https://aplwiki.com/index.php?title=Leading_axis_theory&feed=atom&action=history
Leading axis theory - Revision history
2024-03-29T15:23:35Z
Revision history for this page on the wiki
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https://aplwiki.com/index.php?title=Leading_axis_theory&diff=9330&oldid=prev
Adám Brudzewsky: Text replacement - "</source>" to "</syntaxhighlight>"
2022-09-10T21:46:13Z
<p>Text replacement - "</source>" to "</syntaxhighlight>"</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 21:46, 10 September 2022</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l5">Line 5:</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>The leading axis theory as a complete model of programming is best exemplified by [[J]], since it was designed entirely using the theory from the start. While various APLs have developed or adopted features of the leading axis model, [[backwards compatibility]] requirements can prevent them from making certain changes to align with the theory.</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 leading axis theory as a complete model of programming is best exemplified by [[J]], since it was designed entirely using the theory from the start. While various APLs have developed or adopted features of the leading axis model, [[backwards compatibility]] requirements can prevent them from making certain changes to align with the theory.</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>J defines all one-dimensional functions to work on the first [[axis]], that is, to manipulate [[major cell]]s of their arguments. In this way it unifies APL's pairs of first- and last-axis functions and operators including [[Reverse]], [[Rotate]], [[Replicate]], [[Expand]], [[Reduce]], and [[Scan]]. J retains two functions corresponding to <syntaxhighlight lang=apl inline>,</<del style="font-weight: bold; text-decoration: none;">source</del>> and <syntaxhighlight lang=apl inline>⍪</<del style="font-weight: bold; text-decoration: none;">source</del>>, with <syntaxhighlight lang=j inline>,</<del style="font-weight: bold; text-decoration: none;">source</del>> as [[Ravel]] and [[Catenate First]] and <syntaxhighlight lang=j inline>,.</<del style="font-weight: bold; text-decoration: none;">source</del>> for second- (rather than last-) axis forms of these functions; <syntaxhighlight lang=j inline>,.</<del style="font-weight: bold; text-decoration: none;">source</del>> is identical to <syntaxhighlight lang=j inline>,"_1</<del style="font-weight: bold; text-decoration: none;">source</del>> (which transliterates to APL <syntaxhighlight lang=apl inline>,⍤¯1</<del style="font-weight: bold; text-decoration: none;">source</del>>) in both valences.</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>J defines all one-dimensional functions to work on the first [[axis]], that is, to manipulate [[major cell]]s of their arguments. In this way it unifies APL's pairs of first- and last-axis functions and operators including [[Reverse]], [[Rotate]], [[Replicate]], [[Expand]], [[Reduce]], and [[Scan]]. J retains two functions corresponding to <syntaxhighlight lang=apl inline>,</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>> and <syntaxhighlight lang=apl inline>⍪</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>, with <syntaxhighlight lang=j inline>,</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>> as [[Ravel]] and [[Catenate First]] and <syntaxhighlight lang=j inline>,.</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>> for second- (rather than last-) axis forms of these functions; <syntaxhighlight lang=j inline>,.</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>> is identical to <syntaxhighlight lang=j inline>,"_1</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>> (which transliterates to APL <syntaxhighlight lang=apl inline>,⍤¯1</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>) in both valences.</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>J also extends [[Rotate]] so that it can work on multiple leading axes rather than a single axis: additional values in the left argument apply to leading axes of the right in order. This aligns Rotate with the [[SHARP APL]] extensions to [[Take]], [[Drop]], and [[Squad]] allowing short left arguments: in each case the left argument is a [[vector]] corresponding to axes of the right argument starting at the first.</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>J also extends [[Rotate]] so that it can work on multiple leading axes rather than a single axis: additional values in the left argument apply to leading axes of the right in order. This aligns Rotate with the [[SHARP APL]] extensions to [[Take]], [[Drop]], and [[Squad]] allowing short left arguments: in each case the left argument is a [[vector]] corresponding to axes of the right argument starting at the first.</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l20">Line 20:</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>! Compatibility !! Functions</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>! Compatibility !! Functions</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>|-</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>|-</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>| Already compatible || [[Grade]] (<syntaxhighlight lang=apl inline>⍋</<del style="font-weight: bold; text-decoration: none;">source</del>>, <syntaxhighlight lang=apl inline>⍒</<del style="font-weight: bold; text-decoration: none;">source</del>>), [[Decode]] (<syntaxhighlight lang=apl inline>⊥</<del style="font-weight: bold; text-decoration: none;">source</del>>), [[Encode]] (<syntaxhighlight lang=apl inline>⊤</<del style="font-weight: bold; text-decoration: none;">source</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>| Already compatible || [[Grade]] (<syntaxhighlight lang=apl inline>⍋</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>, <syntaxhighlight lang=apl inline>⍒</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>), [[Decode]] (<syntaxhighlight lang=apl inline>⊥</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>), [[Encode]] (<syntaxhighlight lang=apl inline>⊤</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</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>|-</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>|-</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>| Use first axis form only || [[Reverse]], [[Rotate]] (<syntaxhighlight lang=apl inline>⊖</<del style="font-weight: bold; text-decoration: none;">source</del>>), [[Replicate]], [[Reduce]] (<syntaxhighlight lang=apl inline>⌿</<del style="font-weight: bold; text-decoration: none;">source</del>>), [[Expand]], [[Scan]] (<syntaxhighlight lang=apl inline>⍀</<del style="font-weight: bold; text-decoration: none;">source</del>>), [[Catenate]] (<syntaxhighlight