Postdoc Category Theory, Computer Proof Assistants And Computer Algebra Systems

ScholarLink Inc.; Netherlands; Remote; EUR 41,000 - 64,000; Full time

Job summary

ScholarLink Inc. in the Netherlands invites a postdoctoral researcher in mathematics or computer science to connect a proof assistant with CAP, using Rocq, Lean or Agda to be decided at the start.

The work will formalise the categorical doctrines behind CAP, implement open-source software, publish results, and participate in conferences and teaching. The contract is one year, extendable to three years, 32–40 hours per week.

Qualifications

• PhD awarded by start date in mathematics, computer science or closely related field.
• Research in formalisation, computer algebra or category theory with publications or substantial software.
• Strong programming ability and independence; willingness to teach and supervise.
• Excellent written and spoken English; ability to collaborate across groups.

Responsibilities

• Connect a proof assistant with CAP using Rocq, Lean or Agda to be decided.
• Formalise categorical doctrines and implement documented open-source software.
• Publish results and present at conferences/workshops; contribute to open-source libraries.
• Supervise BSc and MSc students; possibly contribute to classroom teaching.

Skills

PhD in mathematics/computer science

Formalisation

Programming

Independent research

English

Supervision

Education

PhD in mathematics or computer science

Tools

GAP

Lean/Agda/Coq

Job description

## About the PositionComputer 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. The aim is to combine efficient categorical computations with the guarantees of a proof assistant. The postdoctoral researcher will design and build a connection between Rocq, Lean or Agda, to be decided at the start of the project, and CAP. The work involves making the categorical doctrines underlying CAP precise enough to formalise, choosing a formal treatment faithful to the constructive content of its algorithms, and implementing documented, openly available software. The researcher will publish results, present them at conferences and workshops, and contribute to the open-source libraries of both projects. There is room to shape the work and develop an independent research agenda. The position is based in the Programming Languages group, Department of Software Technology, at TU Delft, working with Benedikt Ahrens and collaborating with Mohamed Barakat at Universität Siegen, with regular exchange between the groups. The role includes supervision of BSc and MSc students and possibly classroom teaching. Applications are evaluated on a PhD awarded by the start date, or submitted with a defence scheduled, in mathematics, computer science or a closely related field; research experience in interactive theorem proving/formalisation, computer algebra or category theory, demonstrated by publications, a thesis or substantial software contribution; interest in the other two areas and willingness to learn; practical programming ability and comfort with a substantial existing codebase; independent work and collaboration across mathematics and computer science; good written and spoken English; and experience in and willingness to contribute to supervision and teaching. The contract is one year, extensible to a maximum of three years, for 32-40 hours per week. Salary and benefits follow the Collective Labour Agreement for Dutch Universities; the listed salary range is EUR 3706-5760 monthly. Benefits in## Research Interests* Connect a proof assistant with CAP* Formalise categorical doctrines and algorithms* Implement documented open-source software* Publish and present research* Supervise BSc and MSc students* Possibly contribute classroom teaching## Required Skills & Qualifications* PhD in mathematics, computer science or a closely related field by the start date* Research experience in formalisation, computer algebra or category theory* Practical programming ability* Independent and collaborative research* Good written and spoken English* Student supervision and teaching experience## Other Requirements & Additional InfoThe initial one-year contract can be extended to a maximum of three years. Ideally start by 1 March 2027; a later starting date can be discussed.