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Christian Urban

E-mail urbanc at in tum de

Address Institute for Computer Science at the TU Munich (IV), Boltzmannstrasse 3, D-85748 Garching, Germany.

Fax +49 89 289 17307

Isabelle Documentation Project (contains now a draft of a 200-page tutorial on Isabelle programming)
Current Position I have been awarded an Emmy-Noether fellowship to head an independent research group in the Computer Science Department at the TU Munich. This group co-operates with the Theorem Proving Group chaired by Prof. Tobias Nipkow and is accommodated by the institute of Prof. Manfred Broy.

Past Positions Between September 2008 and February 2009, I was an invited research fellow in the Department of Computer Science in Princeton. In 2004/05 I was an Alexander-von-Humboldt fellow in Munich and from 2000 until 2004 I was awarded a Research Fellowship in Cambridge. Before that I did my PhD in Cambridge.

Research Interests theorem provers, programming languages, compilers, algorithms, proof theory, type systems, concurrency, lambda calculus, unification, regular expressions, computability, complexity, functional and logic programming.

Conferences UNIF'06 (member of PC), LFMTP'07 (member of PC), LFMTP'08 (PC co-chair), WMM'08 (member of PC), LSFA'08 (invited speaker), TAASN'09 (member of PC), LSFA'09 (member of PC), IDW'09 (organiser), WMM'09 (PC chair), TPHOLs'09 (PC co-chair), Automatheo'10 (member of PC), ITP'10 (member of PC), UNIF'10 (invited speaker), WMM'10 (invited speaker), IDW'10 (co-organiser), CPP'11 (member of PC), RTA'11 (member of PC), LFMTP'11 (member of PC)

Nominal Isabelle I currently work on Nominal Isabelle. This is joint work with Dr Stefan Berghofer, Dr Markus Wenzel, Dr Cezary Kaliszyk and the Isabelle-team in Munich. Many of the theoretical ideas originate from the nominal logic project - a wonderful project headed by Prof. Andrew Pitts. The aim of my work is to make formal reasoning involving binders as simple as on paper and the hope is to lure masses to automated theorem proving. My funding for this work was provided in 2004 and 2005 by a research fellowship from the Alexander-von-Humboldt foundation. During this time I was a visitor in the group of Prof. Helmut Schwichtenberg. Since 2006 this work is supported by an Emmy-Noether fellowship. There is a webpage and a mailing list about Nominal Isabelle. It also includes a list of projects that use Nominal Isabelle. Users of Nominal Isabelle had their papers appearing at LICS, POPL, FOSSACS, SOS, TPHOLs and CPP.
Myhill-Nerode and Regular Expressions Out of frustration of having to teach inductions in theorem provers using worn-out examples like fib and even/odd, we implemented a large part of regular language theory in Isabelle/HOL. This implementation gives rise to much more interesting examples, as shown here and here. It turns out that formalisations of automata theory are a huge pain in theorem provers, especially in those that are HOL-based. We therefore went against the mainstream and used in our formalisation regular expressions exclusively, because they are much more convenient for formal reasoning. The results we formalised include: the Myhill-Nerode theorem, the closure of regular languages under complementation, finiteness of derivatives of regular expressions and a surprising result about Subseq, which according to this blog should be better known. This is joint work with Prof. Xingyuan Zhang and his student Chunhan Wu from the PLA University of Science and Technology in Nanjing. My funding for this work came from the Chinese-German Research Centre.
Nominal Unification and Alpha-Prolog Nominal unification is one outcome of my involvement in the nominal logic project in Cambridge. Another is the logic programming language alpha-Prolog (joint work with Dr James Cheney), which uses nominal unification - click for details here. The nominal unification algorithm has been formally verified in Isabelle. This was possible since this unification algorithm is formulated in a simple first-order language (unlike other algorithms for higher-order unification). Prof. Daniel Friedman and his group use nominal unification in their alpha-Kanren system implemented in Scheme. Prof. Maribel Fernandez and her student improved the nominal unification algorithm to be quadratic. My funding for this work was provided through a research fellowship from Corpus Christi College, Cambridge.
Classical Logic I was Ph.D. student in the University of Cambridge Computer Laboratory and for three years called Gonville and Caius College my home. I was very lucky to have Dr Gavin Bierman as supervisor. My research in Cambridge was also very much influenced by Prof. Martin Hyland. Some details on my thesis "Classical Logic and Computation" are elsewhere, including a Java Applet that 'visualises' some of the results from the thesis. I completed the writing of the thesis in Marseille in the group of Prof. Jean-Yves Girard. My study in Cambridge was funded by two scholarships from the German government; my year in Marseille by a TMR-fellowship from the EU. My PhD was also one starting point for the EPSRC Project on the Semantics of Classical Proofs. The strong normalisation result in the PhD has recently been used by Prof. Claude Kirchner and his students to prove consistency for their superdeduction system lemuridae.
Forum I implemented Forum, a programming language based on classical linear logic, as my M.Phil. thesis. This was joint work with Dr Roy Dyckhoff. Details can be found here and here. During my M.Phil study I spent one month in Philadelphia invited by Prof. Dale Miller.
G4ip An implementation of G4ip using the imperative language Pizza can be found here. Pizza is a conservative extension of Java and a precursor of Scala. The implementation illustrates the technique of success continuations.

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