Proving with Computer Assistance 2IMF15
Teacher
Herman Geuvers: home page
Room number MF6.079A (only on Thursdays) For contact, use the email address herman at cs dot ru dot nl
Location and time
The course will be given live on
 Thursdays, 10:4512:45 in Atlas 1.822 (with exceptions, see below) and 13:3015:30 in Neuron 0.244 (with exceptions, see below)
Prerequisites
We assume that you are familiar with a bit of logic, especially natural deduction and preferably (untyped) lambda calculus.
 For those not familiar with untyped lambda calculus:
I will do a short recapitulation in hour 2 of the Lecture 1. Furthermore, read the selected pages of Introduction to Lambda Calculus of
Barendregt and Barendsen, Chapter 1, Chapter 4 pp. 2226, Chapter 2
pp. 1214 (read = as betaequality =_{\beta})
As exercises, please make 2.5  2.10.
Material
 On Type
Theory: Introduction
to Type Theory by Herman Geuvers, notes of a summer school course
given in Uruguay in 2008. The material of lectures 2, 3, 5, 6, 13 is
covered in the se notes.
 The
book Type
Theory and Formal Proof  An Introduction (Rob Nederpelt and
Herman Geuvers) has appeared in November 2014 with Cambridge
University Press. The course basically covers the material in the book
with a "hands on experience": using the proof assistant
Coq. The link
above gives background material. You
can order
the book with CUP, or via the teacher.
 On lambda calculus: Introduction to Lambda Calculus  selected pages by Barendregt and Barendsen. (This is a selection of pages from the full Introduction to Lambda Calculus.)
 The slides of the course, please find the pdfs below.
 On the Coq Proof Assistant: you may find one of the following useful:
System we will use
We will be using the Proof Assistant Coq in this course.
 You have to download and install Coq yourself.
 Throughout the course we will be showing a number of Coq files and
for some you will need to fill in the proofs yourself as an
exercise. Your assignment is a formalization in Coq.
 Here is the zip file
with all the Coq files about inductive types.
Some useful links
The course by week
The course will note be recorded, but recordings of the previous
year are provided on Canvas. This year's course will roughly be the
same schedule as last year.
This schedule may be subject to changes! Especially the slides and exercises may be slightly adapted as we go along the course.
 8/2, 10:4512:45 Lecture 1
Overview and Introduction: Proof Assistants,
Verification, Logic, Type Theory, Formulasastypes, Coq.
Short recapitulation of lambda calculus.
 8/2, 13:3015:30 Lecture 2
Simple Type theory and
"FormulasasTypes" for propositional logic.
 15/2, No Lecture because of Carnaval holiday.
 22/2 ( AUD 11), 10:4512:45 Lecture 3
Dependent Type Theory.
 22/2, 13:3015:30 Lecture 4
Natural Deduction in
Coq: proposition logic and predicate logic.
Be sure to have Coq installed on your laptop/computer
 Here is
a page
with a list of simple useful tactics
 Proposition Logic: Here is the file with the
proposition logic Coq exercises
of the lecture. Complete this at home and send it to the teacher
by mail by February 28.
 Here is the proposition_log file with
some answers filled in.
 Predicate logic: Here is a file with
the predicate logic Coq
exercises. Complete this (you can skip the "Challenge
problem") at home and send it to the teacher by mail by
February 28.
 Here is the pred_log file with
some answers filled in, also of
the "Challenge problem".
 29/2, 10:4512:45 Lecture 5
The Curry variant of Simple Type Theory:
principal type algorithm.
 29/2, 13:3015:30 Lecture 6
Polymorphic Types: ML style and full polymorphism
 7/3 ( AUD 11), 10:4512:45 Lecture 7
Higher order logic, Calculus of Constructions
 Here are the
slides
of the lecture.
 Make
the exercises.
 Here are some answers to the exercises.
 For some more handwritten answers to exercises showing how to find these terms and derivations, see Canvas.
 You can also make the exercises with Coq. Here is the Coq .v file.
 Here is a Coq .v file with answers.
 7/3, 13:3015:30 Lecture 8
Inductive Types.
 Here are
the
slides
 Here are three files that have been shown at the lecture and you
can load into Coq:
 Do the files coq_nat_03.v up to coq_nat_10.v from the zip file
(and coq_nat_11.v if you want a challenge) and send
your solutions to the teacher by mail by March 13.
Here is one worked out file:
 14/3, 10:4512:45 Lecture 9
More inductive types; Presentation
of the Coq assignment.
