 1981
4 The QED Manifesto – Boyer - 1994
4 An Outline of PC Mizar. Fond. Philippe le Hodey – Muzalewski - 1993
3 Typing algorithm in type theory with inheritance – Sabi - 1997
2 Un debut de formalisation de l'algebre en Coq et Ctcoq. Web page – Pottier - 2001
1 Complex quanti elimination – Harrison - 2001
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