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  26 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
  27 <a name="phoenix.basics"></a><a class="link" href="basics.html" title="Basics">Basics</a>
  28 </h2></div></div></div>
  29 <p>
  30       Almost everything is a function in the Phoenix library that can be evaluated
  31       as <code class="computeroutput"><span class="identifier">f</span><span class="special">(</span><span class="identifier">a1</span><span class="special">,</span> <span class="identifier">a2</span><span class="special">,</span> <span class="special">...,</span> a/n/<span class="special">)</span></code>, where <span class="emphasis"><em>n</em></span> is the function's
  32       arity, or number of arguments that the function expects. Operators are also
  33       functions. For example, <code class="computeroutput"><span class="identifier">a</span> <span class="special">+</span> <span class="identifier">b</span></code> is just
  34       a function with arity == 2 (or binary). <code class="computeroutput"><span class="identifier">a</span>
  35       <span class="special">+</span> <span class="identifier">b</span></code>
  36       is the same as <code class="computeroutput"><span class="identifier">add</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">b</span><span class="special">)</span></code>, <code class="computeroutput"><span class="identifier">a</span>
  37       <span class="special">+</span> <span class="identifier">b</span> <span class="special">+</span> <span class="identifier">c</span></code> is the
  38       same as <code class="computeroutput"><span class="identifier">add</span><span class="special">(</span><span class="identifier">add</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">b</span><span class="special">),</span>
  39       <span class="identifier">c</span><span class="special">)</span></code>.
  40     </p>
  41 <div class="note"><table border="0" summary="Note">
  42 <tr>
  43 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/src/images/note.png"></td>
  44 <th align="left">Note</th>
  45 </tr>
  46 <tr><td align="left" valign="top"><p>
  47         Amusingly, functions may even return functions. We shall see what this means
  48         in a short while.
  49       </p></td></tr>
  50 </table></div>
  51 <h4>
  52 <a name="phoenix.basics.h0"></a>
  53       <span><a name="phoenix.basics.partial_function_application"></a></span><a class="link" href="basics.html#phoenix.basics.partial_function_application">Partial
  54       Function Application</a>
  55     </h4>
  56 <p>
  57       Think of a function as a black box. You pass arguments and it returns something
  58       back. The figure below depicts the typical scenario.
  59     </p>
  60 <p>
  61       <span class="inlinemediaobject"><img src="../images/fbox.png"></span>
  62     </p>
  63 <p>
  64       A fully evaluated function is one in which all the arguments are given. All
  65       functions in plain C++ are fully evaluated. When you call the <code class="computeroutput"><span class="identifier">sin</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span></code> function, you have to pass a number x. The
  66       function will return a result in return: the sin of x. When you call the <code class="computeroutput"><span class="identifier">add</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span> <span class="identifier">y</span><span class="special">)</span></code>
  67       function, you have to pass two numbers x and y. The function will return the
  68       sum of the two numbers. The figure below is a fully evaluated <code class="computeroutput"><span class="identifier">add</span></code> function.
  69     </p>
  70 <p>
  71       <span class="inlinemediaobject"><img src="../images/adder.png"></span>
  72     </p>
  73 <p>
  74       A partially applied function, on the other hand, is one in which not all the
  75       arguments are supplied. If we are able to partially apply the function <code class="computeroutput"><span class="identifier">add</span></code> above, we may pass only the first argument.
