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<HTML lang=en>
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<HEAD>
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<TITLE> Christian Urban </TITLE>
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<BASE HREF="http://www4.in.tum.de/~urbanc/">
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</HEAD>
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<BODY TEXT="#000000"
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BGCOLOR="#000080"
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LINK="#0000EF"
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VLINK="#51188E"
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ALINK="#FF0000">
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<TABLE WIDTH="100%"
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COLS="2"
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BGCOLOR="#000080"
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BORDER="0"
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FRAME="none"
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CELLPADDING="10"
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CELLSPACING="2"
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RULES="COLS,ROWS">
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<!-- left column -->
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<TR>
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<TD BGCOLOR="#FFFFFF"
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WIDTH="24%"
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VALIGN="TOP"
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ROWSPAN="2">
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<B>Links</B><BR>
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<A HREF="http://www4.in.tum.de/~urbanc/index.html">Home</A><BR>
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<A HREF="http://www4.in.tum.de/~urbanc/Cut/cutapplet.html">Applet Home</A><BR><BR>
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<B>Java Versions</B><BR>
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<A HREF="http://www4.in.tum.de/~urbanc/Cut/CL.html">CL</A><BR>
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<A HREF="http://www4.in.tum.de/~urbanc/Cut/LJT.html">LJT</A><BR>
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<A HREF="http://www4.in.tum.de/~urbanc/Cut/ND.html">ND</A><BR><BR>
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<B>Plugin Versions</B><BR>
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<A HREF="http://www4.in.tum.de/~urbanc/Cut/CL-plugin.html">CL</A><BR>
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<A HREF="http://www4.in.tum.de/~urbanc/Cut/LJT-plugin.html">LJT</A><BR>
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<A HREF="http://www4.in.tum.de/~urbanc/Cut/ND-plugin.html">ND</A><BR>
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<BR>
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<BR>
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<A HREF="http://isabelle.in.tum.de/nominal/">
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<IMG SRC="ribbon.gif" ALT="" style="width: 114px; height: 100px;" align="left">
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</A>
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</TD>
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<!-- right column -->
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<TD BGCOLOR="#FFFFFF" WIDTH="75%">
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<A NAME="Home"></A>
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<H2>Applet for Cut-Elimination and Normalisation </H2>
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<FONT COLOR="#800000"><B>Warning:</B></FONT>
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These pages are still under construction and designed for the conoscenti
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only. If you encounter any problems, email me. Some general information
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about the applet is given below.<p>
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The applet is outcome of my interest in cut-elimination. It helps to
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explore reduction trees in a slight variant of the sequent calculus LK,
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and also reduction trees in Herbelin's calculus LJT (as presented
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<A HREF="http://www-theory.dcs.st-and.ac.uk/~rd/publications/MJES/">here</A>)
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and in the standard formulation of natural deduction for intuitionistic
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logic. Given for example the following classical sequent proof<p>
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<center>
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<IMG SRC="Cut/ex1.jpg" ALT="" ALIGN=CENTER>
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</center><p>
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you can produce by simply pressing the buttons L and R the following
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two cut-free proofs.<p>
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<center>
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<IMG SRC="Cut/ex2.jpg" ALT="" ALIGN=CENTER>
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<IMG SRC="Cut/ex3.jpg" ALT="" ALIGN=CENTER>
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</center><p>
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If you ever have done cut-elimination by hand, then you
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know how useful this applet is.<p>
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<img ALIGN=BOTTOM ALT="" SRC="new.gif"> The applet is particularly useful for doing
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some calculations finding out what the (proof-theoretical) semantics for classical logic
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should look like. Some informal notes are
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<A HREF="http://www4.in.tum.de/~urbanc/Cut/notes.html">here</A>.
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<p>
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The applet needs at least <B>Java 1.2</B> including the
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<B>Swing</B> libraries. Some browsers support these requirements
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directly, and if you are one of the lucky to have such a browser
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you can access the three calculi by pressing on one of the
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following links.
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<UL>
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<LI><A HREF="http://www4.in.tum.de/~urbanc/Cut/CL.html">CL - cut-elimination
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in classical logic</A>
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<LI><A HREF="http://www4.in.tum.de/~urbanc/Cut/LJT.html">LJT - cut-elimination in
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intuitionistic logic</A>
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<LI><A HREF="http://www4.in.tum.de/~urbanc/Cut/ND.html">ND - normalisation in
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intuitionistic natural deduction</A><p>
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</UL><p>
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If not, then your browser can most probably run the applet with
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the help of a Java plugin. In this case follow the links below.
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<UL>
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<LI><A HREF="http://www4.in.tum.de/~urbanc/Cut/CL-plugin.html">CL - cut-elimination
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in classical logic</A>
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<LI><A HREF="http://www4.in.tum.de/~urbanc/Cut/LJT-plugin.html">LJT - cut-elimination in
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intuitionistic logic</A>
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<LI><A HREF="http://www4.in.tum.de/~urbanc/Cut/ND-plugin.html">ND - normalisation in
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intuitionistic natural deduction</A><p>
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</UL><p>
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<TR>
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<TD BGCOLOR="#FFFFFF" WIDTH="75%">
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For the curious: the applet is written in MLJ, which is being
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developed by
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<A HREF="http://research.microsoft.com/~nick/">Benton</A>,
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<A HREF="http://research.microsoft.com/~akenn/">Kennedy</A> and
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<A HREF="http://research.microsoft.com/~crusso/">Russo</A>.
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MLJ is a dialect of SML that provides access to Java libraries; in my
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opinion it is a really nifty language! I am using an improved version of
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the MLJ-0.2 compiler.
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</TD>
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</TR>
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</TABLE>
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<P><!-- Created: Tue Jul 3 21:01:42 BST 2001 -->
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<!-- hhmts start -->
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Last modified: Sat Mar 3 05:16:36 CET 2007
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<!-- hhmts end -->
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</BODY>
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</HTML>
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