computer science

Fer-Jan de Vries

Interests

• Computation: We work on theory and applications of term rewriting systems and lambda calculi. A chapter summarising work we have done with Jan Willem Klop, Richard Kennaway, Vincent van Oostrom and Ronan Sleep has appeared in the book "Term Rewriting Systems". That book contains a nice general description of term rewriting:

  Term rewriting systems developed out of mathematical logic and are an important part of theoretical computer science. They consist of sequences of discrete transformation steps where one term is replaced with another and have applications in many areas, from functional programming to automatic theorem proving and computer algebra.
  [Terese, 2003]

  In particular we work with infinite rewriting systems, that explicitly can deal with infinite computations and infinite terms. We believe that infinite computations are meaningful (eg., think of calculating the decimal expansion of the square root of 2) and therefore should be incorporated in the computational paradigm that one studies. Infinite rewriting systems can be used as semantics for lazy computation.

  Extending a finite rewrite system into an infinite rewrite system so that a property like confluence is preserved is a non-trivial process. In our current approach we first identify a set U of so called meaningless terms may be rewritten to a new bottom term. Think of terms that are unfinished, in the sense that any part of them can still be rewritten and can not be already printed in an attempt to output at least partial information of the final outcome.

  Interestingly, it turns out that there are many different choices for such a set U of meaningless terms. In the particular case of lambda calculus we can now construct a great variety of different complete infinite extensions of finite lambda calculus. Each of them gives rise to a model of the lambda calculus. Most of these models are new. The properties of these models can be rather surprising: at TLCA05 we have presented a paper showing that there exist besides usual two continuous models (the Böhm Model and the Lévy-Longo Model) also discontinuous models. These discontinuous models can even be non-monotone. In our CSL2005 paper we show that there are even (and quite a lot) models of lambda calculus that can not be ordered.

  We are currently working on the Axioms of Meaninglessness: we like to have axioms that not only are sufficient but also needed for producing complete infinite bot extensions of finite lambda calculus. Only when we have a set of necessary and sufficient axioms, can we embark on a description of the possible sets of meaningless terms, the collection of which is a complete lattice, if we oreder them via the subset relation. Understanding this lattice and the corresponding lattices of finity lambda theories and infinitary lambda theorems is an interesting next step. And we are still interested in the quaeste for new infinite extensional bot extensions of finite lambda calculus

• Language: With Jan van Eijck we have worked on two topics in the border area of logic and computational linguistics: dynamic semantics and update logic.

• Logic: When I was a student in the Logic Group of Dirk van Dalen at the University of Utrecht I worked on constructive mathematics and toposes. A neat generalised higher order Godel/Friedman translation of intuitionistic type theory into classical type theory was one of the outcomes.

• Research
• Publications

• Rewriting Links
• Researchers in Rewriting
• Rewriting Homepage

• Curiosity
• Academic Ancestors

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Author: Fer-Jan de Vries.
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