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     Parsing Expression Grammars For Lua, version 0.12
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<h1>LPeg</h1>

<ul>
  <li><strong>Home</strong>
  <ul>
    <li><a href="#intro">Introduction</a></li>
    <li><a href="#func">Functions</a></li>
    <li><a href="#basic">Basic Constructions</a></li>
    <li><a href="#grammar">Grammars</a></li>
    <li><a href="#captures">Captures</a></li>
    <li><a href="#ex">Some Examples</a></li>
    <li><a href="re.html">The <code>re</code> Module</a></li>
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<h2><a name="intro">Introduction</a></h2>

<p>
<em>LPeg</em> is a new pattern-matching library for Lua,
based on
<a href="http://pdos.csail.mit.edu/%7Ebaford/packrat/">
Parsing Expression Grammars</a> (PEGs).
This text is a reference manual for the library.
For a more formal treatment of LPeg,
as well as some discussion about its implementation,
see
<a href="http://www.inf.puc-rio.br/~roberto/docs/peg.pdf">
A Text Pattern-Matching Tool based on Parsing Expression Grammars</a>.
(You may also be interested in my
<a href="http://vimeo.com/1485123">talk about LPeg</a>
given at the III Lua Workshop.)
</p>

<p>
Following the Snobol tradition,
LPeg defines patterns as first-class objects.
That is, patterns are regular Lua values
(represented by userdata).
The library offers several functions to create
and compose patterns.
With the use of metamethods,
several of these functions are provided as infix or prefix
operators.
On the one hand,
the result is usually much more verbose than the typical
encoding of patterns using the so called
<em>regular expressions</em>
(which typically are not regular expressions in the formal sense).
On the other hand,
first-class patterns allow much better documentation
(as it is easy to comment the code,
to break complex definitions in smaller parts, etc.)
and are extensible,
as we can define new functions to create and compose patterns.
</p>

<p>
For a quick glance of the library,
the following table summarizes its basic operations
for creating patterns:
</p>
<table border="1">
<tbody><tr><td><b>Operator</b></td><td><b>Description</b></td></tr>
<tr><td><a href="#op-p"><code>lpeg.P(string)</code></a></td>
  <td>Matches <code>string</code> literally</td></tr>
<tr><td><a href="#op-p"><code>lpeg.P(n)</code></a></td>
  <td>Matches exactly <code>n</code> characters</td></tr>
<tr><td><a href="#op-s"><code>lpeg.S(string)</code></a></td>
  <td>Matches any character in <code>string</code> (Set)</td></tr>
<tr><td><a href="#op-r"><code>lpeg.R("<em>xy</em>")</code></a></td>
  <td>Matches any character between <em>x</em> and <em>y</em> (Range)</td></tr>
<tr><td><a href="#op-pow"><code>patt^n</code></a></td>
  <td>Matches at least <code>n</code> repetitions of <code>patt</code></td></tr>
<tr><td><a href="#op-pow"><code>patt^-n</code></a></td>
  <td>Matches at most <code>n</code> repetitions of <code>patt</code></td></tr>
<tr><td><a href="#op-mul"><code>patt1 * patt2</code></a></td>
  <td>Matches <code>patt1</code> followed by <code>patt2</code></td></tr>
<tr><td><a href="#op-add"><code>patt1 + patt2</code></a></td>
  <td>Matches <code>patt1</code> or <code>patt2</code>
      (ordered choice)</td></tr>
<tr><td><a href="#op-sub"><code>patt1 - patt2</code></a></td>
  <td>Matches <code>patt1</code> if <code>patt2</code> does not match</td></tr>
<tr><td><a href="#op-unm"><code>-patt</code></a></td>
  <td>Equivalent to <code>("" - patt)</code></td></tr>
<tr><td><a href="#op-len"><code>#patt</code></a></td>
  <td>Matches <code>patt</code> but consumes no input</td></tr>
<tr><td><a href="#op-behind"><code>lpeg.B(patt)</code></a></td>
  <td>Matches <code>patt</code> behind the current position,
      consuming no input</td></tr>
</tbody></table>

