PhD Position Systematic Derivation of Formal Languages Correctness

From Semantics to Syntax — Systematic Derivation of Formal Languages and Their Correctness

Formal languages, such as type theories and program logics, let us state and prove precisely what software should do. Today, each new language is designed by hand: experts invent the syntax, then check that it really means what it should. This is slow, and it has to be redone for every new problem. This project explores a different approach: start from the mathematical meaning of a language and derive the language itself from it, together with a proof that the two match.

Several recent type theories were built this way, but each one with its own ad hoc techniques. Together, we want to find out whether there is one general recipe behind them. You will develop this theory using tools from category theory and type theory, and check your results in the Agda proof assistant. You will be supervised by Dr. Benedikt Ahrens in the Department of Software Technology at TU Delft.

Your responsibilities will include:

• conducting this research, both individually and as part of a team;
• participating in scientific life at TU Delft and in the Netherlands, for example by attending and organizing seminars;
• participating in scientific life more globally, including publishing papers and attending workshops and conferences;
• contributing to teaching in computer science, providing the opportunity to gain teaching experience.

Job requirements

Applications will be evaluated on the following criteria:

• Masters degree in mathematics, computer science, or a related field
• Experience in both category theory and theoretical computer science (e.g., type theory, logic or programming language semantics), or a strong motivation and ability to learn them.
• Experience with a proof assistant (e.g., Agda, Rocq or Lean) is a plus, but not required.
• Enjoyment of precise mathematical reasoning,
• Ability to work independently and to collaborate across the maths/CS boundary;
• Excellent written and spoken English
• Willingness to contribute to, and possibly experience in, student supervision and teaching

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.

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.

Faculty of 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…