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17 <div class="section" id="the-lambda-metafunction">
18 <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>
19 <p>We can <em>generate</em> a metafunction class from
20 <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>
21 <pre class="literal-block">
22 template &lt;class X&gt;
23 struct two_pointers
24 : twice&lt;<strong>typename mpl::lambda&lt;boost::add_pointer&lt;_1&gt; &gt;::type</strong>, X&gt;
25 {};
26
27 BOOST_STATIC_ASSERT((
28 boost::is_same&lt;
29 two_pointers&lt;int&gt;::type
30 , int**
31 &gt;::value
32 ));
33 </pre>
34 <!-- @ prefix.append('#include <boost/mpl/lambda.hpp>')
35 compile('all') -->
36 <p>We'll refer to metafunction classes like <tt class="literal"><span class="pre">add_pointer_f</span></tt> and
37 placeholder expressions like <tt class="literal"><span class="pre">boost::add_pointer&lt;_1&gt;</span></tt>
38 as <strong>lambda expressions</strong>. The term, meaning &quot;unnamed function
39 object,&quot; was introduced in the 1930s by the logician Alonzo Church
40 as part of a fundamental theory of computation he called the
41 <em>lambda-calculus</em>. <a class="footnote-reference" href="#lambda" id="id10" name="id10">[4]</a> MPL uses the somewhat obscure word
42 <tt class="literal"><span class="pre">lambda</span></tt> because of its well-established precedent in functional
43 programming languages.</p>
44 <table class="footnote" frame="void" id="lambda" rules="none">
45 <colgroup><col class="label" /><col /></colgroup>
46 <tbody valign="top">
47 <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
48 an in-depth treatment, including a reference to Church's paper
49 proving that the equivalence of lambda expressions is in general
50 not decidable.</td></tr>
51 </tbody>
52 </table>
53 <p>Although its primary purpose is to turn placeholder expressions
54 into metafunction classes, <tt class="literal"><span class="pre">mpl::lambda</span></tt> can accept any lambda
55 expression, even if it's already a metafunction class. In that
56 case, <tt class="literal"><span class="pre">lambda</span></tt> returns its argument unchanged. MPL algorithms
57 like <tt class="literal"><span class="pre">transform</span></tt> call <tt class="literal"><span class="pre">lambda</span></tt> internally, before invoking the
58 resulting metafunction class, so that they work equally well with
59 either kind of lambda expression. We can apply the same strategy
60 to <tt class="literal"><span class="pre">twice</span></tt>:</p>
61 <pre class="literal-block">
62 template &lt;class F, class X&gt;
63 struct twice
64 : apply1&lt;
65 typename mpl::lambda&lt;F&gt;::type
66 , typename apply1&lt;
67 typename mpl::lambda&lt;F&gt;::type
68 , X
69 &gt;::type
70 &gt;
71 {};
72 </pre>
73 <p>Now we can use <tt class="literal"><span class="pre">twice</span></tt> with metafunction classes <em>and</em>
74 placeholder expressions:</p>
75 <pre class="literal-block">
76 int* x;
77
78 twice&lt;<strong>add_pointer_f</strong>, int&gt;::type p = &amp;x;
79 twice&lt;<strong>boost::add_pointer&lt;_1&gt;</strong>, int&gt;::type q = &amp;x;
80 </pre>
81 <!-- @ stack[-2:] = [ apply1, stack[-2], add_pointer_f, stack[-1]]
82 compile('all') -->
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