An experimental library of formalized Mathematics based on the univalent foundations

Mathematical Structures in Computer Science - Tập 25 Số 5 - Trang 1278-1294 - 2015
Vladimir Voevodsky1
1School of Mathematics,Institute for Advanced Study,Princeton,New Jersey,U.S.A.Email:[email protected]

Tóm tắt

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 Kapulkinet al.2012).

Từ khóa


Tài liệu tham khảo

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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.

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Kapulkin C. , LeFanu Lumsdaine P. and Voevodsky V. (2012) The simplicial model of univalent foundations. Preprint, arXiv:1211.2851.

10.1016/0890-5401(88)90005-3

Univalent Foundations Project (2013) Homotopy type theory: Univalent foundations for mathematics. Available at: http://homotopytypetheory.org/book.

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.

Voevodsky V. (2011) Resizing rules, slides from a talk at TYPES2011. Available at: https://github.com/vladimirias/2011_Bergen.