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 <div class="section">
 <div class="titlepage"><div><div><h3 class="title">
 <a name="spirit.abstracts.parsing_expression_grammar"></a><a class="link" href="parsing_expression_grammar.html" title="Parsing Expression Grammar">Parsing
       Expression Grammar</a>
 </h3></div></div></div>
 <p>
         Parsing Expression Grammars (PEG) <sup>[<a name="id791566" href="#ftn.id791566" class="footnote">6</a>]</sup> are a derivative of Extended Backus-Naur Form (EBNF) <sup>[<a name="id791578" href="#ftn.id791578" class="footnote">7</a>]</sup> with a different interpretation, designed to represent a recursive
         descent parser. A PEG can be directly represented as a recursive-descent
         parser.
       </p>
 <p>
         Like EBNF, PEG is a formal grammar for describing a formal language in terms
         of a set of rules used to recognize strings of this language. Unlike EBNF,
         PEGs have an exact interpretation. There is only one valid parse tree (see
         Abstract Syntax Tree) for each PEG grammar.
       </p>
 <a name="spirit.abstracts.parsing_expression_grammar.sequences"></a><h5>
 <a name="id791598"></a>
         <a class="link" href="parsing_expression_grammar.html#spirit.abstracts.parsing_expression_grammar.sequences">Sequences</a>
       </h5>
 <p>
         Sequences are represented by juxtaposition like in EBNF:
       </p>
 <pre class="programlisting"><span class="identifier">a</span> <span class="identifier">b</span>
 </pre>
 <p>
         The PEG expression above states that, in order for this to succeed, <code class="computeroutput"><span class="identifier">b</span></code> must follow <code class="computeroutput"><span class="identifier">a</span></code>.
         Here's the syntax diagram:
       </p>
 <div class="blockquote"><blockquote class="blockquote"><p>
           <span class="inlinemediaobject"><img src="../.././images/sequence.png" alt="sequence"></span>
         </p></blockquote></div>
 <p>
         Here's a trivial example:
       </p>
 <pre class="programlisting"><span class="char">'x'</span> <span class="identifier">digit</span>
 </pre>
 <p>
         which means the character <code class="computeroutput"><span class="identifier">x</span></code>
         must be followed by a digit.
       </p>
 <div class="note"><table border="0" summary="Note">
 <tr>
 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../images/note.png"></td>
 <th align="left">Note</th>
 </tr>
 <tr><td align="left" valign="top"><p>
           In <span class="emphasis"><em>Spirit.Qi</em></span>, we use the <code class="computeroutput"><span class="special">&gt;&gt;</span></code>
           for sequences since C++ does not allow juxtaposition, while in <span class="emphasis"><em>Spirit.Karma</em></span>
           we use the <code class="computeroutput"><span class="special">&lt;&lt;</span></code> instead.
         </p></td></tr>
 </table></div>
 <a name="spirit.abstracts.parsing_expression_grammar.alternatives"></a><h5>
 <a name="id791727"></a>
         <a class="link" href="parsing_expression_grammar.html#spirit.abstracts.parsing_expression_grammar.alternatives">Alternatives</a>
       </h5>
 <p>
         Alternatives are represented in PEG using the slash:
       </p>
 <pre class="programlisting"><span class="identifier">a</span> <span class="special">/</span> <span class="identifier">b</span>
 </pre>
 <div class="note"><table border="0" summary="Note">
 <tr>
 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../images/note.png"></td>
 <th align="left">Note</th>
 </tr>
 <tr><td align="left" valign="top"><p>
           In <span class="emphasis"><em>Spirit.Qi</em></span> and <span class="emphasis"><em>Spirit.Karma</em></span>,
           we use the <code class="computeroutput"><span class="special">|</span></code> for alternatives
           just as in EBNF.
         </p></td></tr>
 </table></div>
 <p>
         Alternatives allow for choices. The expression above reads: try to match
         <code class="computeroutput"><span class="identifier">a</span></code>. If <code class="computeroutput"><span class="identifier">a</span></code>
         succeeds, success, if not try to match <code class="computeroutput"><span class="identifier">b</span></code>.
         This is a bit of a deviation from the usual EBNF interpretation where you
         simply match <code class="computeroutput"><span class="identifier">a</span></code> <span class="bold"><strong>or</strong></span> <code class="computeroutput"><span class="identifier">b</span></code>.
         Here's the syntax diagram:
       </p>
 <div class="blockquote"><blockquote class="blockquote"><p>
           <span class="inlinemediaobject"><img src="../.././images/alternative.png" alt="alternative"></span>
         </p></blockquote></div>
 <p>
         PEGs allow for ambiguity in the alternatives. In the expression above, both
         <code class="computeroutput"><span class="identifier">a</span></code> or <code class="computeroutput"><span class="identifier">b</span></code>
         can both match an input string. However, only the first matching alternative
         is valid. As noted, there can only be one valid parse tree.
