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| <font size="6" face="Verdana, Arial, Helvetica, sans-serif"><b>Operators</b></font> |
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| <p>Operators are used as a means for object composition and embedding. Simple |
| parsers may be composed to form composites through operator overloading, crafted |
| to approximate the syntax of an Extended Backus-Normal Form (EBNF) variant. |
| An expression such as:</p> |
| <pre><code><font color="#000000"> <span class=identifier>a </span><span class=special>| </span><span class=identifier>b</span></font></code></pre> |
| <p>actually yields a new parser type which is a composite of its operands, a and |
| b. Taking this example further, if a and b were of type <tt>chlit</tt><>, |
| the result would have the composite type:</p> |
| <pre><code><font color="#000000"> <span class=identifier>alternative</span><span class=special><</span><span class=identifier>chlit</span><span class=special><>, </span><span class=identifier>chlit</span><span class=special><> </span><span class=special>></span></font></code></pre> |
| <p> In general, for any binary operator, it will take its two arguments, parser1 |
| and parser2, and create a new composed parser of the form</p> |
| <pre><code><font color="#000000"> <span class=identifier>op</span><span class=special><</span><span class=identifier>parser1</span><span class=special>, </span><span class=identifier>parser2</span><span class=special>></span></font></code></pre> |
| <p>where parser1 and parser2 can be arbitrarily complex parsers themselves, with |
| the only limitations being what your compiler imposes. </p> |
| <h3>Set Operators</h3> |
| <table width="90%" border="0" align="center"> |
| <tr> |
| <td class="table_title" colspan="3">Set operators</td> |
| </tr> |
| <tr> |
| <td class="table_cells" width="20%"><code><span class=identifier>a </span><span class=special>| |
| </span><span class=identifier>b</span></code></td> |
| <td class="table_cells" width="24%">Union</td> |
| <td class="table_cells" width="56%">Match a or b. Also referred to as alternative</td> |
| </tr> |
| <tr> |
| <td class="table_cells" width="20%"><code><span class=identifier>a </span><span class=special>& |
| </span><span class=identifier>b</span></code></td> |
| <td class="table_cells" width="24%">Intersection</td> |
| <td class="table_cells" width="56%">Match a and b</td> |
| </tr> |
| <tr> |
| <td class="table_cells" width="20%"><code><span class=identifier>a </span><span class=special>- |
| </span><span class=identifier>b</span></code></td> |
| <td class="table_cells" width="24%">Difference</td> |
| <td class="table_cells" width="56%">Match a but not b. If both match and b's |
| matched text is shorter than a's matched text, a successful match is made</td> |
| </tr> |
| <tr> |
| <td class="table_cells" width="20%"><code><span class=identifier>a </span><span class=special>^ |
| </span><span class=identifier>b</span></code></td> |
| <td class="table_cells" width="24%">XOR</td> |
| <td class="table_cells" width="56%">Match a or b, but not both</td> |
| </tr> |
| </table> |
| <p><b>Short-circuiting</b></p> |
| <p>Alternative operands are tried one by one on a first come first served basis |
| starting from the leftmost operand. After a successfully matched alternative |
| is found, the parser concludes its search, essentially short-circuiting the |
| search for other potentially viable candidates. This short-circuiting implicitly |
| gives the highest priority to the leftmost alternative.</p> |
| <p>Short-circuiting is done in the same manner as C or C++'s logical expressions; |
| e.g. <tt>if</tt> <tt><span class="operators">(</span>x <span class="operators"><</span> |
| 3 <span class="operators">||</span> y <span class="operators"><</span> 2<span class="operators">)</span></tt> |
| where, if <tt>x</tt> evaluates to be less than 3, the <tt>y <span class="operators"><</span> |
| 2</tt> test is not done at all. In addition to providing an implicit priority |
| rule for alternatives which is necessary, given the non-deterministic nature |
| of the Spirit parser compiler, short-circuiting improves the execution time. |
| If the order of your alternatives is logically irrelevant, strive to put the |
| (expected) most common choice first for maximum efficiency.</p> |
| <table width="80%" border="0" align="center"> |
| <tr> |
| <td class="note_box"><img src="theme/lens.gif" width="15" height="16"> <b>Intersections</b><br> |
| <br> |
| Some researchers assert that the intersections (e.g. <tt>a & b</tt>) |
