Introduction to Functional Programming (dIFP)

Q1 2015-2016, Tuesday 14:00-17:00, Location: ny184 (5335-184).
Bring your computer

Teacher

Robbert Krebbers
Email: robbert AT cs DOT au DOT dk
Office: Turing 213

Teaching assistants

Kristoffer Just Andersen
Email: kja AT cs DOT au DOT dk
Office: Turing 217

Kent Grigo
Email: kentg AT cs DOT au DOT dk
Office: Turing 214

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.

Course material

Coq 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.

We will be using part of the online textbook Software Foundations by Benjamin C. Pierce et al. It is freely available on the web.

Homework

The course includes a track of weekly mandatory exercises. The exercises should be handed in each Friday before 23:59 following the lecture.

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.

The homework will be graded on the scale [inadequate, fair, good]. We will give comments following the grading rules for the term project as listed below. You are not allowed to use Coq tactics in the homework that we have not yet discussed (for example tauto, eauto and omega are forbidden).

Coq project

The course finishes with a Coq project, a list of suggestions can be found 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 teacher.

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

Registration to the final project by sending an email to the teacher with the choice of the project. This deliverable is due on 9 October.
A set of Coq .v files containing the solution to your project and a corresponding written report. This deliverable is due on 21 October.

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

Name and student number.
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.
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.
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

The grade of the course is computed as follows:

([grade of the Coq project] + [grade of the oral exam]) / 2.

Both grades have to be at least 02 (adequate).

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:

Correctness: whether the Coq definitions and lemmas correctly model the problem.
Completeness: whether all lemmas are proven (e.g. no lemmas omitted and proofs finished with admit or Admitted).
Style: whether the Coq code follows the style guidelines (e.g. use of Case tactic, sensible variable names and use of implicit arguments).
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).
Report: style, presentation, language and correctness of the report.

During the oral exam we will test whether you are able to create a small extension of the project, ask you to explain proofs of the project in an informal way, query you about the contents of your report, and ask general questions about the contents of the course.

Preliminary schedule

Date	Topics	Course material and homework
25 August	Installing Coq Basic inductive types Proving using computation Rewriting	Preface and Basics Optional: `andb_eq_orb`, `binary` and `decreasing`
1 September	Induction on natural numbers Proofs within proofs Formal vs. informal proofs	Induction Optional: `evenb_n__oddb_Sn`, `plus_swap'`, `binary_commute` and `binary_inverse`
8 September	More inductive types (products, lists and options) Induction on lists Polymorphic inductive types	Lists and Poly (Section 'Polymorphism') Optional: `bag_count_sum`, `dictionary_invariant1` and `dictionary_invariant2`
15 September	Higher-order functions Partial application and currying Anonymous functions Additional Coq tactics (apply, symmetry and inversion) Varying the induction hypothesis	Poly and MoreCoq Optional: `church_numerals`
22 September	Curry Howard correspondence Propositional logic Inductively defined propositions Induction over evidence Inversion over evidence Existential quantification	Logic and Prop (up to, but not including 'Relations') Optional: constructive logic, additional exercises and `palindrome_converse`
29 September	Semantics as a function Optimization Coq automation Semantics as a relation State	Imp (we are using a modified version, which can be obtained here) Optional: `optimizer`, `no_whiles_terminating` and additional exercises
6 October	Introduction of the Coq projects Recap	Coq projects Choose a Coq project
9 October	Registration Coq project due before 23:59
13 October	Question session Coq project
21 October	Coq project due before 23:59
26-28 October	Oral exams

Prerequisites

The first-year course on programming languages in general and its lecture notes in particular.