Nominal/users.html
author Christian Urban <christian.urban@kcl.ac.uk>
Fri, 16 Jun 2023 10:14:34 +0100
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<?xml version="1.0" encoding="utf-8"?>
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
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<html>
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<head>
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  <title>Nominal Methods Group</title>
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  <link rel="stylesheet" href="nominal.css">
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</head>
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<body>
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<div align="right" style="position:relative; left:15%; width:80%">
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<P>
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<small>
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<SCRIPT LANGUAGE="JAVASCRIPT" type="text/javascript">
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<!--
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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var r_text = new Array ();
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r_text[0] = "<em>\"Proving theorems about substitutions (and related operations such as alpha-conversion) required far more time and HOL code than any other variety of theorem.\"<br><\/em>M. VanInwegen using a concrete representation for binders in her PhD-thesis, 1996";
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r_text[1] = "<em>\"When doing the formalization, I discovered that the core part of the proof... is fairly straightforward and only requires a good understanding of the paper version. However, in completing the proof I observed that in certain places I had to invest much more work than expected, e.g. proving lemmas about substitution and weakening.\"<\/em><br>T. Altenkirch using de Bruijn indices in Proc. of TLCA, 1993";
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r_text[2] = "<em>\"Technical work, however, still represents the biggest part of our implementation, mainly due to the managing of de Bruijn indexes...Of our 800 proved lemmas, about 600 are concerned with operators on free names.\"<\/em><br>D. Hirschkoff in Proc. of TPHOLs, 1997";
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r_text[3] = "<em>\"It took the author many long months to complete the work on this formalization...The part concerning substitution is by far the largest part of the whole development.\"<\/em><br>A. Koprowski using de Bruijn indices in a draft paper, 2006";
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r_text[4] = "<em>\"We thank T. Thacher Robinson for showing us on August 19, 1962 by a counterexample the existence of an error in our handling of bound variables.\"<\/em><br>S. Kleene in J. of Symbolic Logic 27(1):11-18, 1962";
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r_text[5] = "<em>\"The main drawback in HOAS is the difficulty of dealing with metatheoretic issues concerning names in processes...As a consequence, some metatheoretic properties involving substitution and freshness of names inside proofs and processes cannot be proved inside the framework and instead have to be postulated.\"<\/em><br>F. Honsell, M. Miculan and I. Scagnetto in Theoretical Computer Science, 253(2):239-285, 2001";
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r_text[6] = "<em>\"Because Twelf metatheorems are proved using totality assertions about LF type families, the class of metatheorems that can be mechanized is restricted to All/Exists-statements over LF types. On the one hand, as the successful Twelf formalizations cited in Section 5 demonstrate, these All/Exists-statements have proved to be sufficient for formalizing a wide variety of metatheorems about programming languages and logics. On the other hand, we have no way to quantify when metatheorems of this form will be sufficient, and there are some well-known examples of proofs that cannot be formalized directly using Twelf as metatheorem language. For example, proofs by logical relations often require more quantifier complexity than All/Exists-statements afford.\"<\/em><br>Robert Harper and Daniel Licata in a paper on Twelf, 2007";
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r_text[7] = "<em>\"So we cannot, hand-on-heart, recommend the vanilla LN style for anything but small, kernel language developments. \"<\/em><br>in F-ing Modules by Rossberg, Russo and Dreyer, TLDI 2010";
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r_text[8] = "<em>\"Higher-order abstract syntax is a convenient way to approach languages with binding, but it is possible to imagine a problem where manipulating a fully concrete object without binding is simpler. In these cases, it is possible to establish a bijection between your HOAS terms and de Bruijn versions of the same terms. \"<\/em><br>Interesting responses from the <A HREF=\"http://twelf.plparty.org/wiki/Ask_Twelf_Elf\">Twelf wiki.</A> (To be honest, the same comment applies to Nominal. --cu)";
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r_text[9] = "<em>\"I wonder if de Bruijn was any good at remembering names. \"<\/em><br>Darius Jahandarie according to Haskell Digest, Vol 97, Issue 1";
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var i = Math.floor(r_text.length * Math.random());
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document.write(r_text[i]);
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//-->
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</SCRIPT>
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</small>
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</P>
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</div>
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<H1>Users of Nominal Isabelle</H1>
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<P>
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If you want to see a simple example illustrating our results on Nominal Isabelle click
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<A HREF="example.html">here</A>. For more interesting results, we already
