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| <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="id832300"></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="id832491"></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="id832671"></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="id833675"></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="id833816"></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> |
| </div></td> |
| </tr></table> |
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