223 lines
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223 lines
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<font size="6" face="Verdana, Arial, Helvetica, sans-serif"><b>Operators</b></font>
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<td width="112"><a href="http://spirit.sf.net"><img src="theme/spirit.gif" width="112" height="48" align="right" border="0"></a></td>
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<p>Operators are used as a means for object composition and embedding. Simple
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parsers may be composed to form composites through operator overloading, crafted
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to approximate the syntax of an Extended Backus-Normal Form (EBNF) variant.
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An expression such as:</p>
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<pre><code><font color="#000000"> <span class=identifier>a </span><span class=special>| </span><span class=identifier>b</span></font></code></pre>
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<p>actually yields a new parser type which is a composite of its operands, a and
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b. Taking this example further, if a and b were of type <tt>chlit</tt><>,
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the result would have the composite type:</p>
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<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>
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<p> In general, for any binary operator, it will take its two arguments, parser1
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and parser2, and create a new composed parser of the form</p>
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<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>
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<p>where parser1 and parser2 can be arbitrarily complex parsers themselves, with
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the only limitations being what your compiler imposes. </p>
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<h3>Set Operators</h3>
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<table width="90%" border="0" align="center">
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<tr>
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<td class="table_title" colspan="3">Set operators</td>
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</tr>
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<tr>
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<td class="table_cells" width="20%"><code><span class=identifier>a </span><span class=special>|
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</span><span class=identifier>b</span></code></td>
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<td class="table_cells" width="24%">Union</td>
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<td class="table_cells" width="56%">Match a or b. Also referred to as alternative</td>
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</tr>
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<td class="table_cells" width="20%"><code><span class=identifier>a </span><span class=special>&
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</span><span class=identifier>b</span></code></td>
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<td class="table_cells" width="24%">Intersection</td>
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<td class="table_cells" width="56%">Match a and b</td>
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</tr>
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<td class="table_cells" width="20%"><code><span class=identifier>a </span><span class=special>-
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</span><span class=identifier>b</span></code></td>
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<td class="table_cells" width="24%">Difference</td>
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<td class="table_cells" width="56%">Match a but not b. If both match and b's
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matched text is shorter than a's matched text, a successful match is made</td>
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</tr>
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<tr>
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<td class="table_cells" width="20%"><code><span class=identifier>a </span><span class=special>^
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</span><span class=identifier>b</span></code></td>
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<td class="table_cells" width="24%">XOR</td>
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<td class="table_cells" width="56%">Match a or b, but not both</td>
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</tr>
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</table>
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<p><b>Short-circuiting</b></p>
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<p>Alternative operands are tried one by one on a first come first served basis
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starting from the leftmost operand. After a successfully matched alternative
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is found, the parser concludes its search, essentially short-circuiting the
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search for other potentially viable candidates. This short-circuiting implicitly
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gives the highest priority to the leftmost alternative.</p>
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<p>Short-circuiting is done in the same manner as C or C++'s logical expressions;
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e.g. <tt>if</tt> <tt><span class="operators">(</span>x <span class="operators"><</span>
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3 <span class="operators">||</span> y <span class="operators"><</span> 2<span class="operators">)</span></tt>
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where, if <tt>x</tt> evaluates to be less than 3, the <tt>y <span class="operators"><</span>
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2</tt> test is not done at all. In addition to providing an implicit priority
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rule for alternatives which is necessary, given the non-deterministic nature
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of the Spirit parser compiler, short-circuiting improves the execution time.
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If the order of your alternatives is logically irrelevant, strive to put the
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(expected) most common choice first for maximum efficiency.</p>
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<table width="80%" border="0" align="center">
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<tr>
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<td class="note_box"><img src="theme/lens.gif" width="15" height="16"> <b>Intersections</b><br>
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<br>
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Some researchers assert that the intersections (e.g. <tt>a & b</tt>)
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let us define context sensitive languages (<a href="references.html#intersections">"XBNF"</a>
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[citing Leu-Weiner, 1973]). "The theory of defining a language as the
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intersection of a finite number of context free languages was developed
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by Leu and Weiner in 1973".<br>
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<br>
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<b><img src="theme/lens.gif" width="15" height="16"> <b></b>~ Operator</b><br>
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<br>
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The complement operator <tt>~</tt> was originally put into consideration.
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Further understanding of its value and meaning leads us to uncertainty.
