Interactive Proof Assistants (IPA)
Interactive theorem proving is concerned with carrying out machine-checked proofs and developing the systems that check these proofs—proof assistants. Proof assistants, like Coq, Lean, and Isabelle, are used today to build highly critical systems and verify deep mathematical results. Landmark achievements in this area include formally verified compilers, operating system kernels, and distributed systems, as well as formal proofs of deep mathematical results, such as the four-colour, the Feit–Thompson, and Gödel's incompleteness theorems, and the Kepler conjecture.
The IPA course is a hands-on course about using a proof assistant to construct formal models of algorithms, protocols, and programming languages and to reason about their properties. The focus is on applying logical methods to concrete problems. The course will demonstrate the challenges of formal rigour and the benefits of machine support in modeling, proving and validating.
In the course, we will use the Isabelle proof assistant. The course is structured in two parts: The first part introduces basic and advanced modeling techniques (functional programs, inductive definitions, modules), the associated proof techniques (term rewriting, resolution, induction, proof automation), and compilation of the models to certified executable code. In the second part, the students work in groups on a project assignment in which they apply these techniques: they build a formal model and prove its desired properties. The project lies in the area of programming languages, model checking, and information security.
- Logic and natural deduction
- Modeling techniques
- Proof techniques
- Effectively use a proof assistant to write precise and concise models and specifications (i.e., apply the above modeling techniques).
- Use the proof assistant as a tool for checking and analyzing such models and for taming their complexity (i.e., apply the above proof techniques).
- Extract certified executable implementations from specifications.
- Create unambiguous formal models and analyse them.
- Discuss what it means for a program/algorithm/system/model to be correct and rigorously demonstrate correctness.
The course progresses from teaching (lectures with exercises) to
project work and finally preparation for presentation/oral exam:
▪ Lecture phase: lectures and exercises, formation of project groups (4 weeks)
▪ Project phase: project work (4 weeks)
▪ Presentation and exam preparation (1 week)
See Absalon for the course literature.
It is expected that students have a working knowledge of
programming and programming languages corresponding to the course
Advanced Programming (AP) or equivalent.
Semantics and Types (SaT) is recommended, but not required.
Academic qualifications equivalent to a BSc degree is recommended.
Students receive feedback from the instructors during the
exercise sessions and during project work. Students give each
other feedback within the project groups.
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- 7,5 ECTS
- Type of assessment
Written assignmentOral examination, 30 minutes
- Type of assessment details
- Specifically, the exam consists of two parts:
1. Submission of the developed Isabelle formalization as part of the group project (written assignment).
2. An individual oral examination (without preparation) based on the project work (with a special emphasis on the part of the project the student has co-authored) and on the general course topics.
The project and oral examination are not weighted, and thus only a single overall assessment is provided for the two parts of the exam.
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
Several internal examiners.
Criteria for exam assessment
See Learning Outcome.
Single subject courses (day)
- Project work
- Exam Preparation
- Course number
- 7,5 ECTS
- Programme level
- Full Degree Master
- Block 1
- No limit
The number of seats may be reduced in the late registration period
- Study Board of Mathematics and Computer Science
- Department of Computer Science
- Faculty of Science
- Dmitriy Traytel (7-7775647c77686f43676c316e7831676e)
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