1<?xml version="1.0" encoding="utf-8" ?> 2<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> 3<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"> 4<!-- Copyright Aleksey Gurtovoy 2006. Distributed under the Boost --> 5<!-- Software License, Version 1.0. (See accompanying --> 6<!-- file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) --> 7<head> 8<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> 9<meta name="generator" content="Docutils 0.3.6: http://docutils.sourceforge.net/" /> 10<title>THE BOOST MPL LIBRARY: Higher-Order Metafunctions</title> 11<link rel="stylesheet" href="../style.css" type="text/css" /> 12</head> 13<body class="docframe"> 14<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> 15<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> 16</tr></table><div class="header-separator"></div> 17<div class="section" id="higher-order"> 18<h1><a class="toc-backref" href="./tutorial-metafunctions.html#id47" name="higher-order">Higher-Order Metafunctions</a></h1> 19<p>In the previous section we used two different forms — 20metafunction classes and placeholder expressions — 21to pass and return metafunctions just like any other metadata. 22Bundling metafunctions into "first class metadata" allows 23<tt class="literal"><span class="pre">transform</span></tt> to perform an infinite variety of different 24operations: in our case, multiplication and division of dimensions. 25Though the idea of using functions to manipulate other functions 26may seem simple, its great power and flexibility <a class="citation-reference" href="#hudak89" id="id9" name="id9">[Hudak89]</a> has 27earned it a fancy title: <strong>higher-order functional programming</strong>. 28A function that operates on another function is known as a 29<strong>higher-order function</strong>. It follows that <tt class="literal"><span class="pre">transform</span></tt> is a 30higher-order 31metafunction: a metafunction that operates on another metafunction.</p> 32<table class="citation" frame="void" id="hudak89" rules="none"> 33<colgroup><col class="label" /><col /></colgroup> 34<tbody valign="top"> 35<tr><td class="label"><a class="fn-backref" href="#id9" name="hudak89">[Hudak89]</a></td><td>Paul Hudak. "Conception, Evolution, and Application of 36Functional Programming Languages," ACM Computing Surveys 21, 37no. 3 Pages: 359 - 411. New York: ACM Press. 1989. 38ISSN:0360-0300. http://doi.acm.org/10.1145/72551.72554.</td></tr> 39</tbody> 40</table> 41<p>Now that we've seen the power of higher-order metafunctions at 42work, it would be good to be able to create new ones. In order to 43explore the basic mechanisms, let's try a simple example. Our task 44is to write a metafunction called <tt class="literal"><span class="pre">twice</span></tt>, which — given a unary 45metafunction <em>f</em> and arbitrary metadata <em>x</em> — computes:</p> 46<blockquote> 47<em>twice</em>(<em>f</em>, <em>x</em>) := <em>f</em>(<em>f</em>(<em>x</em>))</blockquote> 48<p>This might seem like a trivial example, and in fact it is. You 49won't find much use for <tt class="literal"><span class="pre">twice</span></tt> in real code. We hope you'll 50bear with us anyway: Because it doesn't do much more than accept 51and invoke a metafunction, <tt class="literal"><span class="pre">twice</span></tt> captures all the essential 52elements of "higher-orderness" without any distracting details.</p> 53<p>If <em>f</em> is a metafunction class, the definition of <tt class="literal"><span class="pre">twice</span></tt> is 54straightforward:</p> 55<pre class="literal-block"> 56template <class F, class X> 57struct twice 58{ 59 typedef typename F::template apply<X>::type once; // f(x) 60 typedef typename F::template apply<once>::type type; // f(f(x)) 61}; 62</pre> 63<!-- @ prefix.append( 64 '''#include <boost/type_traits/add_pointer.hpp> 65 #include <boost/static_assert.hpp> 66 #include <boost/type_traits/is_same.hpp>''') 67 68twice_test = ''' 69#include <boost/mpl/assert.hpp> 70struct add_pointer_f 71{ 72 template <class T> struct apply : boost::add_pointer<T> 73 {}; 74}; 75BOOST_MPL_ASSERT((boost::is_same<twice<add_pointer_f,int>::type,int**>)); 76''' 77example.append(twice_test) 78compile() --> 79<!-- @litre_translator.line_offset -= 7 --> 80<p>Or, applying metafunction forwarding:</p> 81<pre class="literal-block"> 82template <class F, class X> 83struct twice 84 : F::template apply< 85 typename F::template apply<X>::type 86 > 87{}; 88</pre> 89<!-- @ example.append(twice_test) 90compile() --> 91<div class="admonition-c-language-note admonition"> 92<p class="admonition-title first">C++ Language Note</p> 93<p>The C++ standard requires the <tt class="literal"><span class="pre">template</span></tt> keyword when we use a 94<strong>dependent name</strong> that refers to a member template. 95<tt class="literal"><span class="pre">F::apply</span></tt> may or may not name a template, <em>depending</em> on the 96particular <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 97information about <tt class="literal"><span class="pre">template</span></tt>.</p> 98</div> 99<p>Given the need to sprinkle our code with the <tt class="literal"><span class="pre">template</span></tt> keyword, 100it would be nice to reduce the syntactic burden of invoking 101metafunction classes. As usual, the solution is to factor the 102pattern into a metafunction:</p> 103<pre class="literal-block"> 104template <class UnaryMetaFunctionClass, class Arg> 105struct apply1 106 : UnaryMetaFunctionClass::template apply<Arg> 107{}; 108</pre> 109<p>Now <tt class="literal"><span class="pre">twice</span></tt> is just:</p> 110<pre class="literal-block"> 111template <class F, class X> 112struct twice 113 : apply1<F, typename apply1<F,X>::type> 114{}; 115</pre> 116<p>To see <tt class="literal"><span class="pre">twice</span></tt> at work, we can apply it to a little metafunction 117class built around the <tt class="literal"><span class="pre">add_pointer</span></tt> metafunction:</p> 118<pre class="literal-block"> 119struct add_pointer_f 120{ 121 template <class T> 122 struct apply : boost::add_pointer<T> {}; 123}; 124</pre> 125<!-- @litre_translator.line_offset -= 7 --> 126<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 127pointers-to-pointers:</p> 128<pre class="literal-block"> 129BOOST_STATIC_ASSERT(( 130 boost::is_same< 131 twice<add_pointer_f, int>::type 132 , int** 133 >::value 134)); 135</pre> 136<!-- @ apply1 = stack[-4] 137add_pointer_f = stack[-2] 138compile('all', pop = 0) --> 139</div> 140 141<div class="footer-separator"></div> 142<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> 143</tr></table></body> 144</html> 145