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Modelling algebraic structures and morphisms in ACL2

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Abstract

In this paper, we present how algebraic structures and morphisms can be modelled in the ACL2 theorem prover. Namely, we illustrate a methodology for implementing a set of tools that facilitates the formalisations related to algebraic structures—as a result, an algebraic hierarchy ranging from setoids to vector spaces has been developed. The resultant tools can be used to simplify the development of generic theories about algebraic structures. In particular, the benefits of using the tools presented in this paper, compared to a from-scratch approach, are especially relevant when working with complex mathematical structures; for example, the structures employed in Algebraic Topology. This work shows that ACL2 can be a suitable tool for formalising algebraic concepts coming, for instance, from computer algebra systems.

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Acknowledgments

The authors would like to thank the reviewers for the useful suggestions andcomments.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of La Rioja, Edificio Vives, Luis de Ulloa, s/n, 26004, Logroño, Spain

    Jónathan Heras & Vico Pascual

  2. Computational Logic Group, Department of Computer Science and Artificial Intelligence, University of Seville, E.T.S.I. Informática, Avda. Reina Mercedes, s/n, 41012, Seville, Spain

    Francisco Jesús Martín-Mateos

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  1. Jónathan Heras
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  2. Francisco Jesús Martín-Mateos
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  3. Vico Pascual
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Correspondence to Jónathan Heras.

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This work was partially supported by Ministerio de Educación y Ciencia, project MTM2009-13842-C02-01, and by the European Union’s 7th Framework Programme under Grant Agreement No. 243847 (ForMath).

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Heras, J., Martín-Mateos, F.J. & Pascual, V. Modelling algebraic structures and morphisms in ACL2. AAECC 26, 277–303 (2015). https://doi.org/10.1007/s00200-015-0252-9

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