19. – 24. August 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)

Auskunft zu diesem Dagstuhl-Seminar erteilt

Dagstuhl Service Team


Dagstuhl Report, Volume 8, Issue 8 Dagstuhl Report
Gemeinsame Dokumente


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


Bücher der Teilnehmer 

Buchausstellung im Erdgeschoss der Bibliothek

(nur in der Veranstaltungswoche).


In der Reihe Dagstuhl Reports werden alle Dagstuhl-Seminare und Dagstuhl-Perspektiven-Workshops dokumentiert. Die Organisatoren stellen zusammen mit dem Collector des Seminars einen Bericht zusammen, der die Beiträge der Autoren zusammenfasst und um eine Zusammenfassung ergänzt.


Download Übersichtsflyer (PDF).


Es besteht weiterhin die Möglichkeit, eine umfassende Kollektion begutachteter Arbeiten in der Reihe Dagstuhl Follow-Ups zu publizieren.

Dagstuhl's Impact

Bitte informieren Sie uns, wenn eine Veröffentlichung ausgehend von
Ihrem Seminar entsteht. Derartige Veröffentlichungen werden von uns in der Rubrik Dagstuhl's Impact separat aufgelistet  und im Erdgeschoss der Bibliothek präsentiert.