       </p>
 <a name="spirit.abstracts.parsing_expression_grammar.loops"></a><h5>
 <a name="id791869"></a>
         <a class="link" href="parsing_expression_grammar.html#spirit.abstracts.parsing_expression_grammar.loops">Loops</a>
       </h5>
 <p>
         Again, like EBNF, PEG uses the regular-expression Kleene star and the plus
         loops:
       </p>
 <pre class="programlisting"><span class="identifier">a</span><span class="special">*</span>
 <span class="identifier">a</span><span class="special">+</span>
 </pre>
 <div class="note"><table border="0" summary="Note">
 <tr>
 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../images/note.png"></td>
 <th align="left">Note</th>
 </tr>
 <tr><td align="left" valign="top"><p>
           <span class="emphasis"><em>Spirit.Qi</em></span> and <span class="emphasis"><em>Spirit.Karma</em></span> use
           the prefix star and plus since there is no postfix star or plus in C++.
         </p></td></tr>
 </table></div>
 <p>
         Here are the syntax diagrams:
       </p>
 <div class="blockquote"><blockquote class="blockquote"><p>
           <span class="inlinemediaobject"><img src="../.././images/kleene.png" alt="kleene"></span>
         </p></blockquote></div>
 <div class="blockquote"><blockquote class="blockquote"><p>
           <span class="inlinemediaobject"><img src="../.././images/plus.png" alt="plus"></span>
         </p></blockquote></div>
 <p>
         The first, called the Kleene star, matches zero or more of its subject <code class="computeroutput"><span class="identifier">a</span></code>. The second, plus, matches one ore more
         of its subject <code class="computeroutput"><span class="identifier">a</span></code>.
       </p>
 <p>
         Unlike EBNF, PEGs have greedy loops. It will match as much as it can until
         its subject fails to match without regard to what follows. The following
         is a classic example of a fairly common EBNF/regex expression failing to
         match in PEG:
       </p>
 <pre class="programlisting"><span class="identifier">alnum</span><span class="special">*</span> <span class="identifier">digit</span>
 </pre>
 <p>
         In PEG, alnum will eat as much alpha-numeric characters as it can leaving
         nothing more left behind. Thus, the trailing digit will get nothing. Loops
         are simply implemented in recursive descent code as for/while loops making
         them extremely efficient. That is a definite advantage. On the other hand,
         those who are familiar with EBNF and regex behavior might find the behavior
         a major gotcha. PEG provides a couple of other mechanisms to circumvent this.
         We will see more of these other mechanisms shortly.
       </p>
 <a name="spirit.abstracts.parsing_expression_grammar.difference"></a><h5>
 <a name="id792010"></a>
         <a class="link" href="parsing_expression_grammar.html#spirit.abstracts.parsing_expression_grammar.difference">Difference</a>
       </h5>
 <p>
         In some cases, you may want to restrict a certain expression. You can think
         of a PEG expression as a match for a potentially infinite set of strings.
         The difference operator allows you to restrict this set:
       </p>
 <pre class="programlisting"><span class="identifier">a</span> <span class="special">-</span> <span class="identifier">b</span>
 </pre>
 <p>
         The expression reads: match <code class="computeroutput"><span class="identifier">a</span></code>
         but not <code class="computeroutput"><span class="identifier">b</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="../../images/note.png"></td>
 <th align="left">Note</th>
 </tr>
 <tr><td align="left" valign="top"><p>
           There is no difference operator in <span class="emphasis"><em>Spirit.Karma</em></span>, as
           the concept does not make sense in the context of output generation.
         </p></td></tr>
 </table></div>
 <div class="footnotes">
 <br><hr width="100" align="left">
 <div class="footnote"><p><sup>[<a name="ftn.id791566" href="#id791566" class="para">6</a>] </sup>
           Bryan Ford: Parsing Expression Grammars: A Recognition-Based Syntactic
           Foundation, <a href="http://pdos.csail.mit.edu/~baford/packrat/popl04/" target="_top">http://pdos.csail.mit.edu/~baford/packrat/popl04/</a>
         </p></div>
 <div class="footnote"><p><sup>[<a name="ftn.id791578" href="#id791578" class="para">7</a>] </sup>
           Richard E. Pattis: EBNF: A Notation to Describe Syntax, <a href="http://www.cs.cmu.edu/~pattis/misc/ebnf.pdf" target="_top">http://www.cs.cmu.edu/~pattis/misc/ebnf.pdf</a>
         </p></div>
 </div>
 </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; 2001-2010 Joel de Guzman, Hartmut Kaiser<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>
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	<html>
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	<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
	<title>Parsing Expression Grammar</title>
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	</div>
	<div class="section">
	<div class="titlepage"><div><div><h3 class="title">
	<a name="spirit.abstracts.parsing_expression_grammar"></a><a class="link" href="parsing_expression_grammar.html" title="Parsing Expression Grammar">Parsing
	Expression Grammar</a>
	</h3></div></div></div>
	<p>
	Parsing Expression Grammars (PEG) <sup>[<a name="id791566" href="#ftn.id791566" class="footnote">6</a>]</sup> are a derivative of Extended Backus-Naur Form (EBNF) <sup>[<a name="id791578" href="#ftn.id791578" class="footnote">7</a>]</sup> with a different interpretation, designed to represent a recursive
	descent parser. A PEG can be directly represented as a recursive-descent
	parser.
