IMC010: Type Theory and Coq

A colorful subject!




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 four parts:

The basis

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

9 septemberpropositional logic & simple type theorychapters 1 & 2
16 septemberpredicate logic & dependent typeschapters 4 & 6
23 septemberinductive types & recursionchapter 3
30 septemberinductive predicates & inversionchapter 3 (continued)
7 octoberprogram extractionchapter 5
14 octobersecond-order logic & polymorphismchapters 7 & 8
21 octoberinhabitation & summary of the coursechapter 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.

Advanced topic

The second half of the course will be taught by Herman Geuvers and Robbert Krebbers. A research paper will be studied, together with extra material needed to understand this research paper. Each student will present part of this to the group.

This year the research paper will be:

The presentations will be held during the first hour, 10.45-11.30. The sections of the paper needs to be presented, and a relevant example worked out (a proof term for a proof, a reduction of a term, etc.) During the second hour, 11.45-12.30, the teachers will go deeper into the material presented.

The current schedule for the presentations is:

11 novembersection 11.15 of the Scheme reportBoy Boshoven
(see also Sussman & Steele and Reynolds)
18 novembersection 2 of Sabry & FelleisenWouter Smeenk
25 novembersection 3 of Sabry & FelleisenFabio Zanasi
(see also types in the CPS transform)
2 decembersections 2, 3 & 6 of GriffinTessa Matser
9 decembersections 1, 2 & 3 of Krebbers (see also Parigot)Abel Planting
13 decembersection 2 of Ariola & HerbelinMatus Tejiscak
16 decembersections 3 & 4 of Ariola & Herbelin(Robbert)
20 decemberintro & section 1 of HerbelinBas Westerbaan
(see also a older version of the same paper)
23 decembersection 2 of HerbelinBram Westerbaan

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 course by Femke as well as the contents of the research paper taught by Herman and Robbert. The test will be

Some tests:

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


Each participant will get three grades: one for the presentation in the second part of the course, one for the Coq work, 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.