<p>As a very simple example,
<code>lpeg.R("09")^1</code> creates a pattern that
matches a non-empty sequence of digits.
As a not so simple example,
<code>-lpeg.P(1)</code>
(which can be written as <code>lpeg.P(-1)</code>,
or simply <code>-1</code> for operations expecting a pattern)
matches an empty string only if it cannot match a single character;
so, it succeeds only at the end of the subject.
</p>

<p>
LPeg also offers the <a href="re.html"><code>re</code> module</a>,
which implements patterns following a regular-expression style
(e.g., <code>[09]+</code>).
(This module is 260 lines of Lua code,
and of course it uses LPeg to parse regular expressions and
translate them to regular LPeg patterns.)
</p>


<h2><a name="func">Functions</a></h2>


<h3><a name="f-match"></a><code>lpeg.match (pattern, subject [, init])</code></h3>
<p>
The matching function.
It attempts to match the given pattern against the subject string.
If the match succeeds,
returns the index in the subject of the first character after the match,
or the <a href="#captures">captured values</a>
(if the pattern captured any value).
</p>

<p>
An optional numeric argument <code>init</code> makes the match
start at that position in the subject string.
As usual in Lua libraries,
a negative value counts from the end.
</p>

<p>
Unlike typical pattern-matching functions,
<code>match</code> works only in <em>anchored</em> mode;
that is, it tries to match the pattern with a prefix of
the given subject string (at position <code>init</code>),
not with an arbitrary substring of the subject.
So, if we want to find a pattern anywhere in a string,
we must either write a loop in Lua or write a pattern that
matches anywhere.
This second approach is easy and quite efficient;
see <a href="#ex">examples</a>.
</p>

<h3><a name="f-type"></a><code>lpeg.type (value)</code></h3>
<p>
If the given value is a pattern,
returns the string <code>"pattern"</code>.
Otherwise returns nil.
</p>

<h3><a name="f-version"></a><code>lpeg.version ()</code></h3>
<p>
Returns a string with the running version of LPeg.
</p>

<h3><a name="f-setstack"></a><code>lpeg.setmaxstack (max)</code></h3>
<p>
Sets the maximum size for the backtrack stack used by LPeg to
track calls and choices.
Most well-written patterns need little backtrack levels and
therefore you seldom need to change this maximum;
but a few useful patterns may need more space.
Before changing this maximum you should try to rewrite your
pattern to avoid the need for extra space.
</p>


<h2><a name="basic">Basic Constructions</a></h2>

<p>
The following operations build patterns.
All operations that expect a pattern as an argument
may receive also strings, tables, numbers, booleans, or functions,
which are translated to patterns according to
the rules of function <a href="#op-p"><code>lpeg.P</code></a>.
</p>


<h3><a name="op-p"></a><code>lpeg.P (value)</code></h3>
<p>
Converts the given value into a proper pattern,
according to the following rules:
</p>
<ul>

<li><p>
If the argument is a pattern,
it is returned unmodified.
</p></li>

<li><p>
If the argument is a string,
it is translated to a pattern that matches the string literally.
</p></li>

<li><p>
If the argument is a non-negative number <em>n</em>,
the result is a pattern that matches exactly <em>n</em> characters.
</p></li>

<li><p>
If the argument is a negative number <em>-n</em>,
the result is a pattern that
succeeds only if the input string has less than <em>n</em> characters left:
<code>lpeg.P(-n)</code>
is equivalent to <code>-lpeg.P(n)</code>
(see the  <a href="#op-unm">unary minus operation</a>).
</p></li>

<li><p>
If the argument is a boolean,
the result is a pattern that always succeeds or always fails
(according to the boolean value),
without consuming any input.
</p></li>

<li><p>
If the argument is a table,
it is interpreted as a grammar
(see <a href="#grammar">Grammars</a>).
</p></li>

<li><p>
If the argument is a function,
returns a pattern equivalent to a
<a href="#matchtime">match-time capture</a> over the empty string.
</p></li>

</ul>


<h3><a name="op-behind"></a><code>lpeg.B(patt)</code></h3>
<p>
Returns a pattern that
matches only if the input string at the current position
is preceded by <code>patt</code>.
Pattern <code>patt</code> must match only strings
with some fixed length,
and it cannot contain captures.
</p>

