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+<title>Basics</title>
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+</div>
+<div class="section">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="phoenix.basics"></a><a class="link" href="basics.html" title="Basics">Basics</a>
+</h2></div></div></div>
+<p>
+ Almost everything is a function in the Phoenix library that can be evaluated
+ 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
+ arity, or number of arguments that the function expects. Operators are also
+ functions. For example, <code class="computeroutput"><span class="identifier">a</span> <span class="special">+</span> <span class="identifier">b</span></code> is just
+ a function with arity == 2 (or binary). <code class="computeroutput"><span class="identifier">a</span>
+ <span class="special">+</span> <span class="identifier">b</span></code>
+ 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>
+ <span class="special">+</span> <span class="identifier">b</span> <span class="special">+</span> <span class="identifier">c</span></code> is the
+ 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>
+ <span class="identifier">c</span><span class="special">)</span></code>.
+ </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/src/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+ Amusingly, functions may even return functions. We shall see what this means
+ in a short while.
+ </p></td></tr>
+</table></div>
+<h4>
+<a name="phoenix.basics.h0"></a>
+ <span><a name="phoenix.basics.partial_function_application"></a></span><a class="link" href="basics.html#phoenix.basics.partial_function_application">Partial
+ Function Application</a>
+ </h4>
+<p>
+ Think of a function as a black box. You pass arguments and it returns something
+ back. The figure below depicts the typical scenario.
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../images/fbox.png" alt="fbox"></span>
+ </p>
+<p>
+ A fully evaluated function is one in which all the arguments are given. All
+ 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
+ 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>
+ function, you have to pass two numbers x and y. The function will return the
+ sum of the two numbers. The figure below is a fully evaluated <code class="computeroutput"><span class="identifier">add</span></code> function.
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../images/adder.png" alt="adder"></span>
+ </p>
+<p>
+ A partially applied function, on the other hand, is one in which not all the
+ 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.
+ In doing so, the function does not have all the required information it needs
+ to perform its task to compute and return a result. What it returns instead
+ is another function, a lambda function. Unlike the original <code class="computeroutput"><span class="identifier">add</span></code>
+ function which has an arity of 2, the resulting lambda function has an arity
+ of 1. Why? because we already supplied part of the input: <code class="computeroutput"><span class="number">2</span></code>
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../images/add2.png" alt="add2"></span>
+ </p>
+<p>
+ Now, when we shove in a number into our lambda function, it will return 2 plus
+ whatever we pass in. The lambda function essentially remembers 1) the original
+ function, <code class="computeroutput"><span class="identifier">add</span></code>, and 2) the partial
+ input, 2. The figure below illustrates a case where we pass 3 to our lambda
+ function, which then returns 5:
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../images/add2_call.png" alt="add2_call"></span>
+ </p>
+<p>
+ Obviously, partially applying the <code class="computeroutput"><span class="identifier">add</span></code>
+ function, as we see above, cannot be done directly in C++ where we are expected
+ to supply all the arguments that a function expects. That's where the Phoenix
+ library comes in. The library provides the facilities to do partial function
+ application. And even more, with Phoenix, these resulting functions won't be
+ black boxes anymore.
+ </p>
+<h4>
+<a name="phoenix.basics.h1"></a>
+ <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
+ and higher order functions</a>
+ </h4>
+<p>
+ So, what's all the fuss? What makes partial function application so useful?
+ Recall our original example in the <a class="link" href="starter_kit/lazy_operators.html" title="Lazy Operators">previous
+ section</a>:
+ </p>
+<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>
+</pre>
+<p>
+ The expression <code class="computeroutput"><span class="identifier">arg1</span> <span class="special">%</span>
+ <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
+ be supplied later. Hence, since there's only one unsupplied argument, the lambda
+ function has an arity 1. It just so happens that <code class="computeroutput"><span class="identifier">find_if</span></code>
+ 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>
+ to <code class="computeroutput"><span class="identifier">c</span><span class="special">.</span><span class="identifier">end</span><span class="special">()</span></code>.
+ </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/src/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+ Higher order functions are functions which can take other functions as arguments,
+ and may also return functions as results. Higher order functions are functions
+ that are treated like any other objects and can be used as arguments and
+ return values from functions.