lang=apl inline>⍪</<del style="font-weight: bold; text-decoration: none;">source</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>| Use first axis form only || [[Reverse]], [[Rotate]] (<syntaxhighlight lang=apl inline>⊖</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>), [[Replicate]], [[Reduce]] (<syntaxhighlight lang=apl inline>⌿</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>), [[Expand]], [[Scan]] (<syntaxhighlight lang=apl inline>⍀</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>), [[Catenate]] (<syntaxhighlight lang=apl inline>⍪</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</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>|-</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>|-</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>| Extendible to leading axes || [[Take]] (<syntaxhighlight lang=apl inline>↑</<del style="font-weight: bold; text-decoration: none;">source</del>>), [[Drop]] (<syntaxhighlight lang=apl inline>↓</<del style="font-weight: bold; text-decoration: none;">source</del>>), [[Squad Indexing]] (<syntaxhighlight lang=apl inline>⌷</<del style="font-weight: bold; text-decoration: none;">source</del>>), [[scalar dyadic]]s, [[Unique]] (<syntaxhighlight lang=apl inline>∪</<del style="font-weight: bold; text-decoration: none;">source</del>> or <syntaxhighlight lang=apl inline>↑</<del style="font-weight: bold; text-decoration: none;">source</del>>) and most [[set function]]s (<syntaxhighlight lang=apl inline>⍳∪∩~</<del style="font-weight: bold; text-decoration: none;">source</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>| Extendible to leading axes || [[Take]] (<syntaxhighlight lang=apl inline>↑</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>), [[Drop]] (<syntaxhighlight lang=apl inline>↓</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>), [[Squad Indexing]] (<syntaxhighlight lang=apl inline>⌷</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>), [[scalar dyadic]]s, [[Unique]] (<syntaxhighlight lang=apl inline>∪</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>> or <syntaxhighlight lang=apl inline>↑</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>) and most [[set function]]s (<syntaxhighlight lang=apl inline>⍳∪∩~</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</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>|-</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>|-</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>| Incompatible || [[Split]] (<syntaxhighlight lang=apl inline>↓</<del style="font-weight: bold; text-decoration: none;">source</del>>), [[First]] (<syntaxhighlight lang=apl inline>↑</<del style="font-weight: bold; text-decoration: none;">source</del>> or <syntaxhighlight lang=apl inline>⊃</<del style="font-weight: bold; text-decoration: none;">source</del>>), [[Membership]] (<syntaxhighlight lang=apl inline>∊</<del style="font-weight: bold; text-decoration: none;">source</del>>), [[Partition]] (<syntaxhighlight lang=apl inline>⊂</<del style="font-weight: bold; text-decoration: none;">source</del>> and <syntaxhighlight lang=apl inline>⊆</<del style="font-weight: bold; text-decoration: none;">source</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>| Incompatible || [[Split]] (<syntaxhighlight lang=apl inline>↓</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>), [[First]] (<syntaxhighlight lang=apl inline>↑</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>> or <syntaxhighlight lang=apl inline>⊃</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>), [[Membership]] (<syntaxhighlight lang=apl inline>∊</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>), [[Partition]] (<syntaxhighlight lang=apl inline>⊂</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>> and <syntaxhighlight lang=apl inline>⊆</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</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>|-</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>|-</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>| Unclear || [[Find]] (<syntaxhighlight lang=apl inline>⍷</<del style="font-weight: bold; text-decoration: none;">source</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>| Unclear || [[Find]] (<syntaxhighlight lang=apl inline>⍷</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</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>|-</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>|-</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>| Designed for leading axes || [[Rank operator]] (<syntaxhighlight lang=apl inline>⍤</<del style="font-weight: bold; text-decoration: none;">source</del>>), [[Tally]] (<syntaxhighlight lang=apl inline>≢</<del style="font-weight: bold; text-decoration: none;">source</del>>), [[Interval Index]] (<syntaxhighlight lang=apl inline>⍸</<del style="font-weight: bold; text-decoration: none;">source</del>>), [[Key]] (<syntaxhighlight lang=apl inline>⌸</<del style="font-weight: bold; text-decoration: none;">source</del>>), [[Raze]] (<syntaxhighlight lang=apl inline>⊃</<del style="font-weight: bold; text-decoration: none;">source</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>| Designed for leading axes || [[Rank operator]] (<syntaxhighlight lang=apl inline>⍤</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>), [[Tally]] (<syntaxhighlight lang=apl inline>≢</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>), [[Interval Index]] (<syntaxhighlight lang=apl inline>⍸</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>), [[Key]] (<syntaxhighlight lang=apl inline>⌸</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>), [[Raze]] (<syntaxhighlight lang=apl inline>⊃</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</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>|}</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>|}</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>|}</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>|}</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>[[Index Of]] in SHARP APL was not extended to apply to left argument [[major cell]]s as in J and Dyalog; instead it was given rank <syntaxhighlight lang=apl inline>1 0</<del style="font-weight: bold; text-decoration: none;">source</del>> making such a change impossible. In A+ not only [[Index Of]] but also [[Membership]] was changed to follow the leading axis model, breaking compatibility with other APLs. A+ also restricts [[Take]] and [[Drop]] to allow only a [[singleton]] left argument (but any right argument rank is permitted).</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>[[Index Of]] in SHARP APL was not extended to apply to left argument [[major cell]]s as in J and Dyalog; instead it was given rank <syntaxhighlight lang=apl inline>1 0</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>> making such a change impossible. In A+ not only [[Index Of]] but also [[Membership]] was changed to follow the leading axis model, breaking compatibility with other APLs. A+ also restricts [[Take]] and [[Drop]] to allow only a [[singleton]] left argument (but any right argument rank is permitted).</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>== History ==</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>== History ==</div></td></tr>
