ForCUTT
Financiado
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...
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.
ver más
Duración del proyecto: 65 meses
Fecha Inicio: 2022-05-19
Fecha Fin: 2027-10-31
Fecha Fin: 2027-10-31
Línea de financiación: concedida
El organismo HORIZON EUROPE notifico la concesión del proyecto el día 2022-05-19
Línea de financiación objetivo
El proyecto se financió a través de la siguiente ayuda:
ERC-2021-ADG:
ERC ADVANCED GRANTS
Cerrada
hace 3 años
Presupuesto
El presupuesto total del proyecto asciende a
2M€
Líder del proyecto
GOETEBORGS UNIVERSITET
No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico
TRL
4-5
Perfil tecnológico
TRL
4-5