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<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<span class="emphasis"><em>n</em></span><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>
<a name="phoenix.basics.partial_function_application"></a><h3>
<a name="id763540"></a>
<a class="link" href="basics.html#phoenix.basics.partial_function_application">Partial Function
Application</a>
</h3>
<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 --another black box. 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.
</p>
<a name="phoenix.basics.stl_and_higher_order_functions"></a><h3>
<a name="id763771"></a>
<a class="link" href="basics.html#phoenix.basics.stl_and_higher_order_functions">STL and higher
order functions</a>
</h3>
<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.html" title="Starter Kit">previous
section</a>:
</p>
<pre class="programlisting"><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>
<a name="phoenix.basics.lazy_evaluation"></a><h3>
<a name="id763976"></a>
<a class="link" href="basics.html#phoenix.basics.lazy_evaluation">Lazy Evaluation</a>
</h3>
<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"><</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">></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">&&</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">// <--- 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">cout</span> <span class="special"><<</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"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// prints 1 or true
</span><span class="identifier">cout</span> <span class="special"><<</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"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// prints 0 or false
</span></pre>
<a name="phoenix.basics.forwarding_function_problem"></a><h3>
<a name="id764488"></a>
<a class="link" href="basics.html#phoenix.basics.forwarding_function_problem">Forwarding Function
Problem</a>
</h3>
<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>. Be aware that the second
stage cannot accept non-const temporaries and literal constants. Hence, this
will fail:
</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="number">123</span><span class="special">)</span> <span class="comment">// Error!
</span></pre>
<p>
Disallowing non-const rvalues partially solves the "<a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2002/n1385.htm" target="_top">Forwarding
Function Problem</a>" but prohibits code like above.
</p>
<a name="phoenix.basics.polymorphic_functions"></a><h3>
<a name="id764657"></a>
<a class="link" href="basics.html#phoenix.basics.polymorphic_functions">Polymorphic Functions</a>
</h3>
<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 © 2002-2005 Joel
de Guzman, Dan Marsden<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>
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