</table>
Adám Brudzewsky
https://aplwiki.com/index.php?title=Leading_axis_theory&diff=9120&oldid=prev
Adám Brudzewsky: Text replacement - "<source" to "<syntaxhighlight"
2022-09-10T20:55:57Z
<p>Text replacement - "<source" to "<syntaxhighlight"</p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 20:55, 10 September 2022</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l5">Line 5:</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>The leading axis theory as a complete model of programming is best exemplified by [[J]], since it was designed entirely using the theory from the start. While various APLs have developed or adopted features of the leading axis model, [[backwards compatibility]] requirements can prevent them from making certain changes to align with the theory.</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 leading axis theory as a complete model of programming is best exemplified by [[J]], since it was designed entirely using the theory from the start. While various APLs have developed or adopted features of the leading axis model, [[backwards compatibility]] requirements can prevent them from making certain changes to align with the theory.</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>J defines all one-dimensional functions to work on the first [[axis]], that is, to manipulate [[major cell]]s of their arguments. In this way it unifies APL's pairs of first- and last-axis functions and operators including [[Reverse]], [[Rotate]], [[Replicate]], [[Expand]], [[Reduce]], and [[Scan]]. J retains two functions corresponding to <<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>,</source> and <<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>⍪</source>, with <<del style="font-weight: bold; text-decoration: none;">source </del>lang=j inline>,</source> as [[Ravel]] and [[Catenate First]] and <<del style="font-weight: bold; text-decoration: none;">source </del>lang=j inline>,.</source> for second- (rather than last-) axis forms of these functions; <<del style="font-weight: bold; text-decoration: none;">source </del>lang=j inline>,.</source> is identical to <<del style="font-weight: bold; text-decoration: none;">source </del>lang=j inline>,"_1</source> (which transliterates to APL <<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>,⍤¯1</source>) in both valences.</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>J defines all one-dimensional functions to work on the first [[axis]], that is, to manipulate [[major cell]]s of their arguments. In this way it unifies APL's pairs of first- and last-axis functions and operators including [[Reverse]], [[Rotate]], [[Replicate]], [[Expand]], [[Reduce]], and [[Scan]]. J retains two functions corresponding to <<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>,</source> and <<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>⍪</source>, with <<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=j inline>,</source> as [[Ravel]] and [[Catenate First]] and <<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=j inline>,.</source> for second- (rather than last-) axis forms of these functions; <<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=j inline>,.</source> is identical to <<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=j inline>,"_1</source> (which transliterates to APL <<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>,⍤¯1</source>) in both valences.</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>J also extends [[Rotate]] so that it can work on multiple leading axes rather than a single axis: additional values in the left argument apply to leading axes of the right in order. This aligns Rotate with the [[SHARP APL]] extensions to [[Take]], [[Drop]], and [[Squad]] allowing short left arguments: in each case the left argument is a [[vector]] corresponding to axes of the right argument starting at the first.</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>J also extends [[Rotate]] so that it can work on multiple leading axes rather than a single axis: additional values in the left argument apply to leading axes of the right in order. This aligns Rotate with the [[SHARP APL]] extensions to [[Take]], [[Drop]], and [[Squad]] allowing short left arguments: in each case the left argument is a [[vector]] corresponding to axes of the right argument starting at the first.</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l20">Line 20:</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>! Compatibility !! Functions</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>! Compatibility !! Functions</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>|-</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>|-</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>| Already compatible || [[Grade]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>⍋</source>, <<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>⍒</source>), [[Decode]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>⊥</source>), [[Encode]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>⊤</source>)</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>| Already compatible || [[Grade]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>⍋</source>, <<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>⍒</source>), [[Decode]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>⊥</source>), [[Encode]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>⊤</source>)</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>|-</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>|-</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>| Use first axis form only || [[Reverse]], [[Rotate]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>⊖</source>), [[Replicate]], [[Reduce]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>⌿</source>), [[Expand]], [[Scan]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>⍀</source>), [[Catenate]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>⍪</source>)</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>| Use first axis form only || [[Reverse]], [[Rotate]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>⊖</source>), [[Replicate]], [[Reduce]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>⌿</source>), [[Expand]], [[Scan]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>⍀</source>), [[Catenate]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>⍪</source>)</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>|-</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>|-</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>| Extendible to leading axes || [[Take]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>↑</source>), [[Drop]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>↓</source>), [[Squad Indexing]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>⌷</source>), [[scalar dyadic]]s, [[Unique]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>∪</source> or <<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>↑</source>) and most [[set function]]s (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>⍳∪∩~</source>)</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>| Extendible to leading axes || [[Take]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>↑</source>), [[Drop]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>↓</source>), [[Squad Indexing]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>⌷</source>), [[scalar dyadic]]s, [[Unique]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>∪</source> or <<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>↑</source>) and most [[set function]]s (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>⍳∪∩~</source>)</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>|-</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>|-</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>| Incompatible || [[Split]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>↓</source>), [[First]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>↑</source> or <<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>⊃</source>), [[Membership]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>∊</source>), [[Partition]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>⊂</source> and <<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>⊆</source>)</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>| Incompatible || [[Split]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>↓</source>), [[First]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>↑</source> or <<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>⊃</source>), [[Membership]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>∊</source>), [[Partition]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>⊂</source> and <<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>⊆</source>)</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>|-</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>|-</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>| Unclear || [[Find]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>⍷</source>)</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>| Unclear || [[Find]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>⍷</source>)</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>|-</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>|-</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>| Designed for leading axes || [[Rank operator]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>⍤</source>), [[Tally]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>≢</source>), [[Interval Index]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>⍸</source>), [[Key]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>⌸</source>), [[Raze]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>⊃</source>)</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>| Designed for leading axes || [[Rank operator]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>⍤</source>), [[Tally]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>≢</source>), [[Interval Index]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>⍸</source>), [[Key]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>⌸</source>), [[Raze]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>⊃</source>)</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>|}</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>|}</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>|}</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>|}</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>[[Index Of]] in SHARP APL was not extended to apply to left argument [[major cell]]s as in J and Dyalog; instead it was given rank <<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>1 0</source> making such a change impossible. In A+ not only [[Index Of]] but also [[Membership]] was changed to follow the leading axis model, breaking compatibility with other APLs. A+ also restricts [[Take]] and [[Drop]] to allow only a [[singleton]] left argument (but any right argument rank is permitted).</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>[[Index Of]] in SHARP APL was not extended to apply to left argument [[major cell]]s as in J and Dyalog; instead it was given rank <<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>1 0</source> making such a change impossible. In A+ not only [[Index Of]] but also [[Membership]] was changed to follow the leading axis model, breaking compatibility with other APLs. A+ also restricts [[Take]] and [[Drop]] to allow only a [[singleton]] left argument (but any right argument rank is permitted).</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>== History ==</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>== History ==</div></td></tr>
</table>
Adám Brudzewsky
https://aplwiki.com/index.php?title=Leading_axis_theory&diff=7195&oldid=prev
Marshall: HOPL citation for Whitney inventing Rank
2021-08-08T13:52:17Z
<p>HOPL citation for Whitney inventing Rank</p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 13:52, 8 August 2021</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>== History ==</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>== History ==</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>Leading axis theory was first developed by employees of [[I. P. Sharp Associates]] including [[Ken Iverson]], [[Arthur Whitney]], and [[Bob Bernecky]] in the early 1980s: the [[Rank operator]] itself is attributed to Whitney, who invented it while travelling to the [[APL82]] conference. It was further developed by Iverson and [[Roger Hui]] when creating the [[J]] language in the 1990s and 2000s; the leading axis model and its various incompatibilities with APL had been a major reason to break with APL and create a new language.</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>Leading axis theory was first developed by employees of [[I. P. Sharp Associates]] including [[Ken Iverson]], [[Arthur Whitney]], and [[Bob Bernecky]] in the early 1980s: the [[Rank operator]] itself is attributed to Whitney, who invented it while travelling to the [[APL82]] conference.