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A Formalization of Grassmann-Cayley Algebra in COQ and Its Application to Theorem Proving in Projective Geometry
Abstract : This paper presents a formalization of Grassmann-Cayley algebra that has been done in the COQ proof assistant. The formalization is based on a data structure that represents elements of the algebra as complete binary trees. This allows to define the algebra products recursively. Using this formalization, published proofs of Pappus' and Desargues' theorem are interactively derived. A method that automatically proves projective geometric theorems is also translated successfully into the proposed formalization.
Cited literature [17 references]
https://hal.archives-ouvertes.fr/hal-00657901
Contributor : Laurent Fuchs Connect in order to contact the contributor
Submitted on : Monday, January 9, 2012 - 2:34:35 PM
Last modification on : Saturday, June 25, 2022 - 11:07:02 PM
Long-term archiving on: : Monday, November 19, 2012 - 1:00:56 PM
Contributor : Laurent Fuchs Connect in order to contact the contributor
Submitted on : Monday, January 9, 2012 - 2:34:35 PM
Last modification on : Saturday, June 25, 2022 - 11:07:02 PM
Long-term archiving on: : Monday, November 19, 2012 - 1:00:56 PM
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