Formalization of Algebraic Theorems in PVS (Invited Talk)

Mauricio Ayala-Rincón; Thaynara Arielly de Lima; Andréia B. Avelar; André Luiz Galdino

doi:10.29007/7jbv

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Formalization of Algebraic Theorems in PVS (Invited Talk)

10 pages•Published: June 3, 2023

Mauricio Ayala-Rincon, Thaynara Arielly de Lima, Andréia B. Avelar and André Luiz Galdino

Abstract

This talk discusses current extensions on the theory algebra from the NASA/PVSlibrary on formal developments for the Prototype Verification System (PVS). It discusses the approach to formalizing theorems of the ring theory and how they are applied to infer properties of specific algebraic structures. As cases of study, we will present recent formalizations on the theories of Euclidean Domains and Quaternions. Moreover, we will show how a general verification of Euclid’s division algorithm can be specialized to verify this algorithm for specific Euclidean Domains, and how the abstract theory of Quaternions can be parameterized to deal with the structure of Hamilton’s Quaternions.

Keyphrases: Euclidean Algorithms, Euclidean Domains, Formalization of Algebraic Structures, PVS, Quaternions

In: Ruzica Piskac and Andrei Voronkov (editors). Proceedings of 24th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 94, pages 1--10

Links:	https://easychair.org/publications/paper/93F2
	https://doi.org/10.29007/7jbv

BibTeX entry

@inproceedings{LPAR2023:Formalization_of_Algebraic_Theorems,
  author    = {Mauricio Ayala-Rinc\textbackslash{}'on and Thaynara Arielly de Lima and Andr\textbackslash{}'eia B. Avelar and Andr\textbackslash{}'e Luiz Galdino},
  title     = {Formalization of Algebraic Theorems in PVS (Invited Talk)},
  booktitle = {Proceedings of 24th International Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Ruzica Piskac and Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {94},
  pages     = {1--10},
  year      = {2023},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/93F2},
  doi       = {10.29007/7jbv}}

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