Descripción del proyecto
Los avances del asistente de pruebas podrían aumentar la fiabilidad del álgebra computacional
El uso de ordenadores para formular conjeturas y consolidar los pasos de las pruebas impregna todos los campos de las matemáticas, incluso los más abstractos. La mayoría de las pruebas asistidas por ordenador se realizan mediante cálculos simbólicos utilizando sistemas de álgebra computacional. Sin embargo, estos sistemas adolecen de graves defectos intrínsecos, por lo que la corrección y la verificación computacional suponen un reto. El proyecto FRESCO, financiado con fondos europeos, pretende aclarar si el álgebra computacional puede ser fiable y, al mismo tiempo, rápida. Sus investigadores alterarán la arquitectura de los asistentes de pruebas, que son las mejores herramientas para representar las matemáticas «in silico», gracias a lo cual se enriquecerán sus características de programación al tiempo que preservan la compatibilidad con sus fundamentos lógicos. También diseñarán un novedoso «software» matemático que deberá contar con un entorno de programación de alto nivel orientado al rendimiento para escribir un código eficaz que impulse la matemática computacional.
Objetivo
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.
Ámbito científico
Programa(s)
Régimen de financiación
ERC-COG - Consolidator GrantInstitución de acogida
78153 Le Chesnay Cedex
Francia