PhD Position First-class Coinduction in Proof Assistants

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.

This PhD position is part of the NWO XL project "Cyclic Structures in Programs and Proofs", which has positions in Groningen, Leiden, Twente, and Nijmegen. As a PhD student in this project, you will collaborate with other researchers working within this project by attending the NetTCS workshop ( ) and through individual collaborations.For other vacancies:

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.

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.

At TU Delft we embrace diversity as one of our core values and we actively engage to be a university where you feel at home and can flourish. We value different perspectives and qualities. We believe this makes our work more innovative, the TU Delft community more vibrant and the world more just. Together, we imagine, invent and create solutions using technology to have a positive impact on a global scale. That is why we invite you to apply. Your application will receive fair consideration.

Challenge. Change. Impact!

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.

to go to the website of the Faculty of Electrical Engineering, Mathematics and Computer Science.

Doctoral candidates will be offered a 4-year period of employment in principle, but in the form of 2 employment contracts. An initial 1,5 year contract with an official go/no go progress assessment within 15 months. Followed by an additional contract for the remaining 2,5 years assuming everything goes well and performance requirements are met.

Salary and benefits are in accordance with the Collective Labour Agreement for Dutch Universities, increasing from € 2901 per month in the first year to € 3707 in the fourth year. As a PhD candidate you will be enrolled in the TU Delft Graduate School. The TU Delft Graduate School provides an inspiring research environment with an excellent team of supervisors, academic staff and a mentor. The Doctoral Education Programme is aimed at developing your transferable, discipline-related and research skills.

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

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.

Are you interested in this vacancy? Please apply no later than June 29, 2025, via the application button and upload the following documents, al in PDF format:

• CV.
• A motivation letter (max 1 page A4), in which you motivate why you would be a good fit for our consortium