Section: Partnerships and Cooperations

European Initiatives

• Program: ERC.

• Project acronym: Matryoshka.

• Duration: April 2017 – March 2022.

• Coordinator: Jasmin Blanchette (VU Amsterdam).

• Participants: Daniel El Oraoui, Mathias Fleury, Pascal Fontaine, Hans-Jörg Schurr, Sophie Tourret, Uwe Waldmann.

• Abstract: Proof assistants are increasingly used to verify hardware and software and to formalize mathematics. However, despite some 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 – but only so much can be done when viewing automatic provers as black boxes. We propose to deliver much higher levels of automation to users of proof assistants by fusing and extending two lines of research: automatic and interactive theorem proving. Our approach will be to enrich superposition and SMT with higher-order (HO) reasoning in a careful manner, in order to preserve their desirable properties. 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, and integrate them in proof assistants. Users stand to experience substantial productivity gains: From 2010 to 2016, the success rate of automatic provers on interactive proof obligations from a representative benchmark suite called Judgment Day has risen from 47% to 77%; with this project, we aim at 90%–95% proof automation.

• More information: http://matryoshka.gforge.inria.fr/.

• Program: FET Open CSA.

• Project acronym: SC${}^2$.

• Project title: Symbolic Computation and Satisfiability Checking.

• Duration: July 2016 – August 2018.

• Coordinator: James Davenport (U. of Bath, UK).

• Other partners: see http://www.sc-square.org/CSA/welcome.html.

• Participants: Pascal Fontaine, Thomas Sturm.

• Abstract: The use of advanced methods for solving practical and industrially relevant problems by computers has a long history. Whereas Symbolic Computation is concerned with the algorithmic determination of exact solutions to complex mathematical problems, more recent developments in the area of Satisfiability Checking tackle similar problems but with different algorithmic and technological solutions. Before the project, the two communities were largely disjoint and unaware of the achievements of each other, despite strong reasons for them to discuss and collaborate. Researchers from the two communities rarely interacted, and also their tools lacked common, mutual interfaces for unifiying their strengths. The SC${}^2$ project initiated a wide range of activities to bring the two communities together, identify common challenges, offer global events and bilateral visits, propose standards, and so on. Now that the project is finished, we believe that these activities will continue to foster cross-fertilization of both fields and bring mutual improvements to the techniques and the software tools developed by both communities.

• Program: Erasmus+.

• Project acronym: PIAF.

• Project title: Pensée Informatique et Algorithmique au Fondamental / Computational Thinking in and Algorithmic in Primary Education.

• Coordinator: Université de Liège.

• Other partners: Université du Luxembourg, Saarland University, ESPE Nancy.

• Participant: Marie Duflot-Kremer.

• Abstract: The goal of the PIAF project is threefold: creating a repository of skills related to computational and algorithmic thinking, designing activities aiming at the acquisition of these skills, and evaluating the impact of these activities on primary school children and their computational thinking capacities.