| let us define context sensitive languages (<a href="references.html#intersections">"XBNF"</a> |
| [citing Leu-Weiner, 1973]). "The theory of defining a language as the |
| intersection of a finite number of context free languages was developed |
| by Leu and Weiner in 1973".<br> |
| <br> |
| <b><img src="theme/lens.gif" width="15" height="16"> <b></b>~ Operator</b><br> |
| <br> |
| The complement operator <tt>~</tt> was originally put into consideration. |
| Further understanding of its value and meaning leads us to uncertainty. |
| The basic problem stems from the fact that <tt>~a</tt> will yield <tt>U-a</tt>, |
| where <tt>U</tt> is the universal set of all strings. However, where it |
| makes sense, some parsers can be complemented (see the <a href="primitives.html#negation">primitive |
| character parsers</a> for examples).</td> |
| </tr> |
| </table> |
| <h3>Sequencing Operators</h3> |
| <table width="90%" border="0" align="center"> |
| <tr> |
| <td class="table_title" colspan="3">Sequencing operators</td> |
| </tr> |
| <tr> |
| <td class="table_cells" width="21%"><code><span class=identifier>a </span><span class=special>>> |
| </span><span class=identifier>b</span></code></td> |
| <td class="table_cells" width="23%">Sequence</td> |
| <td class="table_cells" width="56%">Match a and b in sequence</td> |
| </tr> |
| <tr> |
| <td class="table_cells" width="21%"><code><span class=identifier>a </span><span class=special>&& |
| </span><span class=identifier>b</span></code></td> |
| <td class="table_cells" width="23%">Sequential-and</td> |
| <td class="table_cells" width="56%">Sequential-and. Same as above, match a |
| and b in sequence</td> |
| </tr> |
| <tr> |
| <td class="table_cells" width="21%"><code><span class=identifier>a </span><span class=special>|| |
| </span><span class=identifier>b</span></code></td> |
| <td class="table_cells" width="23%">Sequential-or</td> |
| <td class="table_cells" width="56%">Match a or b in sequence</td> |
| </tr> |
| </table> |
| <p>The sequencing operator <tt class="operators">>></tt> can alternatively |
| be thought of as the sequential-and operator. The expression <tt>a <span class="operators">&&</span> |
| b</tt> reads as match a and b in sequence. Continuing this logic, we can also |
| have a sequential-or operator where the expression <tt>a <span class="operators">||</span> |
| b</tt> reads as match a or b and in sequence. That is, if both a and b match, |
| it must be in sequence; this is equivalent to <tt>a >> !b | b</tt>. </p> |
| <h3>Optional and Loops</h3> |
| <table width="90%" border="0" align="center"> |
| <tr> |
| <td class="table_title" colspan="3">Optional and Loops</td> |
| </tr> |
| <tr> |
| <td class="table_cells" width="21%"><code><span class=special>*</span><span class=identifier>a</span></code></td> |
| <td class="table_cells" width="23%">Kleene star</td> |
| <td class="table_cells" width="56%">Match a zero (0) or more times</td> |
| </tr> |
| <tr> |
| <td class="table_cells" width="21%"><code><span class=special>+</span><span class=identifier>a</span></code></td> |
| <td class="table_cells" width="23%">Positive</td> |
| <td class="table_cells" width="56%">Match a one (1) or more times</td> |
| </tr> |
| <tr> |
| <td class="table_cells" width="21%"><code><span class=special>!</span><span class=identifier>a</span></code></td> |
| <td class="table_cells" width="23%">Optional</td> |
| <td class="table_cells" width="56%">Match a zero (0) or one (1) time</td> |
| </tr> |
| <tr> |
| <td class="table_cells" width="21%"><code><span class=identifier>a </span><span class=special>% |
| </span><span class=identifier>b</span></code></td> |
| <td class="table_cells" width="23%">List</td> |
| <td class="table_cells" width="56%">Match a list of one or more repetitions |
| of a separated by occurrences of b. This is the same as <tt>a >> *(b |
| >> a)</tt>. Note that <tt>a</tt> must not also match <tt>b</tt></td> |
| </tr> |
| </table> |
| <p><img src="theme/note.gif" width="16" height="16"> If we look more closely, |
| take note that we generalized the optional expression of the form <tt>!a</tt> |
| in the same category as loops. This is logical, considering that the optional |
| matches the expression following it zero (0) or one (1) time. </p> |
| <p><b>Primitive type operands</b></p> |
| <p> For binary operators, one of the operands but not both may be a <tt>char</tt>, |
| <tt> wchar_t</tt>, <tt>char const<span class="operators">*</span></tt> or <tt>wchar_t |
| const<span class="operators">*</span></tt>. Where P is a parser object, here |
| are some examples:</p> |
