Functional Programming

Bring your computer

Teacher

Bas Spitters

Contact

We will be using the discussion board on Blackboard for general discussions about the exercises, projects, and Coq. Your posts are anonymized, so do not feel hesitant against using it.

Links

• Coq
• Software Foundations

Course material

During this course we will be using the Coq proof assistant. Coq is both a functional programming language, as well as a system that allows one to reason using formal proofs about one's programs. Information on installing Coq is available here. I recommend a recent version of Coq (8.12). The Windows installer is available here. Alternatives are here. There is also the experimental Coq Platform. Choose an IDE. I recommend vscode or emacs.
One can read logical foundations in the browser and use jscoq for collaborative editing. This is still experimental though.

We will be using part of the online textbook Software Foundations by Benjamin C. Pierce et al.

Homework

The course includes a track of weekly exercises. Submission and approval of 10 mandatory assignments is required. Five assignments from the first seven weeks and five from the second.
Work in groups of two (maximally three) is encouraged. The exercises should be handed in each Friday following the TA session before 10:00.

Coq should accept the homework handed in as a .v file in its entirety. The exercise will not be graded if Coq does not accept the file. Use Admitted to make Coq accept incomplete proofs.

Preliminary schedule

Coq project

The course finishes with a Coq project, a list of suggestions can be found here and here. You may also invent a Coq project yourself or do a variation or extension of one of our suggested projects. If you invent a project yourself or use a variation of the suggestions, you have to discuss it with the lecturer.

You are allowed to work in groups. You may also write the report together. However, you are fully responsible for the code and the report. The oral exam will test your understanding.

In order to complete the Coq project, you have to make the following deliverables:

• Register the choice of your final project on blackboard. This deliverable is due on Fri 6 November 2020. Make sure you have discussed your choice before that time with the lecturer. Especially, when you are proposing a project of your own design.
• A set of Coq .v files containing the solution to your project and a corresponding written report. This deliverable is due on Fri 11 Dec 2020.

The written report has to be 5 to 10 pages, should be in academic style, and should include:

1. Name and student number.
2. A small introduction with at least a description of the project you have chosen. You should not just copy the description from the projects file.
3. A description of the problems you have encountered during the project and how you have solved these. If you had multiple solutions in mind, describe these, and explain why you have picked the one you have used.
4. A conclusion with at least your experience using Coq: what did you like and what you did not like.

You should not include unnecessarily long excerpts of Coq code, just use small fragments to illustrate a point. Informal proofs should be formulated in the way taught during the course. Do not paraphrase Coq proofs in natural language by writing: and now we apply tactic X so our goals becomes Y.

Grading

Grade reflects an overall assessment of:

• group project
• individual oral examination

Only students with approved exercises can attend the oral exam and thus pass the course.

The grade of the Coq project is based on the following items:

1. Correctness: whether the Coq definitions and lemmas correctly model the problem.
2. Completeness: whether all lemmas are proven (e.g. no lemmas omitted and proofs finished with admit or Admitted).
3. Style: whether the Coq code follows the style guidelines (e.g. use of Case tactic, sensible variable names and use of implicit arguments).
4. Effectiveness: whether the definitions and proofs are given in an effective way (e.g. no useless proof steps and the induction tactic not used blindly).
5. Report: style, presentation, language and correctness of the report.

During the oral exam we will test your understanding of the project. E.g. by asking you to create a small extension of the project, to explain proofs of the project in an informal way, to query you about the contents of your report, or ask general questions about the contents of the course.
Bring your laptop!