<ins style="font-weight: bold; text-decoration: none;"><ref>[[Roger Hui]] and [[Morten Kromberg]]. [https://dl.acm.org/doi/abs/10.1145/3386319 ''APL since 1978'']. ACM [[HOPL]] IV. 2020-06.</ref> </ins>It was further developed by Iverson and [[Roger Hui]] when creating the [[J]] language in the 1990s and 2000s; the leading axis model and its various incompatibilities with APL had been a major reason to break with APL and create a new language.</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>Leading axis theory was brought to [[Nested array theory|nested]] APLs by [[Dyalog APL]] in the 2010s after [[Dyalog Ltd.]] employed Hui. Working with [[Jay Foad]] and [[Morten Kromberg]], Hui designed and implemented versions of Rank and other J functionality compatible with Dyalog's nested arrays.</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>Leading axis theory was brought to [[Nested array theory|nested]] APLs by [[Dyalog APL]] in the 2010s after [[Dyalog Ltd.]] employed Hui. Working with [[Jay Foad]] and [[Morten Kromberg]], Hui designed and implemented versions of Rank and other J functionality compatible with Dyalog's nested arrays.</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;">== References ==</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;"><references /></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>{{APL features}}[[Category:Leading axis theory| ]]</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>{{APL features}}[[Category:Leading axis theory| ]]</div></td></tr>
</table>
Marshall
https://aplwiki.com/index.php?title=Leading_axis_theory&diff=7191&oldid=prev
Marshall: Revert changes based on APL Campfire, as it's less reliable than HOPL
2021-08-08T13:42:03Z
<p>Revert changes based on APL Campfire, as it's less reliable than HOPL</p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 13:42, 8 August 2021</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>== History ==</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>== History ==</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>Leading axis theory was first developed by <del style="font-weight: bold; text-decoration: none;">[[Arthur Whitney]] </del>of [[I. P. Sharp Associates]] <del style="font-weight: bold; text-decoration: none;">in the early 1980s. Based on this, </del>[[Ken Iverson]] <del style="font-weight: bold; text-decoration: none;">invented the </del>[[<del style="font-weight: bold; text-decoration: none;">Rank operator</del>]]<del style="font-weight: bold; text-decoration: none;">.<ref></del>[[<del style="font-weight: bold; text-decoration: none;">Gitte Christensen</del>]] <del style="font-weight: bold; text-decoration: none;">and </del>[[<del style="font-weight: bold; text-decoration: none;">Joey Tuttle</del>]] <del style="font-weight: bold; text-decoration: none;">at </del>[[<del style="font-weight: bold; text-decoration: none;">APL Campfire</del>]]. <del style="font-weight: bold; text-decoration: none;">Aug 1st, 2021.</ref> The new ideas were </del>further developed by Iverson and [[Roger Hui]] when creating the [[J]] language in the 1990s and 2000s; the leading axis model and its various incompatibilities with APL had been a major reason to break with APL and create a new language.</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>Leading axis theory was first developed by <ins style="font-weight: bold; text-decoration: none;">employees </ins>of [[I. P. Sharp Associates]] <ins style="font-weight: bold; text-decoration: none;">including </ins>[[Ken Iverson]]<ins style="font-weight: bold; text-decoration: none;">, </ins>[[<ins style="font-weight: bold; text-decoration: none;">Arthur Whitney</ins>]]<ins style="font-weight: bold; text-decoration: none;">, and </ins>[[<ins style="font-weight: bold; text-decoration: none;">Bob Bernecky</ins>]] <ins style="font-weight: bold; text-decoration: none;">in the early 1980s: the </ins>[[<ins style="font-weight: bold; text-decoration: none;">Rank operator</ins>]] <ins style="font-weight: bold; text-decoration: none;">itself is attributed to Whitney, who invented it while travelling to the </ins>[[<ins style="font-weight: bold; text-decoration: none;">APL82</ins>]] <ins style="font-weight: bold; text-decoration: none;">conference</ins>. <ins style="font-weight: bold; text-decoration: none;">It was </ins>further developed by Iverson and [[Roger Hui]] when creating the [[J]] language in the 1990s and 2000s; the leading axis model and its various incompatibilities with APL had been a major reason to break with APL and create a new language.</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>Leading axis theory was brought to [[Nested array theory|nested]] APLs by [[Dyalog APL]] in the 2010s after [[Dyalog Ltd.]] employed Hui. Working with [[Jay Foad]] and [[Morten Kromberg]], Hui designed and implemented versions of Rank and other J functionality compatible with Dyalog's nested arrays.</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>Leading axis theory was brought to [[Nested array theory|nested]] APLs by [[Dyalog APL]] in the 2010s after [[Dyalog Ltd.]] employed Hui. Working with [[Jay Foad]] and [[Morten Kromberg]], Hui designed and implemented versions of Rank and other J functionality compatible with Dyalog's nested arrays.</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;">== References ==</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> </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;"><references/></del></div></td><td colspan="2" class="diff-side-added"></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>{{APL features}}[[Category:Leading axis theory| ]]</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>{{APL features}}[[Category:Leading axis theory| ]]</div></td></tr>
</table>
Marshall
https://aplwiki.com/index.php?title=Leading_axis_theory&diff=7139&oldid=prev
Adám Brudzewsky: /* History */
2021-08-01T19:41:49Z