<p>
Like the <a href="#op-len">and predicate</a>,
this pattern never consumes any input,
independently of success or failure.
</p>


<h3><a name="op-r"></a><code>lpeg.R ({range})</code></h3>
<p>
Returns a pattern that matches any single character
belonging to one of the given <em>ranges</em>.
Each <code>range</code> is a string <em>xy</em> of length 2,
representing all characters with code
between the codes of <em>x</em> and <em>y</em>
(both inclusive).
</p>

<p>
As an example, the pattern
<code>lpeg.R("09")</code> matches any digit,
and <code>lpeg.R("az", "AZ")</code> matches any ASCII letter.
</p>


<h3><a name="op-s"></a><code>lpeg.S (string)</code></h3>
<p>
Returns a pattern that matches any single character that
appears in the given string.
(The <code>S</code> stands for <em>Set</em>.)
</p>

<p>
As an example, the pattern
<code>lpeg.S("+-*/")</code> matches any arithmetic operator.
</p>

<p>
Note that, if <code>s</code> is a character
(that is, a string of length 1),
then <code>lpeg.P(s)</code> is equivalent to <code>lpeg.S(s)</code>
which is equivalent to <code>lpeg.R(s..s)</code>.
Note also that both <code>lpeg.S("")</code> and <code>lpeg.R()</code>
are patterns that always fail.
</p>


<h3><a name="op-v"></a><code>lpeg.V (v)</code></h3>
<p>
This operation creates a non-terminal (a <em>variable</em>)
for a grammar.
The created non-terminal refers to the rule indexed by <code>v</code>
in the enclosing grammar.
(See <a href="#grammar">Grammars</a> for details.)
</p>


<h3><a name="op-locale"></a><code>lpeg.locale ([table])</code></h3>
<p>
Returns a table with patterns for matching some character classes
according to the current locale.
The table has fields named
<code>alnum</code>,
<code>alpha</code>,
<code>cntrl</code>,
<code>digit</code>,
<code>graph</code>,
<code>lower</code>,
<code>print</code>,
<code>punct</code>,
<code>space</code>,
<code>upper</code>, and
<code>xdigit</code>,
each one containing a correspondent pattern.
Each pattern matches any single character that belongs to its class.
</p>

<p>
If called with an argument <code>table</code>,
then it creates those fields inside the given table and
returns that table. 
</p>


<h3><a name="op-len"></a><code>#patt</code></h3>
<p>
Returns a pattern that
matches only if the input string matches <code>patt</code>,
but without consuming any input,
independently of success or failure.
(This pattern is called an <em>and predicate</em>
and it is equivalent to
<em>&amp;patt</em> in the original PEG notation.)
</p>


<p>
This pattern never produces any capture.
</p>


<h3><a name="op-unm"></a><code>-patt</code></h3>
<p>
Returns a pattern that
matches only if the input string does not match <code>patt</code>.
It does not consume any input,
independently of success or failure.
(This pattern is equivalent to
<em>!patt</em> in the original PEG notation.)
</p>

<p>
As an example, the pattern
<code>-lpeg.P(1)</code> matches only the end of string.
</p>

<p>
This pattern never produces any captures,
because either <code>patt</code> fails
or <code>-patt</code> fails.
(A failing pattern never produces captures.)
</p>


<h3><a name="op-add"></a><code>patt1 + patt2</code></h3>
<p>
Returns a pattern equivalent to an <em>ordered choice</em>
of <code>patt1</code> and <code>patt2</code>.
(This is denoted by <em>patt1 / patt2</em> in the original PEG notation,
not to be confused with the <code>/</code> operation in LPeg.)
It matches either <code>patt1</code> or <code>patt2</code>,
with no backtracking once one of them succeeds.
The identity element for this operation is the pattern
<code>lpeg.P(false)</code>,
which always fails.
</p>

<p>
If both <code>patt1</code> and <code>patt2</code> are
character sets,
this operation is equivalent to set union.
</p>
<pre class="example">
lower = lpeg.R("az")
upper = lpeg.R("AZ")
letter = lower + upper
</pre>


