145 lines
8.6 KiB
HTML
145 lines
8.6 KiB
HTML
<?xml version="1.0" encoding="utf-8" ?>
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">
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<!-- Copyright Aleksey Gurtovoy 2006. Distributed under the Boost -->
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<!-- Software License, Version 1.0. (See accompanying -->
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<!-- file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -->
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
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<meta name="generator" content="Docutils 0.3.6: http://docutils.sourceforge.net/" />
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<title>THE BOOST MPL LIBRARY: Higher-Order Metafunctions</title>
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<table class="header"><tr class="header"><td class="header-group navigation-bar"><span class="navigation-group"><a href="./implementing-division.html" class="navigation-link">Prev</a> <a href="./handling-placeholders.html" class="navigation-link">Next</a></span><span class="navigation-group-separator"> | </span><span class="navigation-group"><a href="./dimensional-analysis.html" class="navigation-link">Back</a> <a href="./handling-placeholders.html" class="navigation-link">Along</a></span><span class="navigation-group-separator"> | </span><span class="navigation-group"><a href="./tutorial-metafunctions.html" class="navigation-link">Up</a> <a href="../index.html" class="navigation-link">Home</a></span><span class="navigation-group-separator"> | </span><span class="navigation-group"><a href="./tutorial_toc.html" class="navigation-link">Full TOC</a></span></td>
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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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</tr></table><div class="header-separator"></div>
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<div class="section" id="higher-order">
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<h1><a class="toc-backref" href="./tutorial-metafunctions.html#id47" name="higher-order">Higher-Order Metafunctions</a></h1>
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<p>In the previous section we used two different forms —
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metafunction classes and placeholder expressions —
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to pass and return metafunctions just like any other metadata.
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Bundling metafunctions into "first class metadata" allows
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<tt class="literal"><span class="pre">transform</span></tt> to perform an infinite variety of different
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operations: in our case, multiplication and division of dimensions.
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Though the idea of using functions to manipulate other functions
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may seem simple, its great power and flexibility <a class="citation-reference" href="#hudak89" id="id9" name="id9">[Hudak89]</a> has
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earned it a fancy title: <strong>higher-order functional programming</strong>.
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A function that operates on another function is known as a
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<strong>higher-order function</strong>. It follows that <tt class="literal"><span class="pre">transform</span></tt> is a
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higher-order
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metafunction: a metafunction that operates on another metafunction.</p>
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<table class="citation" frame="void" id="hudak89" rules="none">
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<colgroup><col class="label" /><col /></colgroup>
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<tbody valign="top">
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<tr><td class="label"><a class="fn-backref" href="#id9" name="hudak89">[Hudak89]</a></td><td>Paul Hudak. "Conception, Evolution, and Application of
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Functional Programming Languages," ACM Computing Surveys 21,
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no. 3 Pages: 359 - 411. New York: ACM Press. 1989.
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ISSN:0360-0300. http://doi.acm.org/10.1145/72551.72554.</td></tr>
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</tbody>
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</table>
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<p>Now that we've seen the power of higher-order metafunctions at
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work, it would be good to be able to create new ones. In order to
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explore the basic mechanisms, let's try a simple example. Our task
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is to write a metafunction called <tt class="literal"><span class="pre">twice</span></tt>, which — given a unary
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metafunction <em>f</em> and arbitrary metadata <em>x</em> — computes:</p>
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<blockquote>
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<em>twice</em>(<em>f</em>, <em>x</em>) := <em>f</em>(<em>f</em>(<em>x</em>))</blockquote>
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<p>This might seem like a trivial example, and in fact it is. You
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won't find much use for <tt class="literal"><span class="pre">twice</span></tt> in real code. We hope you'll
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bear with us anyway: Because it doesn't do much more than accept
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and invoke a metafunction, <tt class="literal"><span class="pre">twice</span></tt> captures all the essential
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elements of "higher-orderness" without any distracting details.</p>
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<p>If <em>f</em> is a metafunction class, the definition of <tt class="literal"><span class="pre">twice</span></tt> is
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straightforward:</p>
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<pre class="literal-block">
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template <class F, class X>
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struct twice
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{
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typedef typename F::template apply<X>::type once; // f(x)
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typedef typename F::template apply<once>::type type; // f(f(x))
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};
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</pre>
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<!-- @ prefix.append(
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'''#include <boost/type_traits/add_pointer.hpp>
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#include <boost/static_assert.hpp>
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#include <boost/type_traits/is_same.hpp>''')
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twice_test = '''
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#include <boost/mpl/assert.hpp>
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struct add_pointer_f
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{
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template <class T> struct apply : boost::add_pointer<T>
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{};
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};
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BOOST_MPL_ASSERT((boost::is_same<twice<add_pointer_f,int>::type,int**>));
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'''
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example.append(twice_test)
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compile() -->
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<!-- @litre_translator.line_offset -= 7 -->
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<p>Or, applying metafunction forwarding:</p>
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<pre class="literal-block">
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template <class F, class X>
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struct twice
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: F::template apply<
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typename F::template apply<X>::type
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>
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{};
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</pre>
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<!-- @ example.append(twice_test)
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compile() -->
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<div class="admonition-c-language-note admonition">
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<p class="admonition-title first">C++ Language Note</p>
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<p>The C++ standard requires the <tt class="literal"><span class="pre">template</span></tt> keyword when we use a
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<strong>dependent name</strong> that refers to a member template.
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<tt class="literal"><span class="pre">F::apply</span></tt> may or may not name a template, <em>depending</em> on the
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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
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information about <tt class="literal"><span class="pre">template</span></tt>.</p>
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</div>
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<p>Given the need to sprinkle our code with the <tt class="literal"><span class="pre">template</span></tt> keyword,
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it would be nice to reduce the syntactic burden of invoking
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metafunction classes. As usual, the solution is to factor the
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pattern into a metafunction:</p>
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<pre class="literal-block">
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template <class UnaryMetaFunctionClass, class Arg>
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struct apply1
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: UnaryMetaFunctionClass::template apply<Arg>
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{};
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</pre>
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<p>Now <tt class="literal"><span class="pre">twice</span></tt> is just:</p>
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<pre class="literal-block">
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template <class F, class X>
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struct twice
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: apply1<F, typename apply1<F,X>::type>
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{};
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</pre>
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<p>To see <tt class="literal"><span class="pre">twice</span></tt> at work, we can apply it to a little metafunction
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class built around the <tt class="literal"><span class="pre">add_pointer</span></tt> metafunction:</p>
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<pre class="literal-block">
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struct add_pointer_f
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{
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template <class T>
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struct apply : boost::add_pointer<T> {};
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};
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</pre>
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<!-- @litre_translator.line_offset -= 7 -->
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<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
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pointers-to-pointers:</p>
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<pre class="literal-block">
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BOOST_STATIC_ASSERT((
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boost::is_same<
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twice<add_pointer_f, int>::type
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, int**
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>::value
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));
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</pre>
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<!-- @ apply1 = stack[-4]
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add_pointer_f = stack[-2]
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compile('all', pop = 0) -->
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</div>
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