  76       In doing so, the function does not have all the required information it needs
  77       to perform its task to compute and return a result. What it returns instead
  78       is another function, a lambda function. Unlike the original <code class="computeroutput"><span class="identifier">add</span></code>
  79       function which has an arity of 2, the resulting lambda function has an arity
  80       of 1. Why? because we already supplied part of the input: <code class="computeroutput"><span class="number">2</span></code>
  81     </p>
  82 <p>
  83       <span class="inlinemediaobject"><img src="../images/add2.png"></span>
  84     </p>
  85 <p>
  86       Now, when we shove in a number into our lambda function, it will return 2 plus
  87       whatever we pass in. The lambda function essentially remembers 1) the original
  88       function, <code class="computeroutput"><span class="identifier">add</span></code>, and 2) the partial
  89       input, 2. The figure below illustrates a case where we pass 3 to our lambda
  90       function, which then returns 5:
  91     </p>
  92 <p>
  93       <span class="inlinemediaobject"><img src="../images/add2_call.png"></span>
  94     </p>
  95 <p>
  96       Obviously, partially applying the <code class="computeroutput"><span class="identifier">add</span></code>
  97       function, as we see above, cannot be done directly in C++ where we are expected
  98       to supply all the arguments that a function expects. That's where the Phoenix
  99       library comes in. The library provides the facilities to do partial function
 100       application. And even more, with Phoenix, these resulting functions won't be
 101       black boxes anymore.
 102     </p>
 103 <h4>
 104 <a name="phoenix.basics.h1"></a>
 105       <span><a name="phoenix.basics.stl_and_higher_order_functions"></a></span><a class="link" href="basics.html#phoenix.basics.stl_and_higher_order_functions">STL
 106       and higher order functions</a>
 107     </h4>
 108 <p>
 109       So, what's all the fuss? What makes partial function application so useful?
 110       Recall our original example in the <a class="link" href="starter_kit/lazy_operators.html" title="Lazy Operators">previous
 111       section</a>:
 112     </p>
 113 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">find_if</span><span class="special">(</span><span class="identifier">c</span><span class="special">.</span><span class="identifier">begin</span><span class="special">(),</span> <span class="identifier">c</span><span class="special">.</span><span class="identifier">end</span><span class="special">(),</span> <span class="identifier">arg1</span> <span class="special">%</span> <span class="number">2</span> <span class="special">==</span> <span class="number">1</span><span class="special">)</span>
 114 </pre>
 115 <p>
 116       The expression <code class="computeroutput"><span class="identifier">arg1</span> <span class="special">%</span>
 117       <span class="number">2</span> <span class="special">==</span> <span class="number">1</span></code> evaluates to a lambda function. <code class="computeroutput"><span class="identifier">arg1</span></code> is a placeholder for an argument to
 118       be supplied later. Hence, since there's only one unsupplied argument, the lambda
 119       function has an arity 1. It just so happens that <code class="computeroutput"><span class="identifier">find_if</span></code>
 120       supplies the unsupplied argument as it loops from <code class="computeroutput"><span class="identifier">c</span><span class="special">.</span><span class="identifier">begin</span><span class="special">()</span></code>
 121       to <code class="computeroutput"><span class="identifier">c</span><span class="special">.</span><span class="identifier">end</span><span class="special">()</span></code>.
 122     </p>
 123 <div class="note"><table border="0" summary="Note">
 124 <tr>
 125 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/src/images/note.png"></td>
 126 <th align="left">Note</th>
 127 </tr>
 128 <tr><td align="left" valign="top"><p>
 129         Higher order functions are functions which can take other functions as arguments,
 130         and may also return functions as results. Higher order functions are functions
 131         that are treated like any other objects and can be used as arguments and
 132         return values from functions.
 133       </p></td></tr>
 134 </table></div>
 135 <h4>
 136 <a name="phoenix.basics.h2"></a>
 137       <span><a name="phoenix.basics.lazy_evaluation"></a></span><a class="link" href="basics.html#phoenix.basics.lazy_evaluation">Lazy
 138       Evaluation</a>
 139     </h4>
 140 <p>
 141       In Phoenix, to put it more accurately, function evaluation has two stages:
 142     </p>
 143 <div class="orderedlist"><ol class="orderedlist" type="1">
 144 <li class="listitem">
 145           Partial application
 146         </li>
 147 <li class="listitem">
 148           Final evaluation
 149         </li>
 150 </ol></div>
 151 <p>
 152       The first stage is handled by a set of generator functions. These are your
 153       front ends (in the client's perspective). These generators create (through
 154       partial function application), higher order functions that can be passed on
 155       just like any other function pointer or function object. The second stage,
 156       the actual function call, can be invoked or executed anytime in the future,
 157       or not at all; hence <span class="emphasis"><em>"lazy"</em></span>.