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completed formalisations of Church-Rosser and strong-normalisation proofs as
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well as the first part of the <A
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HREF="https://www.seas.upenn.edu/~plclub/poplmark/" target="_top">PoplMark
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Challenge</A>.  We also formalised some typical proofs from SOS, <A
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HREF="http://www.cs.cmu.edu/~crary/" target="_top">Karl Crary</A>'s chapter on
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logical relations from <A
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HREF="http://www.cis.upenn.edu/~bcpierce/attapl/index.html"
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target="_top">Advanced Topics in Types and Programming Languages</A>, and also
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a paper on LF by <A HREF="http://www.cs.cmu.edu/~rwh/" target="_top">Harper</A> and 
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<A HREF="http://www.cs.cmu.edu/~fp/" target="_top">Pfenning</A>. In the latter paper we found a gap in
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the soundness proof and corrected it (we actually gave three solutions to the problem [6]). Urban 
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formalised and also corrected the main result of his PhD, a logical relation argument for
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establishing strong normalisation of cut-elimination in classical logic. Other
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people have used Nominal Isabelle too:
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<H3>PhD Theses using Nominal Isabelle</H3>
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<ul>
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<li>
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<A HREF="http://www.itu.dk/people/jebe/">Jesper Bengtson</A> (now professor at ITU in Copenhagen)   
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finished his PhD in 2010 with a large formalisation of the Psi-Calculus in Nominal Isabelle
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(see <a href="https://www.isa-afp.org/entries/Psi_Calculi.html">here</a>).
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The Psi-calculus is a parametric framework for reasoning about process calculi.
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He also formalised CCS (<a href="http://afp.sourceforge.net/entries/CCS.shtml">here</a>) using Nominal Isabelle. 
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</li>
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</ul>
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<H3>Journal and Conference Papers using Nominal Isabelle</H3>
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<ul>
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<li>
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<A HREF="http://www.itu.dk/people/jebe/">Jesper Bengtson</A>
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and <A HREF="http://user.it.uu.se/~joachim/" target="_top">Joachim Parrow</A>
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used Nominal Isabelle to verify the theory of the
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pi-calculus. They formalised the proof that bisimulation is a congruence (both
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for late and early operational semantics) available 
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<a href="http://afp.sourceforge.net/entries/Pi_Calculus.shtml">here</a>.  Moreover they formalised the proof
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that all late bisimilar processes are early bisimilar. The corresponding
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papers were presented at FOSSACS'07 and SOS'07. They also used Nominal Isabelle
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to formalise their work on Psi-calculi, available 
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<a href="http://afp.sourceforge.net/entries/Psi_Calculi.shtml">here</a>. This was 
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presented at LICS 2009 and LICS 2010.
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All formalisations are part of the <A HREF="http://afp.sourceforge.net/">AFP</A>.
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<li>
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<A HREF="http://www.ccs.neu.edu/home/samth/" target="_top">Sam Tobin-Hochstadt</A>, a student
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of <A HREF="http://www.ccs.neu.edu/home/matthias/" target="_top">Matthias Felleisen</A>, used 
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Nominal Isabelle to formalise their work on Typed Scheme. This was presented at POPL'08. 
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<li>
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<A HREF="http://homepages.inf.ed.ac.uk/ldixon/" target="_top">Lucas Dixon</A>,
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Alan Smaill and <A HREF="http://homepages.inf.ed.ac.uk/bundy/"
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target="_top">Alan Bundy</A> used Nominal Isabelle to formalise
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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proof terms of ILL and studied proof planning with this formalisation
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(EDI-INF-RR-0786). 
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<li>
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<A HREF="http://www.cs.swan.ac.uk/~csteme/" target="_top">Temesghen Kahsai</A>
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and <A HREF="http://users.dimi.uniud.it/~marino.miculan/" target="_top">Marino Miculan</A> formalised
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the spi-calculus using our work - see 
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<A HREF="http://www.cs.swan.ac.uk/~csteme/SpiInIsabelle/SpiInIsabelle.html" target="_top">here</A>.
