Inria project-team


Research themes

The Picube team is a joint project-team of INRIA, Université Paris-Cité and CNRS, within the IRIF's Proofs, Programs and Systems pole. It covers five main research themes:

  • the fundamental structures of logic and mathematical reasoning ;
  • differential and probabilistic tools for programming, reasoning and learning;
  • architecture and design of a proof assistant for mathematicians;
  • formalization and linguistics of mathematics;
  • higher-dimensional algebra and homotopic type theory.

The Picube team wishes to take advantage of recent advances in the fields of:

  • type theory and the foundations of mathematics: homotopic type theory, realizability and forcing, differential linear logic,
  • semantics of programming languages: computational effects, differential and probabilistic programming,
  • architecture and design of proof assistants: mathematical formalization, unification and symbolic elaboration techniques.

in order to reduce the gap between the vernacular language currently used by mathematicians in their daily practice and the formal language used today in proof assistants such as Coq, Agda or Lean. The research project builds on the knowledge and expertise accumulated in the Pi.R2 team and integrates new ingredients in the direction of certified mathematics, differential and probabilistic programming and learning, with a view to tackling the above themes.

Team seminar

Permanent members


Members outside of IRIF

Name@PhoneOfficePositionLocationTeam
Marino Diana @ 01 80 49 40 39 A218 Team assistant CRI Paris picube
Mathurin Anne @ 01 80 49 40 37 A118 Team assistant CRI Paris picube


Non-permanent members


Permanent members

Name@PhoneOfficePositionPoleTeam
Baudart Guillaume @ 4026 Research Scientist - INRIA ISFP PPS picube , preuves , programmes
Curien Pierre-Louis @ 01 57 27 92 23 3013 Senior Research Scientist Emeritus - CNRS PPS picube , algebre , preuves
Ehrhard Thomas @ 01 57 27 92 17 4014a Senior Research Scientist - CNRS PPS algebre , programmes , preuves , picube
Herbelin Hugo @ 01 57 27 90 87 3029 Senior Research Scientist - INRIA PPS algebre , picube , preuves , programmes
Letouzey Pierre @ 01 57 27 93 37 3040 Associate Professor PPS picube , programmes , preuves
Lévy Jean-Jacques @ 01 57 27 92 68 4032 Senior Research Scientist Emeritus - INRIA PPS preuves , picube , programmes
Melliès Paul-André @ 01 57 27 92 48 3023 Senior Research Scientist - CNRS ASV , PPS automates , algebre , preuves , picube
Petrisan Daniela @ 01 57 27 94 00 4016 Associate Professor ASV , PPS automates , algebre , picube
Saurin Alexis @ 01 57 27 93 37 3040 Research Scientist - CNRS PPS algebre , programmes , preuves , picube
Scherer Gabriel @ 4032 Research Scientist - INRIA PPS algebre , programmes , preuves , picube


Non-permanent members