http://www.dagstuhl.de/18341

### August 19 – 24 , 2018, Dagstuhl Seminar 18341

# Formalization of Mathematics in Type Theory

## Organizers

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

Andreas Dolzmann for scientific matters

## Motivation

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.

**License**

Creative Commons BY 3.0 DE

Andrej Bauer, Martín H. Escardó, Peter L. Lumsdaine, and Assia Mahboubi

## Classification

- Semantics / Formal Methods
- Verification / Logic

## Keywords

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