<h3><a name="op-sub"></a><code>patt1 - patt2</code></h3>
<p>
Returns a pattern equivalent to <em>!patt2 patt1</em>.
This pattern asserts that the input does not match
<code>patt2</code> and then matches <code>patt1</code>.
</p>

<p>
When successful,
this pattern produces all captures from <code>patt1</code>.
It never produces any capture from <code>patt2</code>
(as either <code>patt2</code> fails or
<code>patt1 - patt2</code> fails).
</p>

<p>
If both <code>patt1</code> and <code>patt2</code> are
character sets,
this operation is equivalent to set difference.
Note that <code>-patt</code> is equivalent to <code>"" - patt</code>
(or <code>0 - patt</code>).
If <code>patt</code> is a character set,
<code>1 - patt</code> is its complement.
</p>


<h3><a name="op-mul"></a><code>patt1 * patt2</code></h3>
<p>
Returns a pattern that matches <code>patt1</code>
and then matches <code>patt2</code>,
starting where <code>patt1</code> finished.
The identity element for this operation is the
pattern <code>lpeg.P(true)</code>,
which always succeeds.
</p>

<p>
(LPeg uses the <code>*</code> operator
[instead of the more obvious <code>..</code>]
both because it has
the right priority and because in formal languages it is
common to use a dot for denoting concatenation.)
</p>


<h3><a name="op-pow"></a><code>patt^n</code></h3>
<p>
If <code>n</code> is nonnegative,
this pattern is
equivalent to <em>patt<sup>n</sup> patt*</em>:
It matches <code>n</code> or more occurrences of <code>patt</code>.
</p>

<p>
Otherwise, when <code>n</code> is negative,
this pattern is equivalent to <em>(patt?)<sup>-n</sup></em>:
It matches at most <code>|n|</code>
occurrences of <code>patt</code>.
</p>

<p>
In particular, <code>patt^0</code> is equivalent to <em>patt*</em>,
<code>patt^1</code> is equivalent to <em>patt+</em>,
and <code>patt^-1</code> is equivalent to <em>patt?</em>
in the original PEG notation.
</p>

<p>
In all cases,
the resulting pattern is greedy with no backtracking
(also called a <em>possessive</em> repetition).
That is, it matches only the longest possible sequence
of matches for <code>patt</code>.
</p>


<h2><a name="grammar">Grammars</a></h2>

<p>
With the use of Lua variables,
it is possible to define patterns incrementally,
with each new pattern using previously defined ones.
However, this technique does not allow the definition of
recursive patterns.
For recursive patterns,
we need real grammars.
</p>

<p>
LPeg represents grammars with tables,
where each entry is a rule.
</p>

<p>
The call <code>lpeg.V(v)</code>
creates a pattern that represents the nonterminal
(or <em>variable</em>) with index <code>v</code> in a grammar.
Because the grammar still does not exist when
this function is evaluated,
the result is an <em>open reference</em> to the respective rule.
</p>

<p>
A table is <em>fixed</em> when it is converted to a pattern
(either by calling <code>lpeg.P</code> or by using it wherein a
pattern is expected).
Then every open reference created by <code>lpeg.V(v)</code>
is corrected to refer to the rule indexed by <code>v</code> in the table.
</p>

<p>
When a table is fixed,
the result is a pattern that matches its <em>initial rule</em>.
The entry with index 1 in the table defines its initial rule.
If that entry is a string,
it is assumed to be the name of the initial rule.
Otherwise, LPeg assumes that the entry 1 itself is the initial rule.
</p>

<p>
As an example,
the following grammar matches strings of a's and b's that
have the same number of a's and b's:
</p>
<pre class="example">
equalcount = lpeg.P{
  "S";   -- initial rule name
  S = "a" * lpeg.V"B" + "b" * lpeg.V"A" + "",
  A = "a" * lpeg.V"S" + "b" * lpeg.V"A" * lpeg.V"A",
  B = "b" * lpeg.V"S" + "a" * lpeg.V"B" * lpeg.V"B",
} * -1
</pre>
<p>
It is equivalent to the following grammar in standard PEG notation:
</p>
<pre class="example">
  S <- 'a' B / 'b' A / ''
  A <- 'a' S / 'b' A A
  B <- 'b' S / 'a' B B
</pre>


