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Formalisation of Constructive Univalent Type Theory

There has been in the past 15 years remarkable achievements in the field of interactive theorem proving, both for checking complex software and checking non trivial mathematical proofs. For software correctness, X. Leroy (INRIA a... ver más

31/10/2027

UGOT - GOETEBORGS...

2M€

Presupuesto del proyecto: 2M€

Líder del proyecto

GOETEBORGS UNIVERSITET No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

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Financiación concedida El organismo HORIZON EUROPE notifico la concesión del proyecto el día 2022-05-19

ERC-2021-ADG: ERC ADVANCED GRANTS Scope:Objectives

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Cerrada hace 3 años

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1 Participantes

UGOT - GOETEBORGS UNIVERSITE...

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Duración del proyecto: 65 meses Fecha Inicio: 2022-05-19
Fecha Fin: 2027-10-31

Líder del proyecto

GOETEBORGS UNIVERSITET No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 2M€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto There has been in the past 15 years remarkable achievements in the field of interactive theorem proving, both for checking complex software and checking non trivial mathematical proofs. For software correctness, X. Leroy (INRIA and College de France) has been leading since 2006 the CompCert project, with a fully verified C compiler. For mathematical proofs, these systems could handle complex arguments, such as the proof of the 4 color theorem or the formal proof of Feit-Thompson Theorem More recently, the Xena project, lead by K. Buzzard, is developing a large library of mathematical facts, and has been able to help the mathematician P. Scholze (field medalist 2018) to check a highly non trivial proof. All these examples have been carried out in systems based on the formalism of dependent type theory, and on early work of the PI. In parallel to these works, also around 15 years ago, a remarkable and unexpected correspondance was discovered between this formalism and the abstract study of homotopy theory and higher categorical structures. A special year 2012-2013 at the Institute of Advance Study (Princeton) was organised by the late V. Voevodsky (field medalist 2002, Princeton), S. Awodey (CMU) and the PI. Preliminary results indicate that this research direction is productive, both for the understanding of dependent type systems and higher category theory, and suggest several crucial open questions. The objective of this proposal is to analyse these questions, with the ultimate goal of formulating a new way to look at mathematical objects and potentially a new foundation of mathematics. This could in turn be crucial for the design of future proof systems able to handle complex highly modular software systems and mathematical proofs.

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