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The basic problem stems from the fact that <tt>~a</tt> will yield <tt>U-a</tt>,
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where <tt>U</tt> is the universal set of all strings. However, where it
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makes sense, some parsers can be complemented (see the <a href="primitives.html#negation">primitive
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character parsers</a> for examples).</td>
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</tr>
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</table>
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<h3>Sequencing Operators</h3>
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<table width="90%" border="0" align="center">
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<tr>
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<td class="table_title" colspan="3">Sequencing operators</td>
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<td class="table_cells" width="21%"><code><span class=identifier>a </span><span class=special>>>
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</span><span class=identifier>b</span></code></td>
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<td class="table_cells" width="23%">Sequence</td>
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<td class="table_cells" width="56%">Match a and b in sequence</td>
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</tr>
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<td class="table_cells" width="21%"><code><span class=identifier>a </span><span class=special>&&
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</span><span class=identifier>b</span></code></td>
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<td class="table_cells" width="23%">Sequential-and</td>
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<td class="table_cells" width="56%">Sequential-and. Same as above, match a
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and b in sequence</td>
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<td class="table_cells" width="21%"><code><span class=identifier>a </span><span class=special>||
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</span><span class=identifier>b</span></code></td>
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<td class="table_cells" width="23%">Sequential-or</td>
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<td class="table_cells" width="56%">Match a or b in sequence</td>
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</tr>
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</table>
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<p>The sequencing operator <tt class="operators">>></tt> can alternatively
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be thought of as the sequential-and operator. The expression <tt>a <span class="operators">&&</span>
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b</tt> reads as match a and b in sequence. Continuing this logic, we can also
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have a sequential-or operator where the expression <tt>a <span class="operators">||</span>
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b</tt> reads as match a or b and in sequence. That is, if both a and b match,
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it must be in sequence; this is equivalent to <tt>a >> !b | b</tt>. </p>
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<h3>Optional and Loops</h3>
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<table width="90%" border="0" align="center">
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<td class="table_title" colspan="3">Optional and Loops</td>
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<td class="table_cells" width="21%"><code><span class=special>*</span><span class=identifier>a</span></code></td>
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<td class="table_cells" width="23%">Kleene star</td>
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<td class="table_cells" width="56%">Match a zero (0) or more times</td>
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<td class="table_cells" width="21%"><code><span class=special>+</span><span class=identifier>a</span></code></td>
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<td class="table_cells" width="23%">Positive</td>
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<td class="table_cells" width="56%">Match a one (1) or more times</td>
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<td class="table_cells" width="21%"><code><span class=special>!</span><span class=identifier>a</span></code></td>
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<td class="table_cells" width="23%">Optional</td>
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<td class="table_cells" width="56%">Match a zero (0) or one (1) time</td>
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<td class="table_cells" width="21%"><code><span class=identifier>a </span><span class=special>%
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</span><span class=identifier>b</span></code></td>
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<td class="table_cells" width="23%">List</td>
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<td class="table_cells" width="56%">Match a list of one or more repetitions
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of a separated by occurrences of b. This is the same as <tt>a >> *(b
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>> a)</tt>. Note that <tt>a</tt> must not also match <tt>b</tt></td>
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</tr>
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</table>
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<p><img src="theme/note.gif" width="16" height="16"> If we look more closely,
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take note that we generalized the optional expression of the form <tt>!a</tt>
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in the same category as loops. This is logical, considering that the optional
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matches the expression following it zero (0) or one (1) time. </p>
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<p><b>Primitive type operands</b></p>
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<p> For binary operators, one of the operands but not both may be a <tt>char</tt>,
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<tt> wchar_t</tt>, <tt>char const<span class="operators">*</span></tt> or <tt>wchar_t
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const<span class="operators">*</span></tt>. Where P is a parser object, here
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are some examples:</p>
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<pre><code><span class=identifier> </span><span class=identifier>P </span><span class=special>| </span><span class=literal>'x'
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</span><span class=identifier>P </span><span class=special>- </span><span class=identifier>L</span><span class=string>"Hello World"
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</span><span class=literal>'x' </span><span class=special>>> </span><span class=identifier>P
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</span><span class=string>"bebop" </span><span class=special>>> </span><span class=identifier>P</span></code></pre>
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<p>It is important to emphasize that C++ mandates that operators may only be overloaded
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if at least one argument is a user-defined type. Typically, in an expression
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involving multiple operators, explicitly typing the leftmost operand as a parser
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is enough to cause propagation to all the rest of the operands to its right
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to be regarded as parsers. Examples:</p>
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<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
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</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>
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<p>The second case is parsed as follows:</p>
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<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>
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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>
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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>
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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>
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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>
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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>
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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>
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<p><b>Operator precedence and grouping</b></p>
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<p>Since we are defining our meta-language in C++, we follow C/C++'s operator
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precedence rules. Grouping expressions inside the parentheses override this
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(e.g., <tt><span class="operators">*(</span>a <span class="operators">|</span>
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b<span class="operators">)</span></tt> reads: match a or b zero (0) or more
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times). </p>
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<table border="0">
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<td width="10"></td>
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<td width="30"><a href="../index.html"><img src="theme/u_arr.gif" border="0"></a></td>
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</tr>
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</table>
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<br>
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<hr size="1">
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<p class="copyright">Copyright © 1998-2003 Joel de Guzman<br>
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<br>
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<font size="2">Use, modification and distribution is subject to the Boost Software
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License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt) </font> </p>
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<p> </p>
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