View source for Indexing

<table border="1" cellpadding="5" cellspacing="0" rules="none" summary="">
<tr>
  <td>
    <table border="0" cellpadding="5" cellspacing="0" summary="">
    <tr>
      <td valign="top"><apll>Z←R[L]</apll>, <apll>R[L]←A</apll>, and <apll>R[L]<i>f</i>←A</apll></td>
      <td></td>
      <td></td>
      <td>are all extended to allow both <b>Reach</b> and <b>Scatter</b> indexing.</td>
    </tr>
    </table>
  </td>
</tr>
<tr>
  <td><apll>L</apll> is a nested array of integer scalars and/or vectors, suitable for indexing <apll>R</apll>.</td>
</tr>
<tr>
  <td><apll>R</apll> is an arbitrary array.</td>
</tr>
<tr>
  <td><apll>A</apll> is an arbitrary array.</td>
</tr>
<tr>
  <td><b>Reach Indexing</b>:  If <apll>L⊃R</apll> is valid, it is equivalent to <apll>⊃R[⊂L]</apll></td>
</tr>
<tr>
  <td><b>Scatter Indexing</b>:  If <apll>L⌷R</apll> is valid, it is equivalent to <apll>R[⊃∘.,/L]</apll></td>
</tr>
<tr>
  <td>Both Reach and Scatter indexing may appear together within a single instance of <apll>R[L]</apll>, <apll>R[L]←A</apll>, and <apll>R[L]<i>f</i>←A</apll></td>
</tr>
</table>
<br />
<p>For example, in origin-1</p>

<apll>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;V←'123'(⊂4 5)</apll><br />
<apll>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;V[1 (2 ⍬ 1)]</apll><br />
<apll>&nbsp;123 4</apll>

<apll>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;M←2 2⍴(10 20) (30 40 'abc') 50 60<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;M[(1 1)((1 2) 3)]<br />
&nbsp;10 20&nbsp;&nbsp;abc</apll>


<table border="1" cellpadding="5" cellspacing="0" rules="none" summary="">
<tr>
  <td>
    <table border="0" cellpadding="5" cellspacing="0" summary="">
    <tr>
      <td valign="top"><apll>Z←R[L]</apll>, <apll>R[L]←A</apll>, <apll>R[L]<i>f</i>←A</apll>, <apll>L⌷R</apll>, <apll>L⍉R</apll>, and <apll>L⊃R</apll></td>
      <td></td>
      <td></td>
      <td>are all extended to allow negative values in <apll>L</apll>.</td>
    </tr>
    </table>
  </td>
</tr>
<tr>
  <td>For all but transpose, <apll>L</apll> is a nested array of integer scalars and/or vectors, suitable for indexing <apll>R</apll>; for transpose, <apll>L</apll> is an integer scalar or vector of integers, suitable for transposing <apll>R</apll>.</td>
</tr>
<tr>
  <td>That is, if the largest allowed value for <apll>L</apll> is <apll>N</apll>, then the previous allowable range of values was <apll>⎕IO</apll> to <apll>N</apll>, inclusive.  Now, the allowable range of values is <apll>1 ¯1[1]-N</apll> to <apll>N</apll>, inclusive.  For example, <apll>A</apll>, <apll>A[⍳⍴A]</apll>, <apll>A[⍳-⍴A]</apll>, and even <apll>A[⍳¯1 1[?(⍴⍴A)⍴2]×⍴A]</apll> are all identical for any array <apll>A</apll> in either origin.<br />Also, <apll>A</apll>, <apll>(⍳⍴⍴A)⍉A</apll>, and <apll>(⍳-⍴⍴A)⍉A</apll> are all identical for any array <apll>A</apll> in either origin.</td>
</tr>
<tr>
  <td><apll>R</apll> is an arbitrary array.</td>
</tr>
<tr>
  <td><apll>A</apll> is an arbitrary array.</td>
</tr>
</table>
<br />
<p>For example, in origin-1</p>

<apll>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;V←'123'(⊂4 5)</apll><br />
<apll>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;V[¯1 (0 ⍬ ¯1)]</apll><br />
<apll>&nbsp;123 4</apll>