 158     </p>
 159 <p>
 160       If we look more closely, the first step involves partial function application:
 161     </p>
 162 <pre class="programlisting"><span class="identifier">arg1</span> <span class="special">%</span> <span class="number">2</span> <span class="special">==</span> <span class="number">1</span>
 163 </pre>
 164 <p>
 165       The second step is the actual function invocation (done inside the <code class="computeroutput"><span class="identifier">find_if</span></code> function. These are the back-ends
 166       (often, the final invocation is never actually seen by the client). In our
 167       example, the <code class="computeroutput"><span class="identifier">find_if</span></code>, if we
 168       take a look inside, we'll see something like:
 169     </p>
 170 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">InputIterator</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Predicate</span><span class="special">&gt;</span>
 171 <span class="identifier">InputIterator</span>
 172 <span class="identifier">find_if</span><span class="special">(</span><span class="identifier">InputIterator</span> <span class="identifier">first</span><span class="special">,</span> <span class="identifier">InputIterator</span> <span class="identifier">last</span><span class="special">,</span> <span class="identifier">Predicate</span> <span class="identifier">pred</span><span class="special">)</span>
 173 <span class="special">{</span>
 174     <span class="keyword">while</span> <span class="special">(</span><span class="identifier">first</span> <span class="special">!=</span> <span class="identifier">last</span> <span class="special">&amp;&amp;</span> <span class="special">!</span><span class="identifier">pred</span><span class="special">(*</span><span class="identifier">first</span><span class="special">))</span>  <span class="comment">// &lt;--- The lambda function is called here</span>
 175         <span class="special">++</span><span class="identifier">first</span><span class="special">;</span>                            <span class="comment">//      passing in *first</span>
 176     <span class="keyword">return</span> <span class="identifier">first</span><span class="special">;</span>
 177 <span class="special">}</span>
 178 </pre>
 179 <p>
 180       Again, typically, we, as clients, see only the first step. However, in this
 181       document and in the examples and tests provided, don't be surprised to see
 182       the first and second steps juxtaposed in order to illustrate the complete semantics
 183       of Phoenix expressions. Examples:
 184     </p>
 185 <pre class="programlisting"><span class="keyword">int</span> <span class="identifier">x</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span>
 186 <span class="keyword">int</span> <span class="identifier">y</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span>
 187
 188 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="special">(</span><span class="identifier">arg1</span> <span class="special">%</span> <span class="number">2</span> <span class="special">==</span> <span class="number">1</span><span class="special">)(</span><span class="identifier">x</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// prints 1 or true</span>
 189 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="special">(</span><span class="identifier">arg1</span> <span class="special">%</span> <span class="number">2</span> <span class="special">==</span> <span class="number">1</span><span class="special">)(</span><span class="identifier">y</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// prints 0 or false</span>
 190 </pre>
 191 <h4>
 192 <a name="phoenix.basics.h3"></a>
 193       <span><a name="phoenix.basics.forwarding_function_problem"></a></span><a class="link" href="basics.html#phoenix.basics.forwarding_function_problem">Forwarding
 194       Function Problem</a>
 195     </h4>
 196 <p>
 197       Usually, we, as clients, write the call-back functions while libraries (such
 198       as STL) provide the callee (e.g. <code class="computeroutput"><span class="identifier">find_if</span></code>).
 199       In case the role is reversed, e.g. if you have to write an STL algorithm that
 200       takes in a predicate, or develop a GUI library that accepts event handlers,
 201       you have to be aware of a little known problem in C++ called the "<a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2002/n1385.htm" target="_top">Forwarding
 202       Function Problem</a>".
 203     </p>
 204 <p>
 205       Look again at the code above:
 206     </p>
 207 <pre class="programlisting"><span class="special">(</span><span class="identifier">arg1</span> <span class="special">%</span> <span class="number">2</span> <span class="special">==</span> <span class="number">1</span><span class="special">)(</span><span class="identifier">x</span><span class="special">)</span>
 208 </pre>
 209 <p>
 210       Notice that, in the second-stage (the final evaluation), we used a variable
 211       <code class="computeroutput"><span class="identifier">x</span></code>.