	</p>
	<p>
	Like EBNF, PEG is a formal grammar for describing a formal language in terms
	of a set of rules used to recognize strings of this language. Unlike EBNF,
	PEGs have an exact interpretation. There is only one valid parse tree (see
	Abstract Syntax Tree) for each PEG grammar.
	</p>
	<a name="spirit.abstracts.parsing_expression_grammar.sequences"></a><h5>
	<a name="id791598"></a>
	<a class="link" href="parsing_expression_grammar.html#spirit.abstracts.parsing_expression_grammar.sequences">Sequences</a>
	</h5>
	<p>
	Sequences are represented by juxtaposition like in EBNF:
	</p>
	<pre class="programlisting"><span class="identifier">a</span> <span class="identifier">b</span>
	</pre>
	<p>
	The PEG expression above states that, in order for this to succeed, <code class="computeroutput"><span class="identifier">b</span></code> must follow <code class="computeroutput"><span class="identifier">a</span></code>.
	Here's the syntax diagram:
	</p>
	<div class="blockquote"><blockquote class="blockquote"><p>
	<span class="inlinemediaobject"><img src="../.././images/sequence.png" alt="sequence"></span>
	</p></blockquote></div>
	<p>
	Here's a trivial example:
	</p>
	<pre class="programlisting"><span class="char">'x'</span> <span class="identifier">digit</span>
	</pre>
	<p>
	which means the character <code class="computeroutput"><span class="identifier">x</span></code>
	must be followed by a digit.
	</p>
	<div class="note"><table border="0" summary="Note">
	<tr>
	<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../images/note.png"></td>
	<th align="left">Note</th>
	</tr>
	<tr><td align="left" valign="top"><p>
	In <span class="emphasis"><em>Spirit.Qi</em></span>, we use the <code class="computeroutput"><span class="special">>></span></code>
	for sequences since C++ does not allow juxtaposition, while in <span class="emphasis"><em>Spirit.Karma</em></span>
	we use the <code class="computeroutput"><span class="special"><<</span></code> instead.
	</p></td></tr>
	</table></div>
	<a name="spirit.abstracts.parsing_expression_grammar.alternatives"></a><h5>
	<a name="id791727"></a>
	<a class="link" href="parsing_expression_grammar.html#spirit.abstracts.parsing_expression_grammar.alternatives">Alternatives</a>
	</h5>
	<p>
	Alternatives are represented in PEG using the slash:
	</p>
	<pre class="programlisting"><span class="identifier">a</span> <span class="special">/</span> <span class="identifier">b</span>
	</pre>
	<div class="note"><table border="0" summary="Note">
	<tr>
	<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../images/note.png"></td>
	<th align="left">Note</th>
	</tr>
	<tr><td align="left" valign="top"><p>
	In <span class="emphasis"><em>Spirit.Qi</em></span> and <span class="emphasis"><em>Spirit.Karma</em></span>,
	we use the <code class="computeroutput"><span class="special">\|</span></code> for alternatives
	just as in EBNF.
	</p></td></tr>
	</table></div>
	<p>
	Alternatives allow for choices. The expression above reads: try to match
	<code class="computeroutput"><span class="identifier">a</span></code>. If <code class="computeroutput"><span class="identifier">a</span></code>
	succeeds, success, if not try to match <code class="computeroutput"><span class="identifier">b</span></code>.
	This is a bit of a deviation from the usual EBNF interpretation where you
	simply match <code class="computeroutput"><span class="identifier">a</span></code> <span class="bold"><strong>or</strong></span> <code class="computeroutput"><span class="identifier">b</span></code>.
	Here's the syntax diagram:
	</p>
	<div class="blockquote"><blockquote class="blockquote"><p>
	<span class="inlinemediaobject"><img src="../.././images/alternative.png" alt="alternative"></span>
	</p></blockquote></div>
	<p>
	PEGs allow for ambiguity in the alternatives. In the expression above, both
	<code class="computeroutput"><span class="identifier">a</span></code> or <code class="computeroutput"><span class="identifier">b</span></code>
	can both match an input string. However, only the first matching alternative
	is valid. As noted, there can only be one valid parse tree.
