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Univalent Foundations and the UniMath Library. The Architecture of Mathematics.

Bordg, Anthony (2018) Univalent Foundations and the UniMath Library. The Architecture of Mathematics. [Preprint]

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Abstract

We give a concise presentation of the Univalent Foundations of mathematics outlining the main ideas, followed by a discussion of the UniMath library of formalized mathematics implementing the ideas of the Univalent Foundations (section 1), and the challenges one faces in attempting to design a large-scale library of formalized mathematics (section 2). This leads us to a general discussion about the links between architecture and mathematics where a meeting of minds is revealed between architects and mathematicians (section 3). On the way our odyssey from the foundations to the "horizon" of mathematics will lead us to meet the mathematicians David Hilbert and Nicolas Bourbaki as well as the architect Christopher Alexander.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Bordg, Anthonybordg.anthony@gmail.com
Additional Information: To appear in the Synthese Library series, Springer, volume "Reflections on the Foundations of Mathematics: Set Theory, Univalent Foundations and General Thoughts", Chapter II "What are Homotopy Type Theory and the Univalent Foundations?".
Keywords: Univalent Foundations, Univalence Axiom, Homotopy Type Theory, UniMath, architecture, formalization of mathematics, proof assistant.
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics > Proof
Specific Sciences > Computer Science
General Issues > Structure of Theories
Depositing User: Please delete this account
Date Deposited: 25 Sep 2018 17:55
Last Modified: 25 Sep 2018 17:55
Item ID: 15057
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics > Proof
Specific Sciences > Computer Science
General Issues > Structure of Theories
Date: 2018
URI: http://philsci-archive.pitt.edu/id/eprint/15057

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