PhD in Extensible Programming Languages for Data Structures in Monoidal Categories
University of Exeter
This project will build a bridge between the two strands of theoretical computer science, (a) algorithms and complexity theory and (b) logic and programming language theory, and to put the resulting bridge into practical applications such as in the efficient implementations of mechanized proof assistants. Algorithm designers have developed a wealth of sophisticated techniques for organising and processing data. In parallel, logicians and programming language theorists have developed linear type systems, which ch...
This project will build a bridge between the two strands of theoretical computer science, (a) algorithms and complexity theory and (b) logic and programming language theory, and to put the resulting bridge into practical applications such as in the efficient implementations of mechanized proof assistants. Algorithm designers have developed a wealth of sophisticated techniques for organising and processing data. In parallel, logicians and programming language theorists have developed linear type systems, which ch...
Opportunity details
This project will build a bridge between the two strands of theoretical computer science, (a) algorithms and complexity theory and (b) logic and programming language theory, and to put the resulting bridge into practical applications such as in the efficient implementations of mechanized proof assistants. Algorithm designers have developed a wealth of sophisticated techniques for organising and processing data. In parallel, logicians and programming language theorists have developed linear type systems, which check how computational resources are used, and mathematical interpretations of these systems in structures called monoidal categories. The key observation underlying this project is that many existing algorithms can be expressed in suitable linear type systems. Interpreting them in different monoidal categories can therefore yield new algorithms and data structures, allowing established designs to be adapted rather than developed from scratch. Concretely, the student will design and implement a new functional programming language that at the same time (1) can be extended with linear and non-linear type formers and (2) can be interpreted in user-defined monoidal categories. These categories can be either defined internally in the language itself or alternatively another proof assistant such as Isabelle. The project will investigate the design space of such a system, including whether to develop a standalone language or embed it within an existing proof assistant. A central application will be the efficient implementation of proof assistants based on dependent type theory, such as Lean, Rocq and Agda. For example, interpreting catenable lists (a data structure supporting efficient concatenation) in the monoidal category of endofunctors on types yields a represent...
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Funding and benefits
Funding eligibility: UK Students, EU Students, International Students. Funding amount: £21,805 The studentship will provide funding of fees and a stipend per annum for 2026/7.
How to apply
This project will build a bridge between the two strands of theoretical computer science, (a) algorithms and complexity theory and (b) logic and programming language theory, and to put the resulting bridge into practical applications such as in the efficient implementations of mechanized proof assistants. A central application will be the efficient implementation of proof assistants based on dependent type theory, such as Lean, Rocq and Agda.
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Recorded source check: October 27, 2026. A stored check date does not guarantee that every field is complete or still current. Compare the provider, eligibility, funding and deadline with the live official call before applying.
Benefits
Funding eligibility: UK Students, EU Students, International Students. Funding amount: £21,805 The studentship will provide funding of fees and a stipend per annum for 2026/7.
Eligibility summary
Requirements
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