Generalizing a Mathematical Analysis Library in Isabelle/HOL

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9058)

Abstract

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.

Keywords

Theorem proving Isabelle/HOL Type classes Linear Algebra 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Departamento de Matemáticas y ComputaciónUniversidad de La RiojaLogroñoSpain

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