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<div class="section" id="the-lambda-metafunction">
<h1><a class="toc-backref" href="./handling-placeholders.html#id49" name="the-lambda-metafunction">The <tt class="literal"><span class="pre">lambda</span></tt> Metafunction</a></h1>
<p>We can <em>generate</em> a metafunction class from
<tt class="literal"><span class="pre">boost::add_pointer&lt;_1&gt;</span></tt>, using MPL's <tt class="literal"><span class="pre">lambda</span></tt> metafunction:</p>
<pre class="literal-block">
template &lt;class X&gt;
struct two_pointers
  : twice&lt;<strong>typename mpl::lambda&lt;boost::add_pointer&lt;_1&gt; &gt;::type</strong>, X&gt;
{};

BOOST_STATIC_ASSERT((
    boost::is_same&lt;
        two_pointers&lt;int&gt;::type
      , int**
    &gt;::value
));
</pre>
<!-- @ prefix.append('#include <boost/mpl/lambda.hpp>')
compile('all') -->
<p>We'll refer to metafunction classes like <tt class="literal"><span class="pre">add_pointer_f</span></tt> and
placeholder expressions like <tt class="literal"><span class="pre">boost::add_pointer&lt;_1&gt;</span></tt>
as <strong>lambda expressions</strong>.  The term, meaning &quot;unnamed function
object,&quot; was introduced in the 1930s by the logician Alonzo Church
as part of a fundamental theory of computation he called the
<em>lambda-calculus</em>. <a class="footnote-reference" href="#lambda" id="id10" name="id10">[4]</a>  MPL uses the somewhat obscure word
<tt class="literal"><span class="pre">lambda</span></tt> because of its well-established precedent in functional
programming languages.</p>
<table class="footnote" frame="void" id="lambda" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id10" name="lambda">[4]</a></td><td>See <a class="reference" href="http://en.wikipedia.org/wiki/Lambda_calculus" target="_top">http://en.wikipedia.org/wiki/Lambda_calculus</a> for
an in-depth treatment, including a reference to Church's paper
proving that the equivalence of lambda expressions is in general
not decidable.</td></tr>
</tbody>
</table>
<p>Although its primary purpose is to turn placeholder expressions
into metafunction classes, <tt class="literal"><span class="pre">mpl::lambda</span></tt> can accept any lambda
expression, even if it's already a metafunction class.  In that
case, <tt class="literal"><span class="pre">lambda</span></tt> returns its argument unchanged.  MPL algorithms
like <tt class="literal"><span class="pre">transform</span></tt> call <tt class="literal"><span class="pre">lambda</span></tt> internally, before invoking the
resulting metafunction class, so that they work equally well with
either kind of lambda expression.  We can apply the same strategy
to <tt class="literal"><span class="pre">twice</span></tt>:</p>
<pre class="literal-block">
template &lt;class F, class X&gt;
struct twice
   : apply1&lt;
         typename mpl::lambda&lt;F&gt;::type
       , typename apply1&lt;
             typename mpl::lambda&lt;F&gt;::type
           , X
         &gt;::type
     &gt;
{};
</pre>
<p>Now we can use <tt class="literal"><span class="pre">twice</span></tt> with metafunction classes <em>and</em>
placeholder expressions:</p>
<pre class="literal-block">
int* x;

twice&lt;<strong>add_pointer_f</strong>, int&gt;::type           p = &amp;x;
twice&lt;<strong>boost::add_pointer&lt;_1&gt;</strong>, int&gt;::type q = &amp;x;
</pre>
<!-- @ stack[-2:] = [ apply1, stack[-2], add_pointer_f, stack[-1]]
compile('all') -->
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