Phd Position First-class Coinduction in Proof Assistants

**PhD Position First-class Coinduction in Proof Assistants**:
**Jobdescription**:
Essential to writing and reasoning about software that operates continuously is a practically usable language for programs and proofs of coinductive types. Proof assistants currently rely on either syntactic guardedness conditions on programs, sized types, or guarded recursion. However, the syntactic guardedness condition is very restrictive and brittle, while both sized types and guarded recursion require significant additional annotations to the program.

As a PhD student in this project, you will work towards developing a new system for defining and reasoning about coinductive processes in proof assistants. The key challenge is to develop a system that is both modular (so productivity information is propagated through the type system) and user-friendly (so few or no manual annotations are needed).

This project combines and builds on existing approaches proposed in the literature:

- Sized types and guarded type theory, in particular their implementation in Agda (see A. Abel and B. Pientka: “Wellfounded recursion with copatterns: a unified approach to termination and productivity”, ICFP’13).
- Coinductive reasoning in (higher) observational type theory and cubical type theory (see R. Atkey and C. McBride: “Productive coprogramming with guarded recursion”, ICFP’13).

In order to ensure soundness and usability, this project will require a combination of theoretical analysis of a type theory with first-class reasoning about coinductive processes and the development of a prototype implementation of this type theory as an extension to Agda.

**Job requirements**:
We seek strong, highly motivated applicants who:

- Have (or are close to completing) an MSc in Computer Science, Logic, Mathematics, or a related field.
- Have background or research experience in any of the areas above (preferred but not required).
- Have strong communication skills (oral and written) in English.

**TU Delft (Delft University of Technology)**:
Delft University of Technology is built on strong foundations. As creators of the world-famous Dutch waterworks and pioneers in biotech, TU Delft is a top international university combining science, engineering and design. It delivers world class results in education, research and innovation to address challenges in the areas of energy, climate, mobility, health and digital society. For generations, our engineers have proven to be entrepreneurial problem-solvers, both in business and in a social context.

Challenge. Change. Impact

**Faculty Electrical Engineering, Mathematics and Computer Science**:
The Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) brings together three scientific disciplines. Combined, they reinforce each other and are the driving force behind the technology we all use in our daily lives. Technology such as the electricity grid, which our faculty is helping to make completely sustainable and future-proof. At the same time, we are developing the chips and sensors of the future, whilst also setting the foundations for the software technologies to run on this new generation of equipment - which of course includes AI. Meanwhile we are pushing the limits of applied mathematics, for example mapping out disease processes using single cell data, and using mathematics to simulate gigantic ash plumes after a volcanic eruption. In other words: there is plenty of room at the faculty for ground-breaking research. We educate innovative engineers and have excellent labs and facilities that underline our strong international position. In total, more than 1000 employees and 4,000 students work and study in this innovative environment.

, Mathematics and Computer Science.

***Conditions of employment**:
The TU Delft offers a customisable compensation package, discounts on health insurance, and a monthly work costs contribution. Flexible work schedules can be arranged.

Will you need to relocate to the Netherlands for this job? TU Delft is committed to make your move as smooth as possible The HR unit, Coming to Delft Service, offers information on their website to help you prepare your relocation. In addition, Coming to Delft Service organises events to help you settle in the Netherlands, and expand your (social) network in Delft. A Dual Career Programme is available, to support your accompanying partner with their job search in the Netherlands.

**Additional information**:
**Application procedure**:

- CV.
- A motivation letter (max 1 page A4), in which you motivate why you would be a good fit for our consortium and the selected position(s).
- Your MSc thesis, if available; otherwise, another sample of research, such as your BSc thesis.
- Grade transcripts of BSc and MSc studies so far.

Moreover, you are asked to provide names and contacts of two academic references.

**Please note**:

- A pre-employment screening can be part of the selection procedure.
- Please do not contact u