<p><span dir="auto"><span class="autocomment">History</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:41, 1 August 2021</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>== History ==</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>== History ==</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>Leading axis theory was first developed by [[Arthur Whitney]] of [[I. P. Sharp Associates]] in the early 1980s. Based on this, [[Ken Iverson]] invented the [[Rank operator]]. The new ideas were further developed by Iverson and [[Roger Hui]] when creating the [[J]] language in the 1990s and 2000s; the leading axis model and its various incompatibilities with APL had been a major reason to break with APL and create a new language.</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>Leading axis theory was first developed by [[Arthur Whitney]] of [[I. P. Sharp Associates]] in the early 1980s. Based on this, [[Ken Iverson]] invented the [[Rank operator]].<ins style="font-weight: bold; text-decoration: none;"><ref>[[Gitte Christensen]] and [[Joey Tuttle]] at [[APL Campfire]]. Aug 1st, 2021.</ref> </ins>The new ideas were further developed by Iverson and [[Roger Hui]] when creating the [[J]] language in the 1990s and 2000s; the leading axis model and its various incompatibilities with APL had been a major reason to break with APL and create a new language.</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>Leading axis theory was brought to [[Nested array theory|nested]] APLs by [[Dyalog APL]] in the 2010s after [[Dyalog Ltd.]] employed Hui. Working with [[Jay Foad]] and [[Morten Kromberg]], Hui designed and implemented versions of Rank and other J functionality compatible with Dyalog's nested arrays.</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>Leading axis theory was brought to [[Nested array theory|nested]] APLs by [[Dyalog APL]] in the 2010s after [[Dyalog Ltd.]] employed Hui. Working with [[Jay Foad]] and [[Morten Kromberg]], Hui designed and implemented versions of Rank and other J functionality compatible with Dyalog's nested arrays.</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> </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;">== References ==</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;"><references/></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>{{APL features}}[[Category:Leading axis theory| ]]</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>{{APL features}}[[Category:Leading axis theory| ]]</div></td></tr>
</table>
Adám Brudzewsky
https://aplwiki.com/index.php?title=Leading_axis_theory&diff=7138&oldid=prev
Adám Brudzewsky: /* History */
2021-08-01T19:40:41Z
<p><span dir="auto"><span class="autocomment">History</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:40, 1 August 2021</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>== History ==</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>== History ==</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>Leading axis theory was first developed by <del style="font-weight: bold; text-decoration: none;">employees </del>of [[I. P. Sharp Associates<del style="font-weight: bold; text-decoration: none;">]] including [[Ken Iverson]], [[Arthur Whitney]], and [[Bob Bernecky</del>]] in the early 1980s<del style="font-weight: bold; text-decoration: none;">: the </del>[[<del style="font-weight: bold; text-decoration: none;">Rank operator</del>]] <del style="font-weight: bold; text-decoration: none;">itself is attributed to Whitney, who </del>invented <del style="font-weight: bold; text-decoration: none;">it while travelling to </del>the [[<del style="font-weight: bold; text-decoration: none;">APL82</del>]] <del style="font-weight: bold; text-decoration: none;">conference</del>. <del style="font-weight: bold; text-decoration: none;">It was </del>further developed by Iverson and [[Roger Hui]] when creating the [[J]] language in the 1990s and 2000s; the leading axis model and its various incompatibilities with APL had been a major reason to break with APL and create a new language.</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>Leading axis theory was first developed by <ins style="font-weight: bold; text-decoration: none;">[[Arthur Whitney]] </ins>of [[I. P. Sharp Associates]] in the early 1980s<ins style="font-weight: bold; text-decoration: none;">. Based on this, </ins>[[<ins style="font-weight: bold; text-decoration: none;">Ken Iverson</ins>]] invented the [[<ins style="font-weight: bold; text-decoration: none;">Rank operator</ins>]]. <ins style="font-weight: bold; text-decoration: none;">The new ideas were </ins>further developed by Iverson and [[Roger Hui]] when creating the [[J]] language in the 1990s and 2000s; the leading axis model and its various incompatibilities with APL had been a major reason to break with APL and create a new language.</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>Leading axis theory was brought to [[Nested array theory|nested]] APLs by [[Dyalog APL]] in the 2010s after [[Dyalog Ltd.]] employed Hui. Working with [[Jay Foad]] and [[Morten Kromberg]], Hui designed and implemented versions of Rank and other J functionality compatible with Dyalog's nested arrays.</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>Leading axis theory was brought to [[Nested array theory|nested]] APLs by [[Dyalog APL]] in the 2010s after [[Dyalog Ltd.]] employed Hui. Working with [[Jay Foad]] and [[Morten Kromberg]], Hui designed and implemented versions of Rank and other J functionality compatible with Dyalog's nested arrays.</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>{{APL features}}[[Category:Leading axis theory| ]]</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>{{APL features}}[[Category:Leading axis theory| ]]</div></td></tr>
</table>
Adám Brudzewsky
https://aplwiki.com/index.php?title=Leading_axis_theory&diff=6463&oldid=prev
Adám Brudzewsky: /* Adoption in APL */
2021-02-20T20:01:44Z
<p><span dir="auto"><span class="autocomment">Adoption in APL</span></span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<col class="diff-marker" />
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 20:01, 20 February 2021</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>|}</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>|}</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>In addition to these, the [[Rank operator]] and [[scalar dyadic]]s can be extended with [[leading axis agreement]], so that arguments with different-length frames can <del style="font-weight: bold; text-decoration: none;">be </del>match as long as one frame is a prefix of the other. The original introduction of Rank had only an analogue of [[scalar extension]], where an argument with an empty frame is repeated to pair it with an argument with a non-empty frame. The following extensions have been made in order to support leading axis theory:</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>In addition to these, the [[Rank operator]] and [[scalar dyadic]]s can be extended with [[leading axis agreement]], so that arguments with different-length frames can match as long as one frame is a prefix of the other. The original introduction of Rank had only an analogue of [[scalar extension]], where an argument with an empty frame is repeated to pair it with an argument with a non-empty frame. The following extensions have been made in order to support leading axis theory:</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>{|class=wikitable</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>{|class=wikitable</div></td></tr>
</table>
Adám Brudzewsky
https://aplwiki.com/index.php?title=Leading_axis_theory&diff=6462&oldid=prev