 Read slides on lists of
the
slides of last week on inductive types.
 Do the files on lists coq_list_03.v up to coq_list_06.v from the zip file and send your solution to the teacher by mail
by March 20.
 More list programming.

The Coq
file on head and tail of lists and the "option" type.
 Here are the example files, showing how to do the first exercises
on lists in
Coq:
coq_list_01.v
and
coq_list_02.v.
 Here is coq_list_06.v worked out, with some additional comments.
 Do the exercises on trees coq_tree_03.v up to coq_tree_05.v from the zip file and send your solution to the
teacher by mail by March 20.
 Here is an example file, showing how to do the first exercise on
trees in Coq. Look here for the htmized file and look here
for the Coq source file.
 Here is the presentation of the Coq assignment. Alternative suggestions for the Coq assignment can be found here .
 14/3, 13:3015:30 Lecture 10
Programming with inductive types and dependent inductive types; Examples of cool and useful Coq features.
 21/3, 10:4512:45 Lecture 11
Some metatheory of Type Systems (I): ChurchRosser property
 Here are the
slides
of the lecture.
 Here are the
exercises
for the lecture.
 Here are some answers to the exercises.
 21/3, 13:3015:30 Lecture 12
Work on Coq assignment
 Here is a page where an earlier
example assignment has been worked out. It has been created from
a coq .v file .
 We have used the "Proviola" system (by Carst Tankink) to produce this documented page.
 28/3, 10:4512:45 Lecture 13
Work on Coq assignment
 28/3, 13:3015:30 Lecture 14
Some metatheory of Type Systems (II): Normalization
 4/4, 10:4512:45 Lecture 15
Recap of all paper
exercises of previous lectures: here are
some extra
exercises relating to normalization and ChurchRosser. Possibility
to ask questions about the Coq assignment.
 For some handwritten answers
to these exercises, see Canvas.
 4/4 ( Neuron 0.264), 13:3015:30 Lecture 16
Treatment of old exams and
possibility to ask questions about earlier exercises and the Coq
assignment.
Examination
The mark for the course is determined by the 2
marks you will get for the two items listed below.
 Final mark = (Written Exam mark + Coq Assignment mark)/2
with the condition that your Written Exam mark should be 5 or
higher.
 You don't receive a mark (so I will write "NV") if you haven't
completed all parts of the course.
 Deadline Coq Assignment: Wednesday April 17
 In case your Written Exam mark is below 5, this is also your
Final mark.
 Written exam Monday April 15, Time: 13:3016:30 on campus.
 The written exam will consist of questions comparable to the ones that were given during the lectures: see above for the pdf files.
 It is an open book exam, so you can bring any paper material you want
 Exam consultation that is: you can see your graded work, on Thursday April 25, 16:00 17:00 in MF6.079A.
 Older exams:
 The exam of July 2010.
 Here is the exam of 2008. (NB: the original version, which may still be at the Gewis website, contained a mistake; this is the corrected version.)
For the retake exam ("Hertentamen"), all guidelines above apply with the following dates/deadlines:
 Written exam: Monday June 24, 18:0021:00.
 Coq assignment deadline: Wednesday June 26.
NB. You can choose to only retake one part of the exam, so only the Written exam, or only the Coq assignment. In any case: register for the retake!
Coq Assignments
Deadline: Wednesday April 17; do the assignment in
couples deliver your assignment by mail to the
teacher.
Here is a page about the
of Coq
assignment. (Look here
for some additional comments regarding the use of lists.) To complete
the Coq assignment follow these steps:
 Solve the assignment and write a report (more on that below).
 Deliver your solution (Report + separate Coq .v files) via mail.
A couple of remarks concerning the report:
 Do not make it too long. 15 pages is the absolute maximum but normally it
should be much shorter. Keep in mind that longer does not mean better!
 What you should write:
 Names and student numbers.
 Explanation of the problem and your approach to it.
 Description of the main definitions and the line of your
proofs (e.g. sublemmas you used). If you had some
alternative ideas to solve those problems describe them
and explain your choice for the solution to this
problem.
 Write about your experience with the prover. What did
you like, what you did not like etc.
 Possibly add the Coq code as an appendix. (But note that
you should deliver the Coq .v files separately anyway.)
 What you should not write
 Do not unnecessarily repeat the code. Refer to appendix
and quote the code only to illustrate something.
 Do not write obvious things! Description of the proofs
of the shape:
"the goal is as follows so we apply this tactic and
that is what we get..." are useless.
herman at cs dot ru dot nl