 212     </p>
 213 <p>
 214       In Phoenix we emulated perfect forwarding through preprocessor macros generating
 215       code to allow const and non-const references.
 216     </p>
 217 <p>
 218       We generate these second-stage overloads for Phoenix expression up to <code class="computeroutput"><span class="identifier">BOOST_PHOENIX_PERFECT_FORWARD_LIMIT</span></code>
 219     </p>
 220 <div class="note"><table border="0" summary="Note">
 221 <tr>
 222 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/src/images/note.png"></td>
 223 <th align="left">Note</th>
 224 </tr>
 225 <tr><td align="left" valign="top"><p>
 226         You can set <code class="computeroutput"><span class="identifier">BOOST_PHOENIX_PERFECT_FORWARD_LIMIT</span></code>,
 227         the predefined maximum perfect forward arguments an actor can take. By default,
 228         <code class="computeroutput"><span class="identifier">BOOST_PHOENIX_PERFECT_FORWARDLIMIT</span></code>
 229         is set to 3.
 230       </p></td></tr>
 231 </table></div>
 232 <h4>
 233 <a name="phoenix.basics.h4"></a>
 234       <span><a name="phoenix.basics.polymorphic_functions"></a></span><a class="link" href="basics.html#phoenix.basics.polymorphic_functions">Polymorphic
 235       Functions</a>
 236     </h4>
 237 <p>
 238       Unless otherwise noted, Phoenix generated functions are fully polymorphic.
 239       For instance, the <code class="computeroutput"><span class="identifier">add</span></code> example
 240       above can apply to integers, floating points, user defined complex numbers
 241       or even strings. Example:
 242     </p>
 243 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">h</span><span class="special">(</span><span class="string">"Hello"</span><span class="special">);</span>
 244 <span class="keyword">char</span> <span class="keyword">const</span><span class="special">*</span> <span class="identifier">w</span> <span class="special">=</span> <span class="string">" World"</span><span class="special">;</span>
 245 <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">r</span> <span class="special">=</span> <span class="identifier">add</span><span class="special">(</span><span class="identifier">arg1</span><span class="special">,</span> <span class="identifier">arg2</span><span class="special">)(</span><span class="identifier">h</span><span class="special">,</span> <span class="identifier">w</span><span class="special">);</span>
 246 </pre>
 247 <p>
 248       evaluates to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span><span class="special">(</span><span class="string">"Hello
 249       World"</span><span class="special">)</span></code>. The observant
 250       reader might notice that this function call in fact takes in heterogeneous
 251       arguments where <code class="computeroutput"><span class="identifier">arg1</span></code> is of
 252       type <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span></code> and <code class="computeroutput"><span class="identifier">arg2</span></code>
 253       is of type <code class="computeroutput"><span class="keyword">char</span> <span class="keyword">const</span><span class="special">*</span></code>. <code class="computeroutput"><span class="identifier">add</span></code>
 254       still works because the C++ standard library allows the expression <code class="computeroutput"><span class="identifier">a</span> <span class="special">+</span> <span class="identifier">b</span></code>
 255       where <code class="computeroutput"><span class="identifier">a</span></code> is a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span></code>
 256       and <code class="computeroutput"><span class="identifier">b</span></code> is a <code class="computeroutput"><span class="keyword">char</span>
 257       <span class="keyword">const</span><span class="special">*</span></code>.
 258     </p>
 259 </div>
 260 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 261 <td align="left"></td>
 262 <td align="right"><div class="copyright-footer">Copyright &#169; 2002-2005, 2010, 2014, 2015 Joel de Guzman, Dan Marsden, Thomas
 263       Heller, John Fletcher<p>
 264         Distributed under the Boost Software License, Version 1.0. (See accompanying
 265         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
 266       </p>
 267 </div></td>
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