Project description
An easy to understand language for formal verification
Mathematics and computer science rely on formal verification to ensure the accuracy of reasoning and the safety of critical software. Recent advances, such as the formalisation of the four-colour theorem and verified components in Google’s Chrome browser, have showcased the power of proof assistants. These tools are built on the language of type theory. Despite its success in academia, Homotopy Type Theory (HoTT) has not seen widespread adoption due to its complex syntax and conceptual challenges. With this in mind, the ERC-funded HOTT project aims to develop a new type theory where homotopical content emerges naturally, simplifying the process. By defining equality types through computation, this project will make formalisation more accessible, accelerating progress in mathematics and software verification.
Objective
Recent advancements have enabled proof asistants to formally verify world-class mathematics: the liquid tensor experiment, the four colour theorem and the odd order theorem were formalised. Computer checked arguments are important for mathematicians who want to be certain their reasoning is sound, and for computer scientists to prevent bugs in safety critical software. Examples are formally verified parts of Google's Chrome web browser and verified implementations of the C and ML programming languages.
At the core of these formalisations lies type theory, upon which proof assistants are built. Type theory is both a functional programming language and a foundation of mathematics. Recently, models of type theory built on higher dimensional spaces emerged, where elements of a type are points in the space, and elements of an equality type are paths in the space. Based one these, type theory was extended to homotopy type theory (HoTT), featuring the principle that isomorphic types are equal. This moves formalisation close to actual mathematical practice where isomorphic structures are being treated as the same.
While HoTT is successful among academics, it hasn't been widely adopted. This is because type theories implementing HoTT rely on an explicit syntax for higher dimensional geometry, which is conceptually difficult and hard to use in practice. This creates a substantial barrier for formalisation, which is treated as a low-level, bureaucractic process.
Our project will develop a radically new type theory where homotopical content is emergent, rather than built-in. The idea is to define the equality type via computation. This makes HoTT explainable and conceptually simple. It also improves pragmatic aspects: with more computation, proofs become less tedious. Our theory will contribute to a new era in formalisation of mathematics and verification of software, where developing proofs in abstract, reusable ways becomes standard, accelerating progress in both areas.
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 human-validated.
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 human-validated.
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)
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.
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
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.
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.
HORIZON-ERC - HORIZON ERC Grants
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2024-COG
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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.
1053 BUDAPEST
Hungary
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.