<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 conoscenti+ −
only. If you encounter any problems, email me. Some general information+ −
about 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 being+ −
developed 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>+ −