<h2><a name="captures">Captures</a></h2>

<p>
A <em>capture</em> is a pattern that creates values
(the so called <em>semantic information</em>) when it matches.
LPeg offers several kinds of captures,
which produces values based on matches and combine these values to
produce new values.
Each capture may produce zero or more values.
</p>

<p>
The following table summarizes the basic captures:
</p>
<table border="1">
<tbody><tr><td><b>Operation</b></td><td><b>What it Produces</b></td></tr>
<tr><td><a href="#cap-c"><code>lpeg.C(patt)</code></a></td>
  <td>the match for <code>patt</code> plus all captures
      made by <code>patt</code></td></tr>
<tr><td><a href="#cap-arg"><code>lpeg.Carg(n)</code></a></td>
    <td>the value of the n<sup>th</sup> extra argument to
        <code>lpeg.match</code> (matches the empty string)</td></tr>
<tr><td><a href="#cap-b"><code>lpeg.Cb(name)</code></a></td>
    <td>the values produced by the previous
        group capture named <code>name</code>
        (matches the empty string)</td></tr>
<tr><td><a href="#cap-cc"><code>lpeg.Cc(values)</code></a></td>
    <td>the given values (matches the empty string)</td></tr>
<tr><td><a href="#cap-f"><code>lpeg.Cf(patt, func)</code></a></td>
  <td>a <em>folding</em> of the captures from <code>patt</code></td></tr>
<tr><td><a href="#cap-g"><code>lpeg.Cg(patt [, name])</code></a></td>
    <td>the values produced by <code>patt</code>,
        optionally tagged with <code>name</code></td></tr>
<tr><td><a href="#cap-p"><code>lpeg.Cp()</code></a></td>
    <td>the current position (matches the empty string)</td></tr>
<tr><td><a href="#cap-s"><code>lpeg.Cs(patt)</code></a></td>
  <td>the match for <code>patt</code>
      with the values from nested captures replacing their matches</td></tr>
<tr><td><a href="#cap-t"><code>lpeg.Ct(patt)</code></a></td>
  <td>a table with all captures from <code>patt</code></td></tr>
<tr><td><a href="#cap-string"><code>patt / string</code></a></td>
  <td><code>string</code>, with some marks replaced by captures
      of <code>patt</code></td></tr>
<tr><td><a href="#cap-num"><code>patt / number</code></a></td>
  <td>the n-th value captured by <code>patt</code>,
or no value when <code>number</code> is zero.</td></tr>
<tr><td><a href="#cap-query"><code>patt / table</code></a></td>
  <td><code>table[c]</code>, where <code>c</code> is the (first)
      capture of <code>patt</code></td></tr>
<tr><td><a href="#cap-func"><code>patt / function</code></a></td>
  <td>the returns of <code>function</code> applied to the captures
      of <code>patt</code></td></tr>
<tr><td><a href="#matchtime"><code>lpeg.Cmt(patt, function)</code></a></td>
  <td>the returns of <code>function</code> applied to the captures
      of <code>patt</code>; the application is done at match time</td></tr>
</tbody></table>

<p>
A capture pattern produces its values every time it succeeds.
For instance,
a capture inside a loop produces as many values as matched by the loop.
A capture produces a value only when it succeeds.
For instance,
the pattern <code>lpeg.C(lpeg.P"a"^-1)</code>
produces the empty string when there is no <code>"a"</code>
(because the pattern <code>"a"?</code> succeeds),
while the pattern <code>lpeg.C("a")^-1</code>
does not produce any value when there is no <code>"a"</code>
(because the pattern <code>"a"</code> fails).
</p>

<p>
Usually,
LPeg evaluates all captures only after (and if) the entire match succeeds.
During <em>match time</em> it only gathers enough information
to produce the capture values later.
As a particularly important consequence,
most captures cannot affect the way a pattern matches a subject.
The only exception to this rule is the
so-called <a href="#matchtime"><em>match-time capture</em></a>.
When a match-time capture matches,
it forces the immediate evaluation of all its nested captures
and then calls its corresponding function,
which defines whether the match succeeds and also
what values are produced.
</p>

