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INRIA

French Institute for Research in Computer Science and Automation
Country: France
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473 Projects, page 1 of 95
  • Funder: EC Project Code: 226513
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  • Funder: EC Project Code: 329576
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  • Funder: EC Project Code: 239993
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  • Funder: EC Project Code: 101001995
    Overall Budget: 1,999,930 EURFunder Contribution: 1,999,930 EUR

    The use of computers for formulating conjectures, but also for substantiating proof steps, pervades mathematics, even in its most abstract fields. Most computer proofs are produced by symbolic computations, using computer algebra systems. Sadly, these systems suffer from severe, intrinsic flaws, key to their amazing efficiency, but preventing any flavor of post-hoc verification. But can computer algebra become reliable while remaining fast? Bringing a positive answer to this question represents an outstanding scientific challenge per se, which this project aims at solving. Our starting point is that interactive theorem provers are the best tools for representing mathematics in silico. But we intend to disrupt their architecture, shaped by decades of applications in computer science, so as to dramatically enrich their programming features, while remaining compatible with their logical foundations. We will then design a novel generation of mathematical software, based on the firm grounds of modern programming language theory. This environment will feature a new, high-level, performance-oriented programming language, devised for writing efficient and correct code easily, and for serving the frontline of research in computational mathematics. Users will have access to fast implementations, and to powerful proving technologies for verifying any component à la carte, with high productivity. Logic- and computer-based formal proofs will prevent run-time errors, and incorrect mathematical semantics. We will maintain a close, continuous collaboration with interested high-profile mathematicians, on the verification of cutting-edge research results, today beyond the reach of formal proofs. We ambition to empower mathematical journals to install high-quality artifact evaluation, when peer-reviewing falls short of assessing computer proofs. This project will eventually impact the use of formal methods in engineering, in areas like cryptography or signal-processing.

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  • Funder: EC Project Code: 825492
    Overall Budget: 149,533 EURFunder Contribution: 149,533 EUR

    Spreadsheet applications (such as Microsoft Excel + VBA) are heavily used in a wide range of fields including engineering, finance, management, statistics and health. However, they do not ensure robustness properties, thus spreadsheet errors are hard to avoid, common and potentially very costly. According to estimates, the annual cost of spreadsheet errors is around 7 billion dollars. For instance, in 2013, a series of basic spreadsheet errors at JPMorgan incurred 6 billion dollars trading losses. To avoid such problems, spreadsheet users need better support from rigorous tools, since the development of industrial spreadsheets typically involves multiple tabs, formulas, macros and data read from external sources (e.g., the internet). However, as of today, spreadsheet environment offer almost no verification support, and third party tools do not allow to reason correctly over macros, and future uses of existing formulas. The MemCAD ERC StG project opened the way to novel formal analysis techniques for spreadsheet applications. Indeed, the MemCAD project led to the design of powerful abstraction techniques to reason over complex data-structures such as tables as found in spreadsheets. During this project, we have implemented AiXL, a prototype that was able to analyze large public benchmarks. It uncovered defects that are beyond the scope of other approaches. We propose to leverage these results into a toolbox able to safely verify, optimize and maintain spreadsheets, so as to reduce the likelihood of errors. The envisioned toolbox relies on automatic and conservative semantic static analysis, so that it will report all occurrences of certain classes of errors. It will have an open architecture with plugins, and will easily extend to user specific properties. This works will take place in a partnership with MatrixLEAD, a startup created based on the results of the ERC MemCAD project. MatrixLEAD will provide industrial use-cases and commercialization plans.

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