Ph.D. Student Positions

ULTRA group (Useful Logics, Types, Rewriting, and their Automation)
Computer Science Department
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, Scotland, UK

Description of the Positions

Ph.D. student positions are available in areas involving research into the theories of logics, types, and rewriting and their applications in reasoning about computer systems and mathematics. The positions are in the ULTRA (Useful Logics, Types, Rewriting, and their Automation) group in the Computer Science Department in the School of Mathematical and Computer Sciences at Heriot-Watt University in Edinburgh, the capital of Scotland. The Ph.D. supervisors will be either Fairouz Kamareddine and/or Joe Wells.

Available research topics include work on any of the following:

• The Poly* polymorphic retargetable type system for process and mobility calculi, aimed at the goal of supporting modular reasoning and compositional analysis for systems involving mobility and concurrency (such systems can include combinations of hardware, software, human organizations, biological components, etc.). Possible Poly* work includes:
  • Applying Poly* to the analysis of existing systems expressed in various existing process calculi. This can include not just work on computer systems, but also work on business or biological processes.
  • Improving the implementation of algorithms related to Poly*. This includes better use of graph visualization tools for presenting Poly* types and more compositional and/or more efficient analysis algorithms.
  • Improving the theoretical strength of Poly* to encompass the power of more existing calculi, such as the single-threadedness of Safe Ambients, the different style of polymorphism of the polymorphic pi-calculus, the structured messages of the spi-calculus, the non-local reduction rules of bigraphs, the substitution of entire processes of the higher-order pi-calculus, etc.
  • And lots of other things!
• The MathLang framework for computerizing mathematical text. MathLang tries to keep the computerization as close as possible to the mathematician's text while at the same time providing a formal structure supporting mathematical software systems (e.g., computer algebra systems, theorem provers, etc.). Possible MathLang work includes:
  • Extending the MathLang framework to better handle more aspects of mathematical text. This includes ways to connect mathematical text with its meaning, typesetting issues, document structure issues, informal and formal handling of argumentation and proof, etc.
  • Improving existing MathLang implementations. This includes improving integration of MathLang support into the TeXmacs scientific WYSIWYG editor and better interfaces to other tools (including proof assistants (e.g., Coq, Mizar, Isabelle, OMEGA, etc.) and computer algebra systems).
  • Exercising and evaluating the MathLang framework through building libraries of computerized mathematical texts.
  • And lots of other things!
• The idea of Expansion as a fundamental organizing principle for obtaining flexible and compositional polymorphic type inference for computer software. Possible work on expansion includes:
  • Expanding the scope of the expansion theory. This includes extending it to handle “for all” (∀) quantifiers like those of System F, extending it to handle information flow for security analysis, and getting a better understanding of the semantics of the linearity control already incorporated in expansion theory.
  • Further improvement of the core theory, such as the expansion algebra, unification algorithms, type inference algorithms, and methods for proving subject reduction.
  • Various implementation work using expansion. This includes type inference algorithms, better type error explanation methods, better data structures for representing analysis results, etc.
  • And lots of other things!
• The use of Type Error Slicing as a superior user interface for explaining type errors to users of new programming languages with advanced (and complicated!) type systems.
• Any other reasonable idea which builds on work we have already started, including both theory and implementation. In general, we are interested in the design and implementation of useful and elegant type systems and logics which can reason about or extend existing programming languages and theorem provers.

It will be helpful to have interests (or possibly even competence) in 1 or more of the following background knowledge areas:

• Formal calculi for reasoning about the meaning of systems (including computer programs) such as the lambda calculus, the pi calculus, and the numerous other calculi they have inspired that deal with aspects of concurrency, mobility, modules, components, linking & loading, resource usage, staged compilation, classes & objects, etc.
• Methods for analyzing specific systems (e.g., specific computer programs) represented by individual terms of such formal calculi.
• Formal calculi for representing mathematical texts, including those aspects related to how actual practicing mathematicians (i.e., not mathematical logicians) construct and present mathematics.
• Type systems for the kinds of formal calculi mentioned above, especially those with features similar to intersection, union, dependent, and singleton types.
• Rewriting theories, especially those with higher-order features, such as the lambda calculus, higher-order rewriting (HOR), systems with explicit substitutions, higher-order abstract syntax (HOAS), combinators, etc.
• Constraint solving and unification.
• Theorem provers and mathematical reasoning tools.
• Programming languages especially suitable for use for any of the above.

The expected duration of Ph.D. studentships in the UK is 3 years. The positions will be expected to start around 2007-10-01; alternative start dates can be discussed. Currently, funding is only available for EU citizens. Non-EU-citizens are welcome to apply; they will either need their own funding or alternative funding will need to be found.

The Ph.D. students will probably collaborate on 1 or more of the following activities. The specific activities will be matched to their strengths.

• Designing languages/calculi for representing various aspects of such things as computer programs, concurrent systems, mathematical texts, etc.
• Developing theories for reasoning about such a calculus as a whole as well as individual terms written in the calculus.
• Developing new type systems for such calculi with useful properties.
• Developing analysis algorithms for the new type systems.
• Proving various properties of the above items.
• Making software systems incorporating the new calculi, theories, type systems, and algorithms.
• Publishing scientific reports on the work done.

Contact Information

Inquiries can be directed to Fairouz Kamareddine at:

Inquiries can be directed to Joe Wells at:

Applying for the Positions

Please contact Fairouz Kamareddine and Joe Wells for full details on how to apply. We will want to see your curriculum vitae, as well as 2 (or even 3 if possible) recommendation letters (preferably written by people familiar with your academic and research abilities, but a letter from an industry source is better than no letter at all). We will expect recommendation letters to be sent directly by their authors and will need contact details for the letter authors. You should probably already have a master's degree or equivalent experience. It can be helpful to write a brief statement about why your research interests are a good match for the ULTRA group. If you already have research publications (this is not required), it can be helpful to send 1 (or even 2) of them. There will also be official Heriot-Watt application forms to fill out.

For documents sent by e-mail, please use a public and standard format. The best formats are plain text and PDF. LaTeX is okay if using only standard packages. HTML is okay (if not generated by Microsoft Word). PostScript is ill-advised. Open Document format is undesirable. Microsoft Word format is forbidden except where returning a form we have supplied in that format.

For your information, it is helpful if the writers of recommendation letters provide details of:

• the capacity in which they know the candidate,
• the candidate's skills, abilities and performance in relation to the post applied for,
• the candidate's record including details of the candidate's role(s) and service dates,
• their view of the candidate's suitability for the post as a whole, in light of the attached details and their knowledge of the candidate's experience and abilities,
• any further relevant information which would assist us in choosing the right candidate.