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- <title>THE BOOST MPL LIBRARY: Higher-Order Metafunctions</title>
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- <div class="section" id="higher-order">
- <h1><a class="toc-backref" href="./tutorial-metafunctions.html#id47" name="higher-order">Higher-Order Metafunctions</a></h1>
- <p>In the previous section we used two different forms —
- metafunction classes and placeholder expressions —
- to pass and return metafunctions just like any other metadata.
- Bundling metafunctions into "first class metadata" allows
- <tt class="literal"><span class="pre">transform</span></tt> to perform an infinite variety of different
- operations: in our case, multiplication and division of dimensions.
- Though the idea of using functions to manipulate other functions
- may seem simple, its great power and flexibility <a class="citation-reference" href="#hudak89" id="id9" name="id9">[Hudak89]</a> has
- earned it a fancy title: <strong>higher-order functional programming</strong>.
- A function that operates on another function is known as a
- <strong>higher-order function</strong>. It follows that <tt class="literal"><span class="pre">transform</span></tt> is a
- higher-order
- metafunction: a metafunction that operates on another metafunction.</p>
- <table class="citation" frame="void" id="hudak89" rules="none">
- <colgroup><col class="label" /><col /></colgroup>
- <tbody valign="top">
- <tr><td class="label"><a class="fn-backref" href="#id9" name="hudak89">[Hudak89]</a></td><td>Paul Hudak. "Conception, Evolution, and Application of
- Functional Programming Languages," ACM Computing Surveys 21,
- no. 3 Pages: 359 - 411. New York: ACM Press. 1989.
- ISSN:0360-0300. http://doi.acm.org/10.1145/72551.72554.</td></tr>
- </tbody>
- </table>
- <p>Now that we've seen the power of higher-order metafunctions at
- work, it would be good to be able to create new ones. In order to
- explore the basic mechanisms, let's try a simple example. Our task
- is to write a metafunction called <tt class="literal"><span class="pre">twice</span></tt>, which — given a unary
- metafunction <em>f</em> and arbitrary metadata <em>x</em> — computes:</p>
- <blockquote>
- <em>twice</em>(<em>f</em>, <em>x</em>) := <em>f</em>(<em>f</em>(<em>x</em>))</blockquote>
- <p>This might seem like a trivial example, and in fact it is. You
- won't find much use for <tt class="literal"><span class="pre">twice</span></tt> in real code. We hope you'll
- bear with us anyway: Because it doesn't do much more than accept
- and invoke a metafunction, <tt class="literal"><span class="pre">twice</span></tt> captures all the essential
- elements of "higher-orderness" without any distracting details.</p>
- <p>If <em>f</em> is a metafunction class, the definition of <tt class="literal"><span class="pre">twice</span></tt> is
- straightforward:</p>
- <pre class="literal-block">
- template <class F, class X>
- struct twice
- {
- typedef typename F::template apply<X>::type once; // f(x)
- typedef typename F::template apply<once>::type type; // f(f(x))
- };
- </pre>
- <!-- @ prefix.append(
- '''#include <boost/type_traits/add_pointer.hpp>
- #include <boost/static_assert.hpp>
- #include <boost/type_traits/is_same.hpp>''')
- twice_test = '''
- #include <boost/mpl/assert.hpp>
- struct add_pointer_f
- {
- template <class T> struct apply : boost::add_pointer<T>
- {};
- };
- BOOST_MPL_ASSERT((boost::is_same<twice<add_pointer_f,int>::type,int**>));
- '''
- example.append(twice_test)
- compile() -->
- <!-- @litre_translator.line_offset -= 7 -->
- <p>Or, applying metafunction forwarding:</p>
- <pre class="literal-block">
- template <class F, class X>
- struct twice
- : F::template apply<
- typename F::template apply<X>::type
- >
- {};
- </pre>
- <!-- @ example.append(twice_test)
- compile() -->
- <div class="admonition-c-language-note admonition">
- <p class="admonition-title first">C++ Language Note</p>
- <p>The C++ standard requires the <tt class="literal"><span class="pre">template</span></tt> keyword when we use a
- <strong>dependent name</strong> that refers to a member template.
- <tt class="literal"><span class="pre">F::apply</span></tt> may or may not name a template, <em>depending</em> on the
- particular <tt class="literal"><span class="pre">F</span></tt> that is passed. See <a class="reference" href="./resources.html">the book's</a> Appendix B for more
- information about <tt class="literal"><span class="pre">template</span></tt>.</p>
- </div>
- <p>Given the need to sprinkle our code with the <tt class="literal"><span class="pre">template</span></tt> keyword,
- it would be nice to reduce the syntactic burden of invoking
- metafunction classes. As usual, the solution is to factor the
- pattern into a metafunction:</p>
- <pre class="literal-block">
- template <class UnaryMetaFunctionClass, class Arg>
- struct apply1
- : UnaryMetaFunctionClass::template apply<Arg>
- {};
- </pre>
- <p>Now <tt class="literal"><span class="pre">twice</span></tt> is just:</p>
- <pre class="literal-block">
- template <class F, class X>
- struct twice
- : apply1<F, typename apply1<F,X>::type>
- {};
- </pre>
- <p>To see <tt class="literal"><span class="pre">twice</span></tt> at work, we can apply it to a little metafunction
- class built around the <tt class="literal"><span class="pre">add_pointer</span></tt> metafunction:</p>
- <pre class="literal-block">
- struct add_pointer_f
- {
- template <class T>
- struct apply : boost::add_pointer<T> {};
- };
- </pre>
- <!-- @litre_translator.line_offset -= 7 -->
- <p>Now we can use <tt class="literal"><span class="pre">twice</span></tt> with <tt class="literal"><span class="pre">add_pointer_f</span></tt> to build
- pointers-to-pointers:</p>
- <pre class="literal-block">
- BOOST_STATIC_ASSERT((
- boost::is_same<
- twice<add_pointer_f, int>::type
- , int**
- >::value
- ));
- </pre>
- <!-- @ apply1 = stack[-4]
- add_pointer_f = stack[-2]
- compile('all', pop = 0) -->
- </div>
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