Description du projet
Les progrès de l’assistant de preuve pourraient augmenter la fiabilité du calcul formel
L’utilisation d’ordinateurs pour formuler des conjectures et consolider les étapes de preuve imprègne tous les domaines mathématiques, même les plus abstraits. La plupart des preuves informatiques sont produites par des calculs symboliques, en utilisant des systèmes de calcul formel. Ces systèmes souffrent toutefois de graves défauts intrinsèques, ce qui complexifie la correction et la vérification informatiques. Le projet FRESCO, financé par l’UE, entend déterminer si le calcul formel peut être à la fois fiable et rapide. Les chercheurs bouleverseront l’architecture des assistants de preuve, soit les meilleurs outils de représentation des mathématiques in silico, enrichissant leurs fonctionnalités de programmation tout en préservant leur compatibilité avec leurs fondements logiques. Ils concevront également un nouveau logiciel mathématique qui devrait comporter un environnement de programmation de haut niveau axé sur les performances pour écrire du code efficace afin de stimuler les mathématiques computationnelles.
Objectif
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.
Champ scientifique
Programme(s)
Régime de financement
ERC-COG - Consolidator GrantInstitution d’accueil
78153 Le Chesnay Cedex
France