A Brown-Palsberg self-interpreter for Gödel’s System T

In a paper accepted at POPL 2016 Matt Brown and Jens Palsberg constructed a self-interpreter for System $F_\omega$, a strongly normalizing typed $\lambda$-calculus. This came as a bit of a surprise as it is “common knowledge” that total programming languages do not have self-interpreters.

Thinking about what they did I realized that their conditions allow a self-interpreter for practically any total language expressive enough to encode numbers and pairs. In the PDF note accompanying this post I give such a self-interpreter for Gödel’s System T, the weakest such calculus. It is clear from the construction that I abused the definition given by Brown and Palsberg. Their self-interpreter has good structural properties which mine obviously lacks. So what we really need is a better definition of self-interpreters, one that captures the desired structural properties. Frank Pfenning and Peter Lee called such properties reflexivity, but only at an informal level. Can someone suggest a good definition?

Note: self-interpreter-for-T.pdf

Postdoc position in Ljubljana

A postdoc position in the Effmath research project is available at the University of Ljubljana, Faculty of Mathematics and Physics. The precise topic is flexible, but should generally be aligned with the project (see project description). Possible topics include:

  •  reasoning about computational effects
  •  implementation of computational effects
  • proof assistants and formalization of mathematics

The candidate should have a PhD degree in mathematics or computer science, with background knowledge relevant to the project area. The position is available for a period of one year with possibility of extension, preferably starting in early 2016. No knowledge of the Slovene language is required.

The candidates should contact Andrej Bauer by email as soon as possible, but no later than January 8th 2016. Please include a short CV and a statement of interest.