Modelling algebraic structures and morphisms in ACL2
In this paper, we present how algebraic structures and morphisms can be modelled in the ACL2 theorem prover. Namely, we provide a guide- line to implement a set of tools that facilitates the formalisations related to algebraic structures | as a result, an algebraic hierarchy ranging from se- toids t...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/86550 |
| Acceso en línea: | https://hdl.handle.net/11441/86550 https://doi.org/10.1007/s00200-015-0252-9 |
| Access Level: | acceso abierto |
| Palabra clave: | Mathematical structures ACL2 Algebraic hierarchy Proof engineering Computer Algebra systems Formal veri cation |
| Sumario: | In this paper, we present how algebraic structures and morphisms can be modelled in the ACL2 theorem prover. Namely, we provide a guide- line to implement a set of tools that facilitates the formalisations related to algebraic structures | as a result, an algebraic hierarchy ranging from se- toids 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 bene ts 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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