August 19 – 24 , 2018, Dagstuhl Seminar 18341

Formalization of Mathematics in Type Theory


Andrej Bauer (University of Ljubljana, SI)
Martín H. Escardó (University of Birmingham, GB)
Peter L. Lumsdaine (University of Stockholm, SE)
Assia Mahboubi (INRIA – Nantes, FR)

For support, please contact

Annette Beyer for administrative matters

Shida Kunz for scientific matters

Dagstuhl Reports

As part of the mandatory documentation, participants are asked to submit their talk abstracts, working group results, etc. for publication in our series Dagstuhl Reports via the Dagstuhl Reports Submission System.


List of Participants
Shared Documents
Dagstuhl Seminar Wiki
Dagstuhl Seminar Schedule (Upload here)

(Use seminar number and access code to log in)


Formalized mathematics is mathematical knowledge (definitions, theorems, and proofs) represented in digital form suitable for computer processing. A formalized theorem has a very high correctness guarantee, as its proof is mechanically checked in complete detail. The formalized mathematics community has been growing steadily, with several research groups having recently completed major n goals, each using slightly different approaches and software tools. The complexity and the structure of these efforts resemble those of large software projects. Indeed, the recent successes in formalization can in part be attributed to adoption of software engineering practices and tools for software development.

But formalized mathematics is much more than proof-checking: it can help with verification of large scale computations, discovery of new constructions and proofs, organization of mathematical knowledge, and cooperation between mathematicians that surpasses current practice. The central goal of this seminar is to identify the theoretical advances and practical improvements needed in the area of formalized mathematics, in order to make it a mature technology, truly useful to a larger community of students and researchers in mathematics.

This Dagstuhl Seminar will be a place for sharing ideas, tools, techniques, and the needs of those who formalize mathematics, or want to learn about it. It will bring together the developers of proof assistants, the experts on formalization, and the mathematicians interested in formalization. We will focus not only on bare formalization in proof assistants, but also on tools for mathematical exploration, such as symbolic computation, use of heuristics, and machine learning, as well as interfaces between them and the proof assistants.

Our program will offer tutorials and a limited number of talks. We will leave ample time for work and discussions in smaller groups. The participants will informally report their ideas and findings in a spur-of-the-moment fashion.

  Creative Commons BY 3.0 DE
  Andrej Bauer, Martín H. Escardó, Peter L. Lumsdaine, and Assia Mahboubi


  • Semantics / Formal Methods
  • Verification / Logic


  • Formalized mathematics
  • Type theory
  • Proof assistant
  • Formal methods

Book exhibition

Books from the participants of the current Seminar 

Book exhibition in the library, ground floor, during the seminar week.


In the series Dagstuhl Reports each Dagstuhl Seminar and Dagstuhl Perspectives Workshop is documented. The seminar organizers, in cooperation with the collector, prepare a report that includes contributions from the participants' talks together with a summary of the seminar.


Download overview leaflet (PDF).


Furthermore, a comprehensive peer-reviewed collection of research papers can be published in the series Dagstuhl Follow-Ups.

Dagstuhl's Impact

Please inform us when a publication was published as a result from your seminar. These publications are listed in the category Dagstuhl's Impact and are presented on a special shelf on the ground floor of the library.

NSF young researcher support