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Erschienen in:
2015 | OriginalPaper | Buchkapitel
Generalizing a Mathematical Analysis Library in Isabelle/HOL
verfasst von : Jesús Aransay, Jose Divasón
Erschienen in: NASA Formal Methods
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The HOL Multivariate Analysis Library (
HMA
) of Isabelle/HOL is focused on concrete types such as
$$\mathbb {R}$$
,
$$\mathbb {C}$$
and
$$\mathbb {R}^n$$
and on algebraic structures such as real vector spaces and Euclidean spaces, represented by means of type classes. The generalization of
HMA
to more abstract algebraic structures is something desirable but it has not been tackled yet. Using that library, we were able to prove the Gauss-Jordan algorithm over real matrices, but our interest lied on generating verified code for matrices over arbitrary fields, greatly increasing the range of applications of such an algorithm. This short paper presents the steps that we did and the methodology that we devised to generalize such a library, which were successful to generalize the Gauss-Jordan algorithm to matrices over arbitrary fields.