First year of Master
in Computer Science at ISTIC, and first year of Master in
Cryptography at Université de Rennes

- Subjects:
functional programming, first order logic, formal
specification and formal verification;

- Tools: Isabelle/HOL 2020 (please use this version!) proof assistant and counter-example finders (see a short introduction) and the programming language.

This course is about using formal methods to design verified software components. To tackle this goal we rely on functional programming, first order logic for specifying properties, proof assistant for property checking on programs and the Scala programming language for integrating the verified components into a Java application. With regards to verification, we study and use the powerful proof tactics and counter-example finders embedded in the Isabelle/HOL proof assistant. For code generation, we use the awesome Scala code exportation feature of Isabelle/HOL.

The students' final achievement is a verified Scala component achieving price negociation in a web application. The component is designed and verified in Isabelle/HOL. Then, the functional code is exported to Scala and integrated in the Java (web) application.

Disclaimer: this is a course on formal software design and not on proof design. Students are given a limited set of proof tactics that is enough to prove properties defined during the lab sessions. However, resulting proofs can be long and cumbersome. As a result, it is accepted that properties are not proven but only checked using Isabelle/HOL powerful counter-example finders.

- ACF
on Moodle with forums etc. (Only for students from University of Rennes)
- The course video channel (In french)
- Isabelle/HOL solutions of exercises (uploaded after each lecture)
- Subjects for lab sessions TP0, TP1, ... are is in the tab
- Archive of ACF exams
- Complete lecture notes, in one file
- The Isabelle/HOL survival kit gives an idea of the used subset of Isabelle commands.
- A detailed bibliography for Isabelle/HOL and Scala.
- A complete course with videos on (OCaml) functional programming. This is not the same programming language but can be useful for begginers in functional programming. There is also a book on the same subject.

- We use Isabelle/HOL 2020 (please use this version, if possible). See the installation instruction first! Then, if you plan to use Isabelle/HOL for all lab sessions, you will have to install and configure a few things:
- To have a full quickcheck (with narrowing): install the Gnu Haskell Compiler and in the file $ISABELLE_HOME/etc/settings, set the ISABELLE_GHC variable to the path where the binaries of the compile (i.e. the command ghc) is installed

- Scala 2.13 and SBT (Scala Build Tool). Here are some
explanation on how to use those
tools on ISTIC computers and on your computer.

The course consists of 7 lectures and 11 lab sessions. Lecture notes (cm1.pdf to cm7.pdf) are (almost) in english, the lab notes (tp0.pdf to tp8-10.pdf) are in french. Lectures contains exercises that are solved on Isabelle/HOL by students (available after the lecture). Here is the course schedule, click on one element for more details.

tp0.pdf : teasing... a simple Java lab session ... to
show that designing a (simple) software can be very error prone.
It is nearly impossible to directly come up with the correct
program for this (refined) simple list inclusion test, either in
imperative or in recursive style. The objective is to motivate
the fact that defining the expected properties is crucial to
detect problems and, in the end, be sure that the solution is
correct. An (opaque) Java oracle TP0_ACF.zip
is given to the students to test their code and know how far
their program is from the solution. An overall of 5% students
ended up with the correct program within 2 hours.

tp1.pdf, initial theory for the lab
session tp1.thy : first lab on
Isabelle/HOL: propositional and first order logic
(auto+nitpick). There are some additional exercises for those
who wants to know more about proof techniques in Isabelle/HOL: tp1bis.thy.

cm4.pdf. Video
(in french). Initial theory for the
course cm4.thy : basic proof
tactics
(auto, induct, sledgehammer, nitpick, quickcheck). The more
advanced topics of this course are presented in this other video
(in
french) with
the pc.thy Isabelle/HOL file. Students
interested by a deeper presentation of the proof assistant can
have a look to the Isabelle/HOL tutorial in the short Isabelle/HOL
bibliography.

tp2.pdf :
Recursive functions and basic proof tactics. Defining and
proving usual boolean operations on sets implemented as lists in
this (empty) theory file (tp2.thy). We do the
same for a basic implementation
of tables (table.thy).
We also provide an other exercise which is a simple theory file (tp3Bis.thy)
in which the 4 main lemmas admit counterexamples. Some of the lemmas need some fine
tuning of Nitpick and Quickcheck for the counterexamples to be
found: this is the purpose of this exercise.

cm5.pdf Scala Crash Course. Video
(in french). We
start from the following Scala
source files.
Basics of Scala, functional programming in Scala, object model,
case classes, pattern-matching and interoperability with Java.
Deeper informations on the language are available from
M. Odersky, L. Spoon and B. Venners online
book
and from those selected documents.

tp4.pdf Implementation of an evaluator and a pretty printer for a simple
imperative language... using pattern matching to avoid using the
visitor design pattern. We start from the following project (TP4_ACF.zip).

tp4bis.pdf
Property based testing and
fuzzing. Implementation of a generator for random values
(based on SmallCheck) and black box testing of an opaque
implementation. Fuzzing-based testing. We start from the
following project
(TP4bis_ACF.zip).

tp5.pdf, tp5.thy, TP5_ACF.zip Students have to define a predicate deciding
the equivalence of security policies used by a
firewall. A security policy (also known as a chain) consists of
a list of rules which are applied using their priority,
i.e. their order in the list. Maintaining such policies is a
well-known difficult problem because any update in a policy
(like a simple reordering of the rules) may totally change the
security property enforced by the firewall. Having an
equivalence predicate on policies permits to check (in a
formally proven way) that an update of the security policy
does not change the protection enforced by the firewall.

tp67.pdf, tp67.thy,
TP67_ACF.zip : Students design a
static analyser for a simple toy language, define the
correctness theorem to guarantee the safety of the analyzer,
define the completeness theorem to refine it (using the
counterexamples). Integrated with a Scala parser for the toy
language. Proofs are optional. To carry out the
proofs, you can get inspiration from this short video (in
french) with
the pc.thy Isabelle/HOL file.

tp8-10.pdf, tp8-10.thy,
TP89_ACF.zip, table.thy: Students design a
validation
tool for a price negociation web application. A merchant and a
client send messages to the validation tool to negociate a
price. A price is validated if a price proposed by a client is
superior or equal to a price proposed by the merchant. In the
end, the list of validated should be correct. As with all
protocols, more complex than it seems at first glance. They
define the functions, check the 9 properties and export the
Scala code. All the validations tools of all students are then
deployed on a web site so that all students can attack all
validation tools and report on the attacks found. Proofs are
optional. To carry out the proofs, you
can get inspiration from this short video (in
french) with
the pc.thy Isabelle/HOL file. For this
lab session a list of relevant intermediate lemmas (in french)
is also provided: tp8-10proof.thy

Instructor: Thomas Genet

Many thanks to people of the Isabelle/HOL team at TUM: Tobias Nipkow, Jasmin Blanchette, Lukas Bulwahn, Florian Haftmann and Alexander Krauss for answering questions and for fruitful discussions.

Many thanks to Olivier Barais, Sandrine Blazy, Benoît Combemale, Arnaud Jobin, Julien Richard-Foy and Gweltaz Riou for their help during the preparation of this course.

This work is licensed under CC BY 4.0