IMC010: Type Theory and Coq



Please make sure that you are registered for this course in Blackboard, as it will be used to send email and administrate results.

Structure of the course

The course consists of five parts:

The basis

We use a course by Femke van Raamsdonk of the Free University Amsterdam. This will be taught by Freek using the following schedule:

5 septemberpropositional logic & simple type theorychapters 1 & 2
12 septemberpredicate logic & dependent typeschapters 4 & 6
19 septembersecond-order logic & polymorphismchapters 7 & 8
26 septemberinductive types & recursionchapter 3
3 octoberwrapping up Femke's coursechapters 5 & 9

The students will be expected to have studied the chapters listed, and the material will be discussed then. You are welcome to ask for help at any time if you have any questions, either by email or by walking into our offices.

The practical work in Coq corresponding to Femke's course will be done using the ProofWeb system on the machine Each participant will get a login to the course page on this machine, and will get his/her password by email.

The relevant links are:

Some metatheory

Next we will go through another (slightly more advanced) introduction to Type Theory. This will be taught by Herman, using the following schedule:

10 october
principal types and type checking
sections 4.1-4.3, 6.4
17 octoberChurch-Rosser propertysection 3.1exercises
24 october
normalization of λ→ and λ2
sections 4.4, 5.6

This overlaps with Femke's course, and therefore not all sections of the course notes will be discussed in the lectures in detail. (But you do have to know them for the test!)

The relevant links are:

Research topic

After the fall break the course will be taught by Robbert, Herman and Freek together. A research paper or chapter of a book will be studied, together with extra material needed to understand this. Each student will present part of this to the group.

This year the research paper will be on normalization by evaluation:

Before we get to this paper, we will study parts of:

The student presentations will be held during the first hour. The assigned part of the paper needs to be presented, and we recommend to explain everything as much as possible through examples. During the second hour, the teachers will go deeper into the material presented.

The current schedule for the presentations is:

28 november Oostdijk/Geuvers section 4 Rafael Alejandro Imamgiller
28 november Paulin-Mohring section 5.3 Timothy Fraser
5 december Grégoire/Mahboubi sections 2-3 Timmy Weerwag
5 december Grégoire/Leroy sections 2.1-2.2 Suzanne van den Bosch
12 december Grégoire/Leroy section 2.3 Rik de Kort
12 december Grégoire/Leroy section 3 Fenno Vermeij
19 december Boespflug/Dénès/Grégoire section 1 Maxime Klusman
19 december Boespflug/Dénès/Grégoire section 2 Gerco van Heerdt
9 january Gonthier before combinatorial hypermaps Jasper Piers

Individual Coq exercise

Each student will be doing a small Coq formalization assignment. This assignment will be chosen by the student from the following list of suggestions.

Final test

The test covers both the contents of the courses by Femke and Herman, as well as the contents of the research paper. The first test opportunity will be:

Some tests:

See the "paper exercises" above too, which are also exercises from old tests.


Each participant will get three grades: one for the presentation in the second half of the course, one for the individual Coq exercise, and one for the test. The final grade will be the average of these three grades.

There will be no grade for the practical work for Femke's course in ProofWeb, but this work will need to be finished to be allowed to pass the course.

Some supporting material