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| <title>THE BOOST MPL LIBRARY: Higher-Order Metafunctions</title> |
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| <td class="header-group page-location"><a href="../index.html" class="navigation-link">Front Page</a> / <a href="./tutorial-metafunctions.html" class="navigation-link">Tutorial: Metafunctions and Higher-Order Metaprogramming</a> / <a href="./higher-order.html" class="navigation-link">Higher-Order Metafunctions</a></td> |
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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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