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<li>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Ayesha Yasmeen, a student of  
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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<A HREF="http://www-faculty.cs.uiuc.edu/~egunter/" target="_top">Elsa Gunter</A>,
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formalised an extension of the ambient calculus using Nominal Isabelle. This
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was presented in the Emerging Trends section of TPHOLs'08. 
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<li>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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<A HREF="http://www.ps.uni-saarland.de/~doczkal/" target="_top">Christian Doczkal</A>,
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a student of <A HREF="http://www.ps.uni-saarland.de/~smolka/">Gert Smolka</A>, 
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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finished in 2009 his 
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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<A HREF="http://www.ps.uni-saarland.de/~doczkal/master/master.php" target="_top">master thesis</A> 
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at Saarbr&uuml;cken University using 
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Nominal Isabelle. He formalised the TT-lifting technique in order to prove 
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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strong normalisation of Moggi's computational metalanguage. This is part of
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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the <A HREF="http://afp.sourceforge.net/entries/Lam-ml-Normalization.shtml">AFP repository</A>.
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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   132
<li>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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   133
Armin Heller finished his master thesis at the TU Munich in 2010 with a simple compiler verification
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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   134
using Nominal Isabelle.
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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   135
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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   136
<li>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   137
<A HREF="http://homepages.inf.ed.ac.uk/jcheney/" target="_top">James Cheney</A> 
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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   138
formalised a number of properties of the meta-theory of mini-XQuery in Nominal Isabelle.
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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   139
The plan is to extend this work to full XQuery. The preliminary results appeared at CPP'11.
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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   140
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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   141
<li>
410
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents: 409
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   142
<A HREF="http://cl-informatik.uibk.ac.at/users/cek/" target="_top">Cezary Kaliszyk</A> 
402
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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   143
with input from Henk Barendregt formalised the second fixed point theorem
9e089afe5086 added Nominal
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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   144
of the lambda calculus using Nominal Isabelle 2. This work appeared at CPP'11.
9e089afe5086 added Nominal
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   145
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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   146
<li>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   147
<A HREF="http://www.joachim-breitner.de/blog/" target="_top">Joachim Breitner</A> 
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   148
used Nominal2 for formalising Launchbury's natural semantics for lazy evaluation. This is part
628
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Christian Urban <christian.urban@kcl.ac.uk>
parents: 627
diff changeset
   149
of the <A HREF="http://afp.sourceforge.net/entries/Launchbury.shtml">AFP</A>. 
402
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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   150
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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   151
<li>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   152
<A HREF="http://www.cl.cam.ac.uk/~lp15/" target="_top">Larry Paulson</A> 
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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   153
formalised G&ouml;del's Incompletness Theorems using Nominal2. This work
628
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Christian Urban <christian.urban@kcl.ac.uk>
parents: 627
diff changeset
   154
appeared in the Journal of Automated Reasoning in 2015 and is part of the
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Christian Urban <christian.urban@kcl.ac.uk>
parents: 627
diff changeset
   155
<A HREF="https://www.isa-afp.org/browser_info/current/AFP/Incompleteness/SyntaxN.html">AFP</A>.
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Christian Urban <christian.urban@kcl.ac.uk>
parents: 627
diff changeset
   156
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Christian Urban <christian.urban@kcl.ac.uk>
parents: 627
diff changeset
   157
<li>
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Christian Urban <christian.urban@kcl.ac.uk>
parents: 627
diff changeset
   158
<A HREF="http://www.cl.cam.ac.uk/~lp15/" target="_top">Larry Paulson</A> 
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Christian Urban <christian.urban@kcl.ac.uk>
parents: 627
diff changeset
   159
formalised a second Part of G&ouml;del's Incompletness Theorems using Nominal2. This is part of the
d09365eee0e3 updated
Christian Urban <christian.urban@kcl.ac.uk>
parents: 627
diff changeset
   160
<A HREF="https://www.isa-afp.org/browser_info/current/AFP/Goedel_HFSet_Semanticless/SyntaxN.html">AFP</A>.
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Christian Urban <christian.urban@kcl.ac.uk>
parents: 627
diff changeset
   161
402
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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   162
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   163
<li>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   164
<A HREF="http://www.joachim-breitner.de/blog/" target="_top">Joachim Breitner</A>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   165
proved the correctness of a GHC compiler transformation using Nominal2.
