Postdoc Category Theory, Computer Proof Assistants and Computer Algebra Systems

Computer proof assistants and computer algebra systems have complementary strengths. A proof assistant checks each step of a mathematical argument against a formal foundation, but is not designed for computation; a computer algebra system computes efficiently with large and intricate algebraic structures, but its results depend on code that has not been formally verified. Category theory is a good place to connect the two.

CAP (Categories, Algorithms, Programming) is a software system for computational category theory, implemented in GAP and part of the homalg project. Because it expresses categorical constructions directly as algorithms, it is a suitable target for formalisation. The aim of the project is to bring the two kinds of system together, so that categorical computations can be carried out with the efficiency of a computer algebra system and checked with the guarantees of a proof assistant.

The postdoctoral researcher will design and build this connection between a proof assistant — Rocq, Lean or Agda, to be decided at the start of the project — and CAP. The work is partly conceptual and partly practical: making the categorical doctrines underlying CAP precise enough to formalise, choosing a formal treatment that is faithful to the constructive content of CAP's algorithms, and implementing the result as documented, openly available software.

The researcher will publish the results, present them at conferences and workshops, and contribute to the open‑source libraries of both projects. There is room to shape the direction of the work according to their own interests and expertise, and to develop their own research agenda alongside it.

The position is based in the Programming Languages group, Department of Software Technology, at TU Delft, where the researcher will work with Benedikt Ahrens, and in collaboration with Mohamed Barakat at Universität Siegen, with regular exchange between the two groups. This connects the researcher to both of the relevant communities: formalisation and univalent foundations in Delft, computational category theory and the homalg/CAP ecosystem in Siegen.

The role also includes contributing to the supervision of BSc and MSc students working on related projects, and possibly some classroom teaching.

Applications will be evaluated on the following criteria:

• PhD (awarded by the start date, or submitted with a defence scheduled) in mathematics, computer science, or a closely related field
• Research experience in at least one of: interactive theorem proving/formalisation, computer algebra, or category theory — demonstrated by publications, a thesis, or a substantial software contribution
• Demonstrable interest in the other two, and willingness to learn them to working depth
• Practical programming ability and comfort working with a substantial existing codebase
• Ability to work independently and to collaborate across the maths/CS boundary; good written and spoken English
• Experience in, and willingness to contribute to, student supervision and teaching

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