2023-05929 - Termination of proofs in the lambda-pi calculus modulo theory
Level of qualifications required : Master's or equivalent
Fonction : Internship Research
About the research centre or Inria departmentThe Inria Saclay-Île-de-France Research Centre was established in 2008. It has developed as part of the Saclay site in partnership with Paris-Saclay University and with the Institut Polytechnique de Paris .
The centre has 34 project teams , 27 of which operate jointly with Paris- Saclay University (15 teams) and the Institut Polytechnique de Paris (12 teams). Its activities occupy over 600 people, scientists and research and innovation support staff, including 44 different nationalities.
The centre also hosts the Institut DATAIA , dedicated to data sciences and their disciplinary and application interfaces.
AssignmentLa vérification formelle de preuves est de plus en plus utilisée, que ce soit pour vérifier des résultats mathématiques compliqués ou pour garantir la sûreté des logiciels critiques. Néanmoins, chaque système de preuve utilise une théorie qui lui est propre, ce qui limite les possibilités d'interopérabilité et de conservation des preuves. L'équipe Deducteam développe un langage formel universel, appelé lambda-pi calcul modulo théorie, dans lequel il est possible de définir une théorie et d'y exprimer des démonstrations. Son système de vérification associé est Dedukti. Deduki ouvre la possibilité de traduire une preuve d'une théorie dans une autre.
L'objectif de ce stage de recherche est de prouver la terminaison des termes de preuves dans le lambda-pi calcul modulo théorie, pour une théorie particulière. La terminaison des termes de preuves, équivalente à un théorème d'élimination des coupures, possède de nombreux corollaires, comme les propriétés de disjonction et du témoin pour les preuves constructives.
Ce stage s'inscrit dans le cadre du projet de parcours recherche de CentraleSupélec, centré autour de la définition de la théorie des ensembles dans le lambda-pi calcul modulo théorie et de son implémentation en Dedukti. La terminaison des termes de preuves permettra de prouver un théorème d'élimination des coupures pour cette implémentation.
Main activitiesMain activities (5 maximum) : Research
Additional activities (3 maximum) :
Examples of activities:
Inria is the French national research institute dedicated to digital science and technology. It employs 2,600 people. Its 200 agile project teams, generally run jointly with academic partners, include more than 3,500 scientists and engineers working to meet the challenges of digital technology, often at the interface with other disciplines. The Institute also employs numerous talents in over forty different professions. 900 research support staff contribute to the preparation and development of scientific and entrepreneurial projects that have a worldwide impact.
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