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<a name="Pairwise"></a>
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<a name="Pairwise-1"></a>
<h2 class="section">B.1 Pairwise</h2>

<a name="index-pairwise-1"></a>
<p>This <code>silly</code> code fragment is mentioned in <a href="Reduce.html#Reduce">Reduce</a>, in the
discussion of <code>reduce</code>, and is provided as an example of a solution
to equations <em>E1</em> to <em>E3</em>. It is written in the style of a
higher order function, in that it takes a function <code><var>f</var></code> as an
argument and returns another function, [[<code>pairwise</code>]]
<code><var>f</var></code> as a result.
</p>
<table><tr><td>&nbsp;</td><td><pre class="example">
self     = left
argument = right
head     = left
tail     = right

pairwise =

compose(
   refer,
   compose(
      bu(
         conditional,
         conditional(argument,compose(tail,argument),constant nil)),
      couple(
         (hired couple)(
            (hired compose)(
               identity,
               constant (hired fan head)(
                  argument,
                  compose(tail,argument))),
            constant (hired meta)(
               self,
               compose(tail,compose(tail,argument)))),
         constant argument)))

</pre></td></tr></table>

<p>To see how this works, one should evaluate it symbolically with an
unknown <code><var>f</var></code>, which will result in some <code>silly</code>
pseudocode, and then evaluate that symbolically with some sample lists.
</p>
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