Marshall: /* Adoption in APL */ Looks like SHARP doesn't use leading axis agreement; I think I misread SATN-45 originally
2021-02-19T20:02:44Z
<p><span dir="auto"><span class="autocomment">Adoption in APL: </span> Looks like SHARP doesn't use leading axis agreement; I think I misread SATN-45 originally</span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 20:02, 19 February 2021</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>== Adoption in APL ==</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>== Adoption in APL ==</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>Because APL was designed before the leading axis model was developed, many APL primitives do not naturally adhere to the theory and some are not compatible with it at all. The following table describes how functions and operators that act on specific axes of their arguments (omitting for example [[Enclose]] and [[Match]] which apply to entire arrays) interact with leading axis theory.</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>Because APL was designed before the leading axis model was developed, many APL primitives do not naturally adhere to the theory and some are not <ins style="font-weight: bold; text-decoration: none;">[[</ins>compatible<ins style="font-weight: bold; text-decoration: none;">]] </ins>with it at all. The following table describes how functions and operators that act on specific axes of their arguments (omitting for example [[Enclose]] and [[Match]] which apply to entire arrays) interact with leading axis theory.</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>{|class=wikitable</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>{|class=wikitable</div></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>|}</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>|}</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;">Backwards</del>-<del style="font-weight: bold; text-decoration: none;">compatible language changes are </del>only <del style="font-weight: bold; text-decoration: none;">effective for functions which are extendible </del>to <del style="font-weight: bold; text-decoration: none;">leading axes</del>. The following extensions have been made in order to support leading axis theory:</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;">In addition to these, the [[Rank operator]] and [[scalar dyadic]]s can be extended with [[leading axis agreement]], so that arguments with different</ins>-<ins style="font-weight: bold; text-decoration: none;">length frames can be match as long as one frame is a prefix of the other. The original introduction of Rank had </ins>only <ins style="font-weight: bold; text-decoration: none;">an analogue of [[scalar extension]], where an argument with an empty frame is repeated </ins>to <ins style="font-weight: bold; text-decoration: none;">pair it with an argument with a non-empty frame</ins>. The following extensions have been made in order to support leading axis theory:</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>{|class=wikitable</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>{|class=wikitable</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l44">Line 44:</td>
<td colspan="2" class="diff-lineno">Line 44:</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>| [[Bracket indexing]] || {{No}} || {{No}} || {{Yes}} ||style="text-align:center;"| N/A ||style="text-align:center;"| N/A</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>| [[Bracket indexing]] || {{No}} || {{No}} || {{Yes}} ||style="text-align:center;"| N/A ||style="text-align:center;"| N/A</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>|-</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>|-</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>| [[Scalar dyadic]]s || {{<del style="font-weight: bold; text-decoration: none;">Yes</del>}} <del style="font-weight: bold; text-decoration: none;"> </del>|| {{No}} || {{No}} || {{Yes}} || {{Yes}}</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>| [[Scalar dyadic]]s || {{<ins style="font-weight: bold; text-decoration: none;">No</ins>}} <ins style="font-weight: bold; text-decoration: none;"> </ins>|| {{No}} || {{No}} || {{Yes}} || {{Yes}}</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>|-</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>|-</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>| [[Index Of]] || {{No|Incompatible}} || {{Yes|14.0}} || {{Yes}} || {{Yes}} || {{Yes}}</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>| [[Index Of]] || {{No|Incompatible}} || {{Yes|14.0}} || {{Yes}} || {{Yes}} || {{Yes}}</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l55">Line 55:</td>
<td colspan="2" class="diff-lineno">Line 55:</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>|}</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>|}</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>[[Index Of]] in SHARP APL was not extended to apply to left argument [[major cell]]s as in J and Dyalog; instead it was given rank <source lang=apl inline>1 0</source> making such a change impossible. In A+ not only [[Index Of]] but also [[Membership]] was changed to follow the leading axis model, breaking compatibility with other APLs. A+ also restricts [[Take]] and [[Drop]] to allow only a [[singleton]] left argument (but any right argument rank is permitted)<del style="font-weight: bold; text-decoration: none;">. The leading-axis extension of scalar dyadics in SHARP is a direct consequence of giving them a function rank 0, as SHARP's concept of function rank includes [[prefix agreement]]</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>[[Index Of]] in SHARP APL was not extended to apply to left argument [[major cell]]s as in J and Dyalog; instead it was given rank <source lang=apl inline>1 0</source> making such a change impossible. In A+ not only [[Index Of]] but also [[Membership]] was changed to follow the leading axis model, breaking compatibility with other APLs. A+ also restricts [[Take]] and [[Drop]] to allow only a [[singleton]] left argument (but any right argument rank is permitted).</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>== History ==</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>== History ==</div></td></tr>
</table>
Marshall
https://aplwiki.com/index.php?title=Leading_axis_theory&diff=5480&oldid=prev
RichPark at 15:08, 5 October 2020
2020-10-05T15:08:57Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en-GB">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:08, 5 October 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td>