+ </p></td></tr>
+</table></div>
+<h4>
+<a name="phoenix.basics.h2"></a>
+ <span><a name="phoenix.basics.lazy_evaluation"></a></span><a class="link" href="basics.html#phoenix.basics.lazy_evaluation">Lazy
+ Evaluation</a>
+ </h4>
+<p>
+ In Phoenix, to put it more accurately, function evaluation has two stages:
+ </p>
+<div class="orderedlist"><ol class="orderedlist" type="1">
+<li class="listitem">
+ Partial application
+ </li>
+<li class="listitem">
+ Final evaluation
+ </li>
+</ol></div>
+<p>
+ The first stage is handled by a set of generator functions. These are your
+ front ends (in the client's perspective). These generators create (through
+ partial function application), higher order functions that can be passed on
+ just like any other function pointer or function object. The second stage,
+ the actual function call, can be invoked or executed anytime in the future,
+ or not at all; hence <span class="emphasis"><em>"lazy"</em></span>.
+ </p>
+<p>
+ If we look more closely, the first step involves partial function application:
+ </p>
+<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>
+</pre>
+<p>
+ 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
+ (often, the final invocation is never actually seen by the client). In our
+ example, the <code class="computeroutput"><span class="identifier">find_if</span></code>, if we
+ take a look inside, we'll see something like:
+ </p>
+<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>
+<span class="identifier">InputIterator</span>
+<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>
+<span class="special">{</span>
+ <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>
+ <span class="special">++</span><span class="identifier">first</span><span class="special">;</span> <span class="comment">// passing in *first</span>
+ <span class="keyword">return</span> <span class="identifier">first</span><span class="special">;</span>
+<span class="special">}</span>
+</pre>
+<p>
+ Again, typically, we, as clients, see only the first step. However, in this
+ document and in the examples and tests provided, don't be surprised to see
+ the first and second steps juxtaposed in order to illustrate the complete semantics
+ of Phoenix expressions. Examples:
+ </p>
+<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>
+<span class="keyword">int</span> <span class="identifier">y</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span>
+
+<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>
+<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>
+</pre>
+<h4>
+<a name="phoenix.basics.h3"></a>
+ <span><a name="phoenix.basics.forwarding_function_problem"></a></span><a class="link" href="basics.html#phoenix.basics.forwarding_function_problem">Forwarding
+ Function Problem</a>
+ </h4>
+<p>
+ Usually, we, as clients, write the call-back functions while libraries (such
+ as STL) provide the callee (e.g. <code class="computeroutput"><span class="identifier">find_if</span></code>).
+ In case the role is reversed, e.g. if you have to write an STL algorithm that
+ takes in a predicate, or develop a GUI library that accepts event handlers,
+ 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
+ Function Problem</a>".
+ </p>
+<p>
+ Look again at the code above:
+ </p>
+<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>
+</pre>
+<p>
+ Notice that, in the second-stage (the final evaluation), we used a variable
+ <code class="computeroutput"><span class="identifier">x</span></code>.
+ </p>
+<p>
+ In Phoenix we emulated perfect forwarding through preprocessor macros generating
+ code to allow const and non-const references.
+ </p>
+<p>
+ We generate these second-stage overloads for Phoenix expression up to <code class="computeroutput"><span class="identifier">BOOST_PHOENIX_PERFECT_FORWARD_LIMIT</span></code>
+ </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/src/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+ You can set <code class="computeroutput"><span class="identifier">BOOST_PHOENIX_PERFECT_FORWARD_LIMIT</span></code>,
+ the predefined maximum perfect forward arguments an actor can take. By default,
+ <code class="computeroutput"><span class="identifier">BOOST_PHOENIX_PERFECT_FORWARDLIMIT</span></code>
+ is set to 3.
+ </p></td></tr>
+</table></div>
+<h4>
+<a name="phoenix.basics.h4"></a>
+ <span><a name="phoenix.basics.polymorphic_functions"></a></span><a class="link" href="basics.html#phoenix.basics.polymorphic_functions">Polymorphic
+ Functions</a>
+ </h4>
+<p>
+ Unless otherwise noted, Phoenix generated functions are fully polymorphic.
+ For instance, the <code class="computeroutput"><span class="identifier">add</span></code> example
+ above can apply to integers, floating points, user defined complex numbers
+ or even strings. Example:
+ </p>
+<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>
+<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>
+<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>
+</pre>
+<p>
+ 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
+ World"</span><span class="special">)</span></code>. The observant
+ reader might notice that this function call in fact takes in heterogeneous
+ arguments where <code class="computeroutput"><span class="identifier">arg1</span></code> is of
+ 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>
+ 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>
+ 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>
+ 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>
+ and <code class="computeroutput"><span class="identifier">b</span></code> is a <code class="computeroutput"><span class="keyword">char</span>
+ <span class="keyword">const</span><span class="special">*</span></code>.
+ </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright &#169; 2002-2005, 2010 Joel de Guzman, Dan Marsden, Thomas Heller<p>
+ Distributed under the Boost Software License, Version 1.0. (See accompanying
+ 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>)
+ </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="starter_kit/more.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="organization.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
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