	</p>
	<a name="spirit.abstracts.parsing_expression_grammar.loops"></a><h5>
	<a name="id791869"></a>
	<a class="link" href="parsing_expression_grammar.html#spirit.abstracts.parsing_expression_grammar.loops">Loops</a>
	</h5>
	<p>
	Again, like EBNF, PEG uses the regular-expression Kleene star and the plus
	loops:
	</p>
	<pre class="programlisting"><span class="identifier">a</span><span class="special">*</span>
	<span class="identifier">a</span><span class="special">+</span>
	</pre>
	<div class="note"><table border="0" summary="Note">
	<tr>
	<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../images/note.png"></td>
	<th align="left">Note</th>
	</tr>
	<tr><td align="left" valign="top"><p>
	<span class="emphasis"><em>Spirit.Qi</em></span> and <span class="emphasis"><em>Spirit.Karma</em></span> use
	the prefix star and plus since there is no postfix star or plus in C++.
	</p></td></tr>
	</table></div>
	<p>
	Here are the syntax diagrams:
	</p>
	<div class="blockquote"><blockquote class="blockquote"><p>
	<span class="inlinemediaobject"><img src="../.././images/kleene.png" alt="kleene"></span>
	</p></blockquote></div>
	<div class="blockquote"><blockquote class="blockquote"><p>
	<span class="inlinemediaobject"><img src="../.././images/plus.png" alt="plus"></span>
	</p></blockquote></div>
	<p>
	The first, called the Kleene star, matches zero or more of its subject <code class="computeroutput"><span class="identifier">a</span></code>. The second, plus, matches one ore more
	of its subject <code class="computeroutput"><span class="identifier">a</span></code>.
	</p>
	<p>
	Unlike EBNF, PEGs have greedy loops. It will match as much as it can until
	its subject fails to match without regard to what follows. The following
	is a classic example of a fairly common EBNF/regex expression failing to
	match in PEG:
	</p>
	<pre class="programlisting"><span class="identifier">alnum</span><span class="special">*</span> <span class="identifier">digit</span>
	</pre>
	<p>
	In PEG, alnum will eat as much alpha-numeric characters as it can leaving
	nothing more left behind. Thus, the trailing digit will get nothing. Loops
	are simply implemented in recursive descent code as for/while loops making
	them extremely efficient. That is a definite advantage. On the other hand,
	those who are familiar with EBNF and regex behavior might find the behavior
	a major gotcha. PEG provides a couple of other mechanisms to circumvent this.
	We will see more of these other mechanisms shortly.
	</p>
	<a name="spirit.abstracts.parsing_expression_grammar.difference"></a><h5>
	<a name="id792010"></a>
	<a class="link" href="parsing_expression_grammar.html#spirit.abstracts.parsing_expression_grammar.difference">Difference</a>
	</h5>
	<p>
	In some cases, you may want to restrict a certain expression. You can think
	of a PEG expression as a match for a potentially infinite set of strings.
	The difference operator allows you to restrict this set:
	</p>
	<pre class="programlisting"><span class="identifier">a</span> <span class="special">-</span> <span class="identifier">b</span>
	</pre>
	<p>
	The expression reads: match <code class="computeroutput"><span class="identifier">a</span></code>
	but not <code class="computeroutput"><span class="identifier">b</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="../../images/note.png"></td>
	<th align="left">Note</th>
	</tr>
	<tr><td align="left" valign="top"><p>
	There is no difference operator in <span class="emphasis"><em>Spirit.Karma</em></span>, as
	the concept does not make sense in the context of output generation.
	</p></td></tr>
	</table></div>
	<div class="footnotes">
	<br><hr width="100" align="left">
	<div class="footnote"><p><sup>[<a name="ftn.id791566" href="#id791566" class="para">6</a>] </sup>
	Bryan Ford: Parsing Expression Grammars: A Recognition-Based Syntactic
	Foundation, <a href="http://pdos.csail.mit.edu/~baford/packrat/popl04/" target="_top">http://pdos.csail.mit.edu/~baford/packrat/popl04/</a>
	</p></div>
	<div class="footnote"><p><sup>[<a name="ftn.id791578" href="#id791578" class="para">7</a>] </sup>
	Richard E. Pattis: EBNF: A Notation to Describe Syntax, <a href="http://www.cs.cmu.edu/~pattis/misc/ebnf.pdf" target="_top">http://www.cs.cmu.edu/~pattis/misc/ebnf.pdf</a>
	</p></div>
	</div>
	</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 © 2001-2010 Joel de Guzman, Hartmut Kaiser<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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