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...

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Detalles Bibliográficos
Autores: Heras, Jónathan, Martín Mateos, Francisco Jesús, Pascual, Vico
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
Descripción
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.