Project description
A novel way to view mathematical objects could support improved Interactive theorem proving
While automated proving of mathematical theorems might seem untenable to non-mathematicians, great progress has been made in the fields of mathematics and computer science, bringing us relatively close. Interactive theorem proving refers to the process of a human and computer working together to produce a formal proof. It is also used to check for the correctness of software. The EU-funded ForCUTT project is planning to develop a new way of looking at mathematical objects that could underlie the design of future proof systems. It would expand opportunities to address highly modular and complex mathematical proofs and software systems.
Objective
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.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
This project's classification has been validated by the project's team.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
This project's classification has been validated by the project's team.
Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.1 - European Research Council (ERC)
MAIN PROGRAMME
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Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
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Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
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Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2021-ADG
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
405 30 Goeteborg
Sweden
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