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Cut/cutapplet.html
author Christian Urban <urbanc@in.tum.de>
Tue, 30 Jul 2019 11:18:37 +0100
changeset 584 711958b67779
parent 98 e10eb390c103
permissions -rw-r--r--
updated

<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">

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<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>


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<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>
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