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An experimental library of formalized Mathematics based on the univalent foundations

  • VLADIMIR VOEVODSKY (a1)
Extract

This is a short overview of an experimental library of Mathematics formalized in the Coq proof assistant using the univalent interpretation of the underlying type theory of Coq. I started to work on this library in February 2010 in order to gain experience with formalization of Mathematics in a constructive type theory based on the intuition gained from the univalent models (see Kapulkin et al. 2012).

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References
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Ahrens, B., Kapulkin, C. and Shulman, M. (2014) Univalent categories and the Rezk completion. Mathematical Structures in Computer Science http://dx.doi.org/10.1017/S0960129514000486.
Coquand, T. and Huet, G. (1988) The calculus of constructions. Information and Computation 76 (2–3) 95120.
Grothendieck, A. (1997) Esquisse d'un programme. In: Geometric Galois Actions, 1, London Mathematical Society Lecture Note Series volume 242, Cambridge University Press, Cambridge 548. (With an English translation on pp. 243–283.)
Kapulkin, C., LeFanu Lumsdaine, P. and Voevodsky, V. (2012) The simplicial model of univalent foundations. Preprint, arXiv:1211.2851.
Luo, Z. (1994) Computation and Reasoning. A Type Theory for Computer Science, International Series of Monographs on Computer Science volume 11, The Clarendon Press. Oxford University Press, New York.
Makkai, M. (1995) First order logic with dependent sorts, with applications to category theory. Preprint, Available at: http://www.math.mcgill.ca/makkai/folds/foldsinpdf/FOLDS.pdf.
Paulin-Mohring, C. (1993) Inductive definitions in the system Coq: Rules and properties. In: Typed Lambda Calculi and Applications (Utrecht, 1993), Springer Lecture Notes in Computer Science volume 664 Berlin 328–345.
Pelayo, A., Voevodsky, V. and Warren, M. A. (2014) A preliminary univalent formalization of the p-adic numbers. Mathematical Structures in Computer Science http://dx.doi.org/10.1017/S0960129514000541.
Univalent Foundations Project (2013) Homotopy type theory: Univalent foundations for mathematics. Available at: http://homotopytypetheory.org/book.
Voevodsky, V. (2011) Resizing rules, slides from a talk at TYPES2011. Available at: https://github.com/vladimirias/2011_Bergen.
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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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