<?xml version="1.0" encoding="utf-8" ?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"> <!-- Copyright Aleksey Gurtovoy 2006. Distributed under the Boost --> <!-- Software License, Version 1.0. (See accompanying --> <!-- file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) --> <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <meta name="generator" content="Docutils 0.3.6: http://docutils.sourceforge.net/" /> <title>THE BOOST MPL LIBRARY: Higher-Order Metafunctions</title> <link rel="stylesheet" href="../style.css" type="text/css" /> </head> <body class="docframe"> <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> <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> </tr></table><div class="header-separator"></div> <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> <div class="footer-separator"></div> <table class="footer"><tr class="footer"><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> </tr></table></body> </html>