Cut/LJT.html
author Christian Urban <christian.urban@kcl.ac.uk>
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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/Cut/">
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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="4">
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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><p>
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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>Cut-Elimination in Herbelin's calculus for intuitionistic logic</H2>
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Recommended reading for this applet is a paper by Dyckhoff and Urban, 
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[<A HREF="http://www-theory.dcs.st-and.ac.uk/~rd/publications/MJES/DyckhoffUrbanWestApp01.rev.ps">ps</A>,
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 <A HREF="http://www-theory.dcs.st-and.ac.uk/~rd/publications/MJES/DyckhoffUrbanWestApp01.rev.pdf">pdf</A>].
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Mayor difference between the standard sequent calculus and Herbelin's sequent calculus 
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is that in the cut-free fragment "there are no semantically 
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trivial permutations of the inference rules, where by 'semantically trivial' we mean 
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'interpreted in NJ as true equations between to (normal) deductions'" 
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(from [<A HREF="http://www-theory.dcs.st-and.ac.uk/~rd/publications/SLPaper.corr.ps">ps</A>]). 
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</TD>
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</TR>
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<TR>
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<TD BGCOLOR="#FFFFFF" WIDTH="75%">
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<B>How to use it?</B>&nbsp;
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If your browser is working correctly, then you will see a window 
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with two examples (more added if you suggest some). When pressing on 
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one of the buttons, a new window will pop up. What follows 
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is a brief explanation of all the features available in this window. 
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</TD>
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</TR>
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<TR>
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<TD BGCOLOR="#FFFFFF" WIDTH="75%">
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<B>Buttons and Keys</B>
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<UL>
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<LI> The buttons 
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     &nbsp;&nbsp;&nbsp;<IMG SRC="http://www4.in.tum.de/~urbanc/Cut/x.jpg">&nbsp;&nbsp;&nbsp;
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     `fire' cuts (not all cuts necessarily have such buttons). 
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<LI> If you use the <B>left mouse button</B> for pressing on those buttons,
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     then the new proof will appear inside the window. Whereas if you use 
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     the <B>right mouse button</B>, a new window will pop up and  
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     the new proof will be displayed in this window. Use the right mouse 
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     button if you want to compare a proof and its reduct.
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<LI> The keys <B>Page-up</B> and <B>Page-down</B> zoom in or out of a proof
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     respectively. 
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</UL>
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</TD>
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</TR>
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<TR>
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<TD BGCOLOR="#FFFFFF"  WIDTH="75%">
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<B>Menu Functions</B>
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<UL>
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<LI> <B>Zoom in</B> and <B>Zoom out</B> work like Page-up and Page-down, 
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     respectively.
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<LI> <B>Unicode</B>&nbsp; If this radiobutton is switched on, logic symbols 
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     are displayed in unicode, otherwise in ascii. (This is for the 
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     poor guys who have a browser and/or operating system which cannot handle 
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     unicode.)
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<LI> <B>Labels</B>&nbsp; As mentioned earlier the sequents are composed of 
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     two sets of labelled 
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     formulae, not multisets of formulae as in the standard formulation 
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     of sequent calculus. Enabling this radiobutton causes that labels are 
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     drawn. Use this when you are unsure where implicit contractions are. 
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<LI> <B>Compact printing</B>&nbsp; In the paper referred above weakening
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     is done only in axioms. If this radiobutton is switched on (default),
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     then, in order to save space, formulae are weakened as soon as possible.
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</UL> 
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</TD>
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</TR>
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</TABLE>
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<center>
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<applet archive=MyApplet.zip code="MyApplet.class" width=1 height=1>
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<param name="calculi" value="B">
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<p><blink><FONT COLOR="#800000">
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Applet should appear in a new window, but you don't have Java enabled in your browser.
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</FONT></blink><p>
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</applet>
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</center>
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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 05:17:09 CET 2007
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<!-- hhmts end -->
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</BODY>
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</HTML>