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