| <pre><code><span class=identifier> </span><span class=identifier>P </span><span class=special>| </span><span class=literal>'x' |
| </span><span class=identifier>P </span><span class=special>- </span><span class=identifier>L</span><span class=string>"Hello World" |
| </span><span class=literal>'x' </span><span class=special>>> </span><span class=identifier>P |
| </span><span class=string>"bebop" </span><span class=special>>> </span><span class=identifier>P</span></code></pre> |
| <p>It is important to emphasize that C++ mandates that operators may only be overloaded |
| if at least one argument is a user-defined type. Typically, in an expression |
| involving multiple operators, explicitly typing the leftmost operand as a parser |
| is enough to cause propagation to all the rest of the operands to its right |
| to be regarded as parsers. Examples:</p> |
| <pre><code><font color="#000000"><span class=identifier> </span><span class=identifier>r </span><span class=special>= </span><span class=literal>'a' </span><span class=special>| </span><span class=literal>'b' </span><span class=special>| </span><span class=literal>'c' </span><span class=special>| </span><span class=literal>'d'</span><span class=special>; </span><span class=comment>// ill formed |
| </span><span class=identifier>r </span><span class=special>= </span><span class=identifier>ch_p</span><span class=special>(</span><span class=literal>'a'</span><span class=special>) </span><span class=special>| </span><span class=literal>'b' </span><span class=special>| </span><span class=literal>'c' </span><span class=special>| </span><span class=literal>'d'</span><span class=special>; </span><span class=comment>// OK</span></font></code></pre> |
| <p>The second case is parsed as follows:</p> |
| <pre><code><font color="#000000"> r <font color="#0000ff"><img src="theme/arrow.gif"> <span class=special>(((</span><span class=identifier>chlit</span><span class=special><</span><span class=keyword>char</span><span class=special>> </span><span class=special>| </span><span class=keyword>char</span><span class=special>) </span><span class=special>| </span><span class=keyword>char</span><span class=special>) </span><span class=special>| </span><span class=keyword>char</span><span class=special>)</span></font> |
| |
| a <font color="#0000ff"><img src="theme/arrow.gif"> <span class=special>(</span><span class=identifier>chlit</span><span class=special><</span><span class=keyword>char</span><span class=special>> </span><span class=special>| </span><span class=keyword>char</span><span class=special>)</span></font> |
| r <font color="#0000ff"><img src="theme/arrow.gif"> <span class=special>(((</span><span class=identifier>a</span><span class=special>) </span><span class=special>| </span><span class=keyword>char</span><span class=special>) </span><span class=special>| </span><span class=keyword>char</span><span class=special>)</span></font> |
| |
| b <font color="#0000ff"><img src="theme/arrow.gif"> <span class=special>(</span><span class=identifier>a </span><span class=special>| </span><span class=keyword>char</span><span class=special>)</span></font> |
| r <font color="#0000ff"><img src="theme/arrow.gif"> <span class=special>(((</span><span class=identifier>b</span><span class=special>)) </span><span class=special>| </span><span class=keyword>char</span><span class=special>)</span></font> |
| |
| c <font color="#0000ff"><img src="theme/arrow.gif"> <span class=special>(</span><span class=identifier>b </span><span class=special>| </span><span class=keyword>char</span><span class=special>)</span></font> |
| r <font color="#0000ff"><img src="theme/arrow.gif"> <span class=special>(((</span><span class=identifier>c</span><span class=special>)))</span></font></font></code></pre> |
| <p><b>Operator precedence and grouping</b></p> |
| <p>Since we are defining our meta-language in C++, we follow C/C++'s operator |
| precedence rules. Grouping expressions inside the parentheses override this |
| (e.g., <tt><span class="operators">*(</span>a <span class="operators">|</span> |
| b<span class="operators">)</span></tt> reads: match a or b zero (0) or more |
| times). </p> |
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| <p class="copyright">Copyright © 1998-2003 Joel de Guzman<br> |
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| <font size="2">Use, modification and distribution is subject to the Boost Software |
| License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at |
| http://www.boost.org/LICENSE_1_0.txt) </font> </p> |
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