View source for Dual

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      <td valign="top"><apll>Z←{L} <i>f</i>⍢<i>g</i> R</apll></td>
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      <td>applies the function <apll><i>g</i></apll> then <apll><i>f</i></apll> and then <apll><i>g</i>⍣¯1</apll> to or between the arguments.</td>
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  <td><apll>L</apll> is an optional array.</td>
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  <td><apll>R</apll> is an array.</td>
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  <td><apll><i>f</i></apll> is an arbitrary ambivalent function.</td>
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  <td><apll><i>g</i></apll> is an arbitrary monadic function with an inverse.</td>
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==Introduction==

<p>The concept of the Dual operator was described in Ken Iverson's paper on [https://www.jsoftware.com/papers/opfns.htm Operators and Functions].</p>




==Implementation==

<p>This operator is implemented via the anonymous function:</p>

<apll><pre>
{⍺←⍣0 ⋄ ⍵⍵⍣¯1 (⍵⍵ ⍺) ⍺⍺ ⍵⍵ ⍵}
</pre></apll>