IMC010: Type Theory and Coq


Structure of the course

The course consists of six parts:

1. Lectures on the type theory of Coq

Freek will use the first five weeks to teach part of:

using the schedule:

6 Septemberintroduction & lambda calculus
13 Septemberpropositional logic & simple typeschapters 1 & 2
20 Septemberpredicate logic & dependent typeschapters 4 & 6
27 Septemberinductive types & inductive predicateschapter 3
4 Octobersecond-order logic & polymorphic typeschapters 7 & 8

2. Coq practicum

There will be a Coq practicum corresponding to Femke's course notes. For this you need to install Coq and download a

The completed files need to be handed in in Brightspace. Finishing this practicum is obligatory to be able to pass the course, but there will not be a grade for it.

3. Lectures on some metatheory

Then Herman will use the next three weeks to teach part of:

using the schedule:

11 Octoberprincipal types & type checkingsections 4.1-4.3, 6.4
slides, exercises, answers
18 OctoberChurch-Rosser propertysection 3.1
slides, exercises, answers
8 Novembernormalization of λ→ and λ2sections 4.4, 5.6
slides, exercises, answers

This concludes the first half of the course.

4. Exam

The exam will not be at the end of the course but halfway through. Therefore the subject of the exam will be just the lectures by Freek and Herman, and not the topic of the reading group.

The date of the exam will be:

16 Novembertwo hour exam on the theory in E 2.50 

See at the end of this web page for some material to practise for the exam, like old exams from last years.

5. Reading group with presentations

In the second half of the course we read papers about a specific topic related to a recent research publication (a different topic every year). The topic of this year will be cubical type theory.

The presentations are by the students in pairs. These presentations are 45 minutes, and should contain both examples, as well as the gist of the proofs in the paper. It is more important to explain the important points of the paper well, then to cover everything in full detail.

The book and papers for this year, together with the students that will present them, are:

So the schedule for the presentations is:

30 Novemberpath inductionAron Schöffer &
Tjitske Koster
equivalence, higher groupoidsGé Waayers &
Nick Hendriks
6 Decemberuniverses, univalenceNiels van der Weide
application of univalenceDaniël van Leijenhorst &
Finn van der Velde
7 Decemberh-levels, truncationNiek Terol &
Thomas Somers
examples of HITsDavid Läwen &
Jakob Wuhrer
13 Decemberpath typesBryan van de Ven &
Cas Visser
operations on pathsDaan Spijkers &
Samuel Klumpers
14 Decemberglue typesMika van Emmerloot &
Marten Straatsma
AgdaAlwyn Stiles &
Eef Uijen
20 DecemberCubical AgdaDante van Gemert &
Paul Tiemeijer
the paperAron van Hof &
Bram Pellen
21 Decemberstructure identity principleGerbrich Kroon &
Rutger Dinnissen
using the principleAlex van der Hulst &
Simcha van Collem

6. Coq project

Each student has to do a small Coq project. This project can be chosen from

but if students have a suggestion for an interesting project that they want to do, that is also allowed.

The deadline for the Coq project is 20 January 2023.


You will get three marks: for the exam, the Coq presentations, and the Coq project (items 4, 5 and 6 above). The final mark for the course is the average of those three marks, rounded to a half integral number. A mark of 5.5 will be rounded up to 6, and the mark for the exam has to be at least 5.0.

Some supporting material

Supporting documents

Paper exercises

Old exams

Some slides