9e089afe5086 added Nominal
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   166
This work appeared at the
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   167
<A HREF="https://www.haskell.org/haskell-symposium/2015/">Haskell Symposium 2015</A>.
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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   168
</ul>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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   169
</P>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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   170
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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   171
633
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Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   172
<H3>Entries in the Archive of Formal Proofs (AFP) using Nominal Isabelle</H3>
402
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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   173
633
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Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
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   174
<ul>
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Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   175
<li>
4863462b8ff0 new version
Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   176
<A HREF="https://www.cl.cam.ac.uk/~mpew2/">Mark Wassell</A>, Alasdair
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Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   177
Armstrong, Neel Krishnaswami and Peter Sewell mechanised the
4863462b8ff0 new version
Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   178
Metatheory for the MiniSail ISA Specification Language using Nominal
4863462b8ff0 new version
Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   179
Isabelle. They needed Nominal Isabelle for handling binding.  The AFP
4863462b8ff0 new version
Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   180
entry
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Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   181
is <a href="https://www.isa-afp.org/entries/MiniSail.html">here</a>.
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Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   182
This work appeared in the Proceedings of the 48th International
4863462b8ff0 new version
Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   183
Symposium on Microarchitecture MICRO-48 (2015) and at the Automated
4863462b8ff0 new version
Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   184
Reasoning Workshop (ARW 2018).
402
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   185
633
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Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   186
<li>
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Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   187
  <A HREF="https://www.andreipopescu.uk">Andrei Popescu</A> and
4863462b8ff0 new version
Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   188
  <A HREF="https://traytel.bitbucket.io/">Dmitriy Traytel</A>
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Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   189
  gave a Formally Verified Abstract Account of Gödel's Incompleteness Theorems using Nominal Isabelle.
4863462b8ff0 new version
Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   190
  The AFP entries are
4863462b8ff0 new version
Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   191
  <a href="https://www.isa-afp.org/entries/Goedel_Incompleteness.html">here</a>,
4863462b8ff0 new version
Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   192
  <a href="https://www.isa-afp.org/entries/Goedel_HFSet_Semantic.html">here</a> and
4863462b8ff0 new version
Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   193
  <a href="https://www.isa-afp.org/entries/Goedel_HFSet_Semanticless.html">here</a>.
4863462b8ff0 new version
Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   194
  This work appeared in the Proceedings of the International Conference on Automated Deduction (CADE 2019).  
402
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   195
633
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Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   196
<li>
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Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   197
  <A HREF="https://www.isa-afp.org/authors/brun">Matthias Brun</A> and
4863462b8ff0 new version
Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   198
  <A HREF="https://traytel.bitbucket.io/">Dmitriy Traytel</A> formalised
4863462b8ff0 new version
Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   199
  Generic Authenticated Data Structures using Nominal Isabelle.
4863462b8ff0 new version
Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   200
  The AFP entry is <a href="https://www.isa-afp.org/entries/LambdaAuth.html">here</a>.
4863462b8ff0 new version
Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   201
  This work appeared in the Proceedings of International Conference on Interactive Theorem Proving (ITP 2019).
402
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   202
633
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Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   203
<li>
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Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   204
  <A HREF="https://www.isa-afp.org/authors/brun">Matthias Brun</A> and
4863462b8ff0 new version
Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   205
  <A HREF="https://traytel.bitbucket.io/">Dmitriy Traytel</A> formalised
4863462b8ff0 new version
Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   206
  Generic Authenticated Data Structures using Nominal Isabelle.
4863462b8ff0 new version
Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   207
  The AFP entry is <a href="https://www.isa-afp.org/entries/Modal_Logics_for_NTS.html">here</a>.
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Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   208
  This work appeared in the Proceedings of the International Conference on Concurrency Theory (CONCUR 2015).  
4863462b8ff0 new version
Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   209
</ul>
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Christian Urban <christian.urban@kcl.ac.uk>
parents: 628
diff changeset
   210
</P>
402
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   211
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   212
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   213
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   214
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   215
</TABLE>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   216
</CENTER>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   217
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   218
<P>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   219
<a href="http://validator.w3.org/check/referer" target="_top">[Validate this page.]</a>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   220
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff changeset
   221
</body>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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   222
</html>