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1 <HTML lang=en> |
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2 <HEAD> |
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3 <TITLE> Christian Urban </TITLE> |
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4 <BASE HREF="http://www4.in.tum.de/~urbanc/"> |
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5 </HEAD> |
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6 |
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7 <BODY TEXT="#000000" |
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13 <TABLE WIDTH="100%" |
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21 |
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22 <!-- left column --> |
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23 <TR> |
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24 <TD BGCOLOR="#FFFFFF" |
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25 WIDTH="24%" |
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26 VALIGN="TOP" |
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27 ROWSPAN="2"> |
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28 |
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29 <B>Links</B><BR> |
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30 <A HREF="http://www4.in.tum.de/~urbanc/index.html">Home</A><BR> |
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31 <A HREF="http://www4.in.tum.de/~urbanc/Cut/cutapplet.html">Applet Home</A><BR><BR> |
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32 |
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33 <B>Java Versions</B><BR> |
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34 <A HREF="http://www4.in.tum.de/~urbanc/Cut/CL.html">CL</A><BR> |
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35 <A HREF="http://www4.in.tum.de/~urbanc/Cut/LJT.html">LJT</A><BR> |
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36 <A HREF="http://www4.in.tum.de/~urbanc/Cut/ND.html">ND</A><BR><BR> |
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37 |
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38 <B>Plugin Versions</B><BR> |
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39 <A HREF="http://www4.in.tum.de/~urbanc/Cut/CL-plugin.html">CL</A><BR> |
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40 <A HREF="http://www4.in.tum.de/~urbanc/Cut/LJT-plugin.html">LJT</A><BR> |
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41 <A HREF="http://www4.in.tum.de/~urbanc/Cut/ND-plugin.html">ND</A><BR> |
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42 |
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43 <BR> |
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44 <BR> |
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45 |
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46 <A HREF="http://isabelle.in.tum.de/nominal/"> |
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47 <IMG SRC="ribbon.gif" ALT="" style="width: 114px; height: 100px;" align="left"> |
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48 </A> |
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49 </TD> |
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50 |
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51 |
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52 <!-- right column --> |
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53 <TD BGCOLOR="#FFFFFF" WIDTH="75%"> |
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54 <A NAME="Home"></A> |
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55 <H2>Applet for Cut-Elimination and Normalisation </H2> |
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56 |
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57 <FONT COLOR="#800000"><B>Warning:</B></FONT> |
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58 These pages are still under construction and designed for the conoscenti |
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59 only. If you encounter any problems, email me. Some general information |
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60 about the applet is given below.<p> |
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61 |
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62 The applet is outcome of my interest in cut-elimination. It helps to |
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63 explore reduction trees in a slight variant of the sequent calculus LK, |
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64 and also reduction trees in Herbelin's calculus LJT (as presented |
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65 <A HREF="http://www-theory.dcs.st-and.ac.uk/~rd/publications/MJES/">here</A>) |
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66 and in the standard formulation of natural deduction for intuitionistic |
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67 logic. Given for example the following classical sequent proof<p> |
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68 |
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69 <center> |
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70 <IMG SRC="Cut/ex1.jpg" ALT="" ALIGN=CENTER> |
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71 </center><p> |
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72 |
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73 you can produce by simply pressing the buttons L and R the following |
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74 two cut-free proofs.<p> |
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75 |
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76 <center> |
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77 <IMG SRC="Cut/ex2.jpg" ALT="" ALIGN=CENTER> |
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78 <IMG SRC="Cut/ex3.jpg" ALT="" ALIGN=CENTER> |
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79 </center><p> |
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80 |
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81 If you ever have done cut-elimination by hand, then you |
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82 know how useful this applet is.<p> |
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83 |
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84 <img ALIGN=BOTTOM ALT="" SRC="new.gif"> The applet is particularly useful for doing |
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85 some calculations finding out what the (proof-theoretical) semantics for classical logic |
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86 should look like. Some informal notes are |
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87 <A HREF="http://www4.in.tum.de/~urbanc/Cut/notes.html">here</A>. |
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88 <p> |
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89 |
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90 |
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91 The applet needs at least <B>Java 1.2</B> including the |
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92 <B>Swing</B> libraries. Some browsers support these requirements |
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93 directly, and if you are one of the lucky to have such a browser |
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94 you can access the three calculi by pressing on one of the |
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95 following links. |
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96 |
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97 <UL> |
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98 <LI><A HREF="http://www4.in.tum.de/~urbanc/Cut/CL.html">CL - cut-elimination |
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99 in classical logic</A> |
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100 <LI><A HREF="http://www4.in.tum.de/~urbanc/Cut/LJT.html">LJT - cut-elimination in |
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101 intuitionistic logic</A> |
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102 <LI><A HREF="http://www4.in.tum.de/~urbanc/Cut/ND.html">ND - normalisation in |
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103 intuitionistic natural deduction</A><p> |
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104 </UL><p> |
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105 |
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106 If not, then your browser can most probably run the applet with |
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107 the help of a Java plugin. In this case follow the links below. |
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108 |
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109 <UL> |
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110 <LI><A HREF="http://www4.in.tum.de/~urbanc/Cut/CL-plugin.html">CL - cut-elimination |
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111 in classical logic</A> |
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112 <LI><A HREF="http://www4.in.tum.de/~urbanc/Cut/LJT-plugin.html">LJT - cut-elimination in |
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113 intuitionistic logic</A> |
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114 <LI><A HREF="http://www4.in.tum.de/~urbanc/Cut/ND-plugin.html">ND - normalisation in |
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115 intuitionistic natural deduction</A><p> |
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116 </UL><p> |
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117 |
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118 <TR> |
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119 <TD BGCOLOR="#FFFFFF" WIDTH="75%"> |
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120 For the curious: the applet is written in MLJ, which is being |
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121 developed by |
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122 <A HREF="http://research.microsoft.com/~nick/">Benton</A>, |
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123 <A HREF="http://research.microsoft.com/~akenn/">Kennedy</A> and |
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124 <A HREF="http://research.microsoft.com/~crusso/">Russo</A>. |
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125 MLJ is a dialect of SML that provides access to Java libraries; in my |
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126 opinion it is a really nifty language! I am using an improved version of |
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127 the MLJ-0.2 compiler. |
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128 </TD> |
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129 </TR> |
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130 |
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131 </TABLE> |
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132 <P><!-- Created: Tue Jul 3 21:01:42 BST 2001 --> |
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133 <!-- hhmts start --> |
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134 Last modified: Sat Mar 3 05:16:36 CET 2007 |
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137 </HTML> |