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Train Tables - Revision history
2024-03-28T09:18:32Z
Revision history for this page on the wiki
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http://wiki.nars2000.org/index.php?title=Train_Tables&diff=450&oldid=prev
WikiSysop: /* Tables */
2009-03-05T21:57:29Z
<p><span dir="auto"><span class="autocomment">Tables</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 21:57, 5 March 2009</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> g L (⊢ g)⍨</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> g L (⊢ g)⍨</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> R g R (⊢ g ⊢) (⊢ g⍨)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> R g R (⊢ g ⊢) (⊢ g⍨)</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> R g L (⊢ <del style="font-weight: bold; text-decoration: none;">g ⊣</del>) <del style="font-weight: bold; text-decoration: none;"> </del>(g <del style="font-weight: bold; text-decoration: none;">⊢</del>)<del style="font-weight: bold; text-decoration: none;">⍨</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> R g L <ins style="font-weight: bold; text-decoration: none;">g⍨ </ins>(<ins style="font-weight: bold; text-decoration: none;">g </ins>⊢)<ins style="font-weight: bold; text-decoration: none;">⍨ </ins>(<ins style="font-weight: bold; text-decoration: none;">⊢ </ins>g <ins style="font-weight: bold; text-decoration: none;">⊣</ins>)</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> L g L (⊣ g ⊣)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> L g L (⊣ g ⊣)</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> L g R (g ⊢)</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> L g R <ins style="font-weight: bold; text-decoration: none;">g </ins>(g ⊢)</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Other <apll>LgR</apll> forms using <apll>g</apll> twice may be obtained from <apll>LghR</apll> below.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Other <apll>LgR</apll> forms using <apll>g</apll> twice may be obtained from <apll>LghR</apll> below.</div></td></tr>
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WikiSysop
http://wiki.nars2000.org/index.php?title=Train_Tables&diff=449&oldid=prev
WikiSysop: /* Further Study */
2009-03-05T21:24:33Z
<p><span dir="auto"><span class="autocomment">Further Study</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 21:24, 5 March 2009</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Further Study==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Further Study==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>If you want to better understand this feature, the following [http://www.nars2000.org/download/workspaces/trains.ws.nars workspace] might be helpful. It contains functions to aid in understanding Trains such that you can enter a Train (say) <apll>L (f g h ⊢) R</apll> and it'll output the equivalent expression <apll><del style="font-weight: bold; text-decoration: none;">(</del>L f <del style="font-weight: bold; text-decoration: none;">(</del>(g R) h R<del style="font-weight: bold; text-decoration: none;">))</del></apll>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>If you want to better understand this feature, the following [http://www.nars2000.org/download/workspaces/trains.ws.nars workspace] might be helpful. It contains functions to aid in understanding Trains such that you can enter a Train (say) <apll>L (f g h ⊢) R</apll> and it'll output the equivalent expression <apll>L f (g R) h R</apll>.</div></td></tr>
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WikiSysop
http://wiki.nars2000.org/index.php?title=Train_Tables&diff=448&oldid=prev
WikiSysop at 23:30, 4 March 2009
2009-03-04T23:30:09Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:30, 4 March 2009</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td>
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<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==Introduction==</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The following tables list many possible expressions involving one or two arguments and one or more functions, along with their corresponding Train. These entries may be used to construct the Train which corresponds to more complicated expressions. For example, the expression</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The following tables list many possible expressions involving one or two arguments and one or more functions, along with their corresponding Train. These entries may be used to construct the Train which corresponds to more complicated expressions. For example, the expression</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>may be expressed as a Train as follows:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>may be expressed as a Train as follows:</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><apll><del style="font-weight: bold; text-decoration: none;">&nbsp;&nbsp;&nbsp;</del>L e (L f R) g L h R</apll><<del style="font-weight: bold; text-decoration: none;">br </del>/></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">{| border="0"</ins></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><apll><del style="font-weight: bold; text-decoration: none;">←→ </del>L e L (f g h) R</apll> <del style="font-weight: bold; text-decoration: none;">from </del>the definition of Dyadic Fork<<del style="font-weight: bold; text-decoration: none;">br </del>/></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">| || </ins><apll>L e (L f R) g L h R</apll></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><apll><del style="font-weight: bold; text-decoration: none;">←→ </del>L (⊣ e (f g h)) R</apll> <del style="font-weight: bold; text-decoration: none;">from </del>the <del style="font-weight: bold; text-decoration: none;">form </del>for <apll>L g L h R</apll><del style="font-weight: bold; text-decoration: none;"><br /></del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|-</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|<apll>←→</ins></<ins style="font-weight: bold; text-decoration: none;">apll</ins>> <ins style="font-weight: bold; text-decoration: none;">|| </ins><apll>L e L (f g h) R</apll> <ins style="font-weight: bold; text-decoration: none;"> || &nbsp;&nbsp;&nbsp; || using </ins>the definition of Dyadic Fork</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|-</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|<apll>←→</ins></<ins style="font-weight: bold; text-decoration: none;">apll</ins>> <ins style="font-weight: bold; text-decoration: none;">|| </ins><apll>L (⊣ e (f g h)) R</apll> <ins style="font-weight: bold; text-decoration: none;">|| &nbsp;&nbsp;&nbsp; || using </ins>the <ins style="font-weight: bold; text-decoration: none;">Train </ins>for <apll>L g L h R</apll></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|}</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==Tables==</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><apll>gR:</apll><br /></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><apll>gR:</apll><br /></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"> </del>g R g</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"> </ins>g R g</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"> </del>R g R (g ⊢)</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"> </ins>R g R (g ⊢)</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Other <apll>gR</apll> forms using <apll>g</apll> twice may be obtained from <apll>ghR</apll> below.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Other <apll>gR</apll> forms using <apll>g</apll> twice may be obtained from <apll>ghR</apll> below.</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l71">Line 71:</td>
<td colspan="2" class="diff-lineno">Line 79:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> (L f R) g L h R (f g h) Dyadic Fork</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> (L f R) g L h R (f g h) Dyadic Fork</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==Further Study==</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">If you want to better understand this feature, the following [http://www.nars2000.org/download/workspaces/trains.ws.nars workspace] might be helpful. It contains functions to aid in understanding Trains such that you can enter a Train (say) <apll>L (f g h ⊢) R</apll> and it'll output the equivalent expression <apll>(L f ((g R) h R))</apll>.</ins></div></td></tr>
</table>
WikiSysop
http://wiki.nars2000.org/index.php?title=Train_Tables&diff=445&oldid=prev
WikiSysop: TrainList moved to Train Tables
2009-03-04T22:19:53Z
<p><a href="/index.php?title=TrainList" class="mw-redirect" title="TrainList">TrainList</a> moved to <a href="/index.php?title=Train_Tables" title="Train Tables">Train Tables</a></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<tr class="diff-title" lang="en">
<td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 22:19, 4 March 2009</td>
</tr><tr><td colspan="2" class="diff-notice" lang="en"><div class="mw-diff-empty">(No difference)</div>
</td></tr></table>
WikiSysop
http://wiki.nars2000.org/index.php?title=Train_Tables&diff=442&oldid=prev
WikiSysop: New page: The following tables list many possible expressions involving one or two arguments and one or more functions, along with their corresponding Train. These entries may be used to construct ...
2009-03-04T19:42:51Z
<p>New page: The following tables list many possible expressions involving one or two arguments and one or more functions, along with their corresponding Train. These entries may be used to construct ...</p>
<p><b>New page</b></p><div>The following tables list many possible expressions involving one or two arguments and one or more functions, along with their corresponding Train. These entries may be used to construct the Train which corresponds to more complicated expressions. For example, the expression<br />
<br />
<apll>L e (L f R) g L h R</apll><br />
<br />
may be expressed as a Train as follows:<br />
<br />
<apll>&nbsp;&nbsp;&nbsp;L e (L f R) g L h R</apll><br /><br />
<apll>←→ L e L (f g h) R</apll> from the definition of Dyadic Fork<br /><br />
<apll>←→ L (⊣ e (f g h)) R</apll> from the form for <apll>L g L h R</apll><br /><br />
<br />
<apll>gR:</apll><br /><br />
<br />
g R g<br />
R g R (g ⊢)<br />
<br />
Other <apll>gR</apll> forms using <apll>g</apll> twice may be obtained from <apll>ghR</apll> below.<br />
<br />
<apll>LgR:</apll><br /><br />
<br />
L (⊣ ⊣)<br />
R (⊢ ⊢)<br />
g R (⊢ g)<br />
g L (⊢ g)⍨<br />
R g R (⊢ g ⊢) (⊢ g⍨)<br />
R g L (⊢ g ⊣) (g ⊢)⍨<br />
L g L (⊣ g ⊣)<br />
L g R (g ⊢)<br />
<br />
Other <apll>LgR</apll> forms using <apll>g</apll> twice may be obtained from <apll>LghR</apll> below.<br />
<br />
<apll>ghR:</apll><br /><br />
<br />
g h R ((⊢ g) h)<br />
R g h R (g h) Monadic Hook<br />
g R h R ((⊢ g) (h ⊢))<br />
(g R) h R (g h ⊢) (h⍨ g)<br />
R g R h R (g (h ⊢))<br />
(R g R) h R ((g ⊢) h ⊢)<br />
<br />
<apll>LghR:</apll><br /><br />
<br />
g h R ((⊢ g) h)<br />
g L h R (⊢ (⊢ g) h)<br />
(g L) h R (h⍨ g)⍨<br />
L g h L (⊣ g (⊢ h)⍨)<br />
L g h R (g h) Dyadic Hook<br />
R g h R (⊢ g (⊢ h))<br />
R g h L (g h)⍨<br />
L g L h L (⊣ g ⊣ h ⊣)<br />
L g L h R (⊣ g h)<br />
L g R h L (⊢ g h)⍨<br />
L g R h R (g (h ⊢))<br />
R g L h L (g (h ⊢))⍨<br />
R g L h R (⊢ g h)<br />
R g R h L (⊣ g h)⍨<br />
R g R h R (⊢ g ⊢ h ⊢)<br />
(L g L) h L ((⊢ g⍨) h ⊢)⍨<br />
(L g L) h R (h⍨ (g ⊢))⍨<br />
(L g R) h L (g h ⊣)<br />
(L g R) h R (g h ⊢)<br />
(R g L) h L (g h ⊢)⍨<br />
(R g L) h R (g h ⊣)⍨<br />
(R g R) h L (h⍨ (g ⊢))<br />
(R g R) h R ((⊢ g⍨) h ⊢)<br />
<br />
<apll>fghR:</apll><br /><br />
<br />
(f R) g h R (f g h) Monadic Fork<br />
<br />
<apll>LfghR:</apll><br /><br />
<br />
(L f R) g L h R (f g h) Dyadic Fork</div>
WikiSysop