<td colspan="2" class="diff-lineno">Line 1:</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>'''Leading axis theory''', or the '''leading axis model''', is an approach to array language design and use that emphasizes working with arrays by manipulating their [[cell]]s and mapping functions over leading [[Axis|axes]] implicitly using [[function rank]] or explicitly using the [[Rank operator]]. It was initially developed in [[SHARP APL]] in the early 1980s and is now a major feature of [[J]] and [[Dyalog APL]], as well as languages influenced by these. The name "leading axis" comes from the [[frame]], which consists of leading axes of an array, the related concept of [[leading axis agreement]], which extends [[scalar]] [[conformability]], and the emphasis on first axis forms of functions while deprecating or discarding other [[function axis|choices of axis]].</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>'''Leading axis theory''', or the '''leading axis model''', is an approach to array language design and use that emphasizes working with arrays by manipulating their [[cell]]s and mapping functions over leading [[Axis|axes]] implicitly using [[function rank]] or explicitly using the [[<ins style="font-weight: bold; text-decoration: none;">Rank (operator)|</ins>Rank operator]]. It was initially developed in [[SHARP APL]] in the early 1980s and is now a major feature of [[J]] and [[Dyalog APL]], as well as languages influenced by these. The name "leading axis" comes from the [[frame]], which consists of leading axes of an array, the related concept of [[leading axis agreement]], which extends [[scalar]] [[conformability]], and the emphasis on first axis forms of functions while deprecating or discarding other [[function axis|choices of axis]].</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>== Features ==</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>== Features ==</div></td></tr>
</table>
RichPark
https://aplwiki.com/index.php?title=Leading_axis_theory&diff=5454&oldid=prev
Marshall: /* Adoption in APL */ Add BQN to table
2020-09-29T21:11:49Z
<p><span dir="auto"><span class="autocomment">Adoption in APL: </span> Add BQN to table</span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en-GB">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 21:11, 29 September 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l36">Line 36:</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;"><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>{|class=wikitable</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>{|class=wikitable</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>! Functions !! [[SHARP APL]] !! [[Dyalog APL]] !!style="min-width:5em"| [[A+]] !!style="min-width:5em"| [[J]]</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>! Functions !! [[SHARP APL]] !! [[Dyalog APL]] !!style="min-width:5em"| [[A+]] !!style="min-width:5em"| [[J<ins style="font-weight: bold; text-decoration: none;">]] !!style="min-width:5em"| [[BQN</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>|-</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>|-</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>| [[Take]], [[Drop]] || {{Yes|19.0}} || {{Yes|13.0}} || {{Yes}} || {{Yes}}</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>| [[Take]], [[Drop]] || {{Yes|19.0}} || {{Yes|13.0}} || {{Yes}} <ins style="font-weight: bold; text-decoration: none;">|| {{Yes}} </ins>|| {{Yes}}</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>|-</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>|-</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>| [[Squad Indexing|Indexing]] function <del style="font-weight: bold; text-decoration: none;"> </del>|| {{Yes|19.0}} || {{Yes|13.0}} || {{Yes}} || {{Yes}}</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>| [[Squad Indexing|Indexing]] function <ins style="font-weight: bold; text-decoration: none;"> </ins>|| {{Yes|19.0}} || {{Yes|13.0}} || {{Yes}} <ins style="font-weight: bold; text-decoration: none;">|| {{Yes}} </ins>|| {{Yes}}</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>|-</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>|-</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>| [[Bracket indexing]] || {{No}} || {{No}} || {{Yes}} ||style="text-align:center;"| N/A</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>| [[Bracket indexing]] || {{No}} || {{No}} || {{Yes}} <ins style="font-weight: bold; text-decoration: none;">||style="text-align:center;"| N/A </ins>||style="text-align:center;"| N/A</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>|-</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>|-</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>| [[Scalar dyadic]]s || {{Yes}} || {{No}} || {{No}} || {{Yes}}</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>| [[Scalar dyadic]]s || {{Yes}} || {{No}} || {{No<ins style="font-weight: bold; text-decoration: none;">}} || {{Yes</ins>}} || {{Yes}}</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>|-</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>|-</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>| [[Index Of]] || {{No|Incompatible}} || {{Yes|14.0}} || {{Yes}} || {{Yes}}</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>| [[Index Of]] || {{No|Incompatible}} || {{Yes|14.0}} || {{Yes}} <ins style="font-weight: bold; text-decoration: none;">|| {{Yes}} </ins>|| {{Yes}}</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>|-</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>|-</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>| [[Membership]] || {{No|Incompatible}} || {{No|Incompatible}} || {{Yes}} || {{Yes}}</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>| [[Membership]] || {{No|Incompatible}} || {{No|Incompatible}} || {{Yes}} <ins style="font-weight: bold; text-decoration: none;">|| {{Yes}} </ins>|| {{Yes}}</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>|-</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>|-</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>| [[Unique]] || {{Yes}} || {{Yes|17.0}} ||style="text-align:center;"| N/A || {{Yes}}</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>| [[Unique]] || {{Yes}} || {{Yes|17.0}} ||style="text-align:center;"| N/A <ins style="font-weight: bold; text-decoration: none;">|| {{Yes}} </ins>|| {{Yes}}</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>|-</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>|-</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>| [[Union]], [[Intersection]], [[Without]] || {{No}} || {{No}} ||style="text-align:center;"| N/A || {{Yes}}</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>| [[Union]], [[Intersection]], [[Without]] || {{No}} || {{No}} ||style="text-align:center;"| N/A || {{Yes}} <ins style="font-weight: bold; text-decoration: none;"> ||style="text-align:center;"| N/A</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>|}</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>|}</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>
</table>
Marshall