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<h5 class="subsubsection">2.7.14.4 Transpose</h5>

<p>The <code>transpose</code> operation has the following representation in
virtual code.

     <dl>
<dt><em>T31</em><dd>[[<code>transpose</code>]] = <code>((nil,nil),((nil,nil),(nil,nil)))</code>
</dl>

<p class="noindent"><a name="index-g_t_0040code_007btranspose_007d-346"></a>This function takes a list of equal length lists as an argument, and
returns a list of lists as a result. In the resulting list, the first
item is the list of all first items of lists in the argument. The next
item is the list of all second items, and so on.

   <p>In the specification of the semantics, the <code>silly</code> mnemonic
<a name="index-g_t_0040code_007bflat_007d-347"></a><code>flat</code> is defined by <code>flat = reduce(cat,nil)</code> in the standard
<code>silly</code> prelude, which means that it flattens a list of lists into
one long list.

     <dl>
<dt><em>P41</em><dd>[[<code>transpose</code>]] <var>x</var> = <code>nil</code> if [[<code>flat</code>]] <var>x</var> = <code>nil</code>
<br><dt><em>P42</em><dd>[[<code>transpose</code>]] <var>x</var> =
<code>(</code>[[<code>map left</code>]] <var>x</var><code>,</code>[[<code>transpose</code>]] [[<code>map right</code>]] <var>x</var><code>)</code><br>
&nbsp;<!-- /@w -->&nbsp;<!-- /@w -->&nbsp;<!-- /@w --> if [[<code>flat</code>]] <var>x</var> is a non-<code>nil</code> tree
</dl>

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