Generalizing a mathematical analysis library in Isabelle/HOL

The HOL Multivariate Analysis Library (HMA) of Isabelle/HOL is focused on concrete types such as ℝ, ℂ and ℝn 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...

Descripción completa

Detalles Bibliográficos
Autores: Aransay, J. [0000-0002-4079-8307], Divasón, J. [0000-0002-5173-128X]
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2015
País:España
Institución:Universidad de La Rioja (UR)
Repositorio:RIUR. Repositorio Institucional de la Universidad de La Rioja
OAI Identifier:oai:portal.dialnet.es:doc/5bbc6815b750603269e80234
Acceso en línea:https://investigacion.unirioja.es/documentos/5bbc6815b750603269e80234
Access Level:acceso abierto
Palabra clave:Isabelle/HOL
Linear Algebra
Theorem proving
Type classes
Descripción
Sumario:The HOL Multivariate Analysis Library (HMA) of Isabelle/HOL is focused on concrete types such as ℝ, ℂ and ℝn 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. © Springer International Publishing Switzerland 2015.