Objectif Proof assistants are increasingly used to verify hardware and software and to formalize mathematics. However, despite the success stories, they remain very laborious to use. The situation has improved with the integration of first-order automatic theorem provers -- superposition provers and SMT (satisfiability modulo theories) solvers -- through middleware such as Sledgehammer for Isabelle, codeveloped by the PI; but this research has now reached the point of diminishing returns. Only so much can be done when viewing automatic provers as black boxes.To make interactive verification more cost-effective, we propose to deliver very high levels of automation to users of proof assistants by fusing and extending two lines of research: automatic and interactive theorem proving. This is our grand challenge. Our starting point is that first-order automatic provers are the best tools available for performing most of the logical work. Our approach will be to enrich superposition and SMT with higher-order reasoning in a careful manner, to preserve their desirable properties. We will design proof rules and strategies, guided by representative benchmarks from interactive verification.With higher-order superposition and higher-order SMT in place, we will develop highly automatic provers building on modern superposition provers and SMT solvers, following a novel stratified architecture. To reach end users, these new provers will be integrated in proof assistants, including Coq, Isabelle, and the TLA+ Proof System, and will be available as backends to more specialized verification tools. The users of proof assistants and similar tools stand to experience substantial productivity gains: In the past five years, the success rate of automatic provers on interactive proof obligations from a representative benchmark suite has risen from 47% to 77%; with this project, we aim at 90%--95% proof automation. Champ scientifique natural sciencescomputer and information sciencessoftwaresocial sciencessociologyindustrial relationsautomationsocial scienceseconomics and businesseconomicsproduction economicsproductivitynatural sciencesmathematics Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Thème(s) ERC-2016-STG - ERC Starting Grant Appel à propositions ERC-2016-STG Voir d’autres projets de cet appel Régime de financement ERC-STG - Starting Grant Institution d’accueil STICHTING VU Contribution nette de l'UE € 994 688,00 Adresse DE BOELELAAN 1105 1081 HV Amsterdam Pays-Bas Voir sur la carte Région West-Nederland Noord-Holland Groot-Amsterdam Type d’activité Higher or Secondary Education Establishments Liens Contacter l’organisation Opens in new window Site web Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 994 688,00 Bénéficiaires (3) Trier par ordre alphabétique Trier par contribution nette de l'UE Tout développer Tout réduire STICHTING VU Pays-Bas Contribution nette de l'UE € 994 688,00 Adresse DE BOELELAAN 1105 1081 HV Amsterdam Voir sur la carte Région West-Nederland Noord-Holland Groot-Amsterdam Type d’activité Higher or Secondary Education Establishments Liens Contacter l’organisation Opens in new window Site web Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 994 688,00 INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE France Contribution nette de l'UE € 428 750,00 Adresse DOMAINE DE VOLUCEAU ROCQUENCOURT 78153 Le Chesnay Cedex Voir sur la carte Région Ile-de-France Ile-de-France Yvelines Type d’activité Research Organisations Liens Contacter l’organisation Opens in new window Site web Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 503 750,00 Tiers Entité juridique autre qu’un sous-traitant qui est affiliée ou juridiquement liée à un participant. L’entité réalise des travaux dans les conditions prévues par la convention de subvention, fournit des biens ou des services pour l’action, mais n’a pas signé la convention de subvention. Le tiers respecte les règles applicables au participant qui lui est lié dans le cadre de la convention de subvention en ce qui concerne l’éligibilité des coûts et le contrôle des dépenses. UNIVERSITE DE LORRAINE Participation terminée France Contribution nette de l'UE € 75 000,00 Adresse COURS LEOPOLD 34 54052 Nancy Cedex Voir sur la carte Région Grand Est Lorraine Meurthe-et-Moselle Type d’activité Higher or Secondary Education Establishments Liens Contacter l’organisation Opens in new window Site web Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 75 000,00