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A univalent formalization of the p-adic numbers

  • ÁLVARO PELAYO (a1) (a2), VLADIMIR VOEVODSKY (a2) and MICHAEL A. WARREN (a3)
Abstract

The goal of this paper is to report on a formalization of the p-adic numbers in the setting of the second author's univalent foundations program. This formalization, which has been verified in the Coq proof assistant, provides an approach to the p-adic numbers in constructive algebra and analysis.

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M. Atiyah (1982) Convexity and commuting Hamiltonians. Bulletin of the London Mathematical Society 14 115.

S. Awodey (2012) Type theory and homotopy. In: P. Dybjer , S. Lindström , E. Palmgren and B. G. Sundholm (eds.) Epistemology versus Ontology: Essays on the Philosophy and Foundations of Mathematics in Honour of Per Martin-Löf Logic, Epistemology, and the Unity of Science volume 27, Springer, Dordrecht183201.

Y. Bertot and P. Castéran (2004) Interactive Theorem Proving and Program Development. Coq'Art: The Calculus of Inductive Constructions, Texts Theoretical Computer Science An EATCS Series, Springer-Verlag.

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Á. Pelayo and S. Vũ Ngoc (2009) Semitoric integrable systems on symplectic 4-manifolds, Inventiones Mathematicae 177 571597.

Á. Pelayo and S. Vũ Ngoc (2011) Constructing integrable systems of semitoric type. Acta Mathematica 206 93125.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
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