<h3><a name="cap-c"></a><code>lpeg.C (patt)</code></h3>
<p>
Creates a <em>simple capture</em>,
which captures the substring of the subject that matches <code>patt</code>.
The captured value is a string.
If <code>patt</code> has other captures,
their values are returned after this one.
</p>


<h3><a name="cap-arg"></a><code>lpeg.Carg (n)</code></h3>
<p>
Creates an <em>argument capture</em>.
This pattern matches the empty string and
produces the value given as the n<sup>th</sup> extra
argument given in the call to <code>lpeg.match</code>.
</p>


<h3><a name="cap-b"></a><code>lpeg.Cb (name)</code></h3>
<p>
Creates a <em>back capture</em>.
This pattern matches the empty string and
produces the values produced by the <em>most recent</em>
<a href="#cap-g">group capture</a> named <code>name</code>.
</p>

<p>
<em>Most recent</em> means the last
<em>complete</em>
<em>outermost</em>
group capture with the given name.
A <em>Complete</em> capture means that the entire pattern
corresponding to the capture has matched.
An <em>Outermost</em> capture means that the capture is not inside
another complete capture.
</p>


<h3><a name="cap-cc"></a><code>lpeg.Cc ([value, ...])</code></h3>
<p>
Creates a <em>constant capture</em>.
This pattern matches the empty string and
produces all given values as its captured values.
</p>


<h3><a name="cap-f"></a><code>lpeg.Cf (patt, func)</code></h3>
<p>
Creates a <em>fold capture</em>.
If <code>patt</code> produces a list of captures
<em>C<sub>1</sub> C<sub>2</sub> ... C<sub>n</sub></em>,
this capture will produce the value
<em>func(...func(func(C<sub>1</sub>, C<sub>2</sub>), C<sub>3</sub>)...,
         C<sub>n</sub>)</em>,
that is, it will <em>fold</em>
(or <em>accumulate</em>, or <em>reduce</em>)
the captures from <code>patt</code> using function <code>func</code>.
</p>

<p>
This capture assumes that <code>patt</code> should produce
at least one capture with at least one value (of any type),
which becomes the initial value of an <em>accumulator</em>.
(If you need a specific initial value,
you may prefix a <a href="#cap-cc">constant capture</a> to <code>patt</code>.)
For each subsequent capture,
LPeg calls <code>func</code>
with this accumulator as the first argument and all values produced
by the capture as extra arguments;
the first result from this call
becomes the new value for the accumulator.
The final value of the accumulator becomes the captured value.
</p>

<p>
As an example,
the following pattern matches a list of numbers separated
by commas and returns their addition:
</p>
<pre class="example">
-- matches a numeral and captures its numerical value
number = lpeg.R"09"^1 / tonumber

-- matches a list of numbers, capturing their values
list = number * ("," * number)^0

-- auxiliary function to add two numbers
function add (acc, newvalue) return acc + newvalue end

-- folds the list of numbers adding them
sum = lpeg.Cf(list, add)

-- example of use
print(sum:match("10,30,43"))   --&gt; 83
</pre>


<h3><a name="cap-g"></a><code>lpeg.Cg (patt [, name])</code></h3>
<p>
Creates a <em>group capture</em>.
It groups all values returned by <code>patt</code>
into a single capture.
The group may be anonymous (if no name is given)
or named with the given name.
</p>

<p>
An anonymous group serves to join values from several captures into
a single capture.
A named group has a different behavior.
In most situations, a named group returns no values at all.
Its values are only relevant for a following
<a href="#cap-b">back capture</a> or when used
inside a <a href="#cap-t">table capture</a>.
</p>


<h3><a name="cap-p"></a><code>lpeg.Cp ()</code></h3>
<p>
Creates a <em>position capture</em>.
It matches the empty string and
captures the position in the subject where the match occurs.
The captured value is a number.
</p>


<h3><a name="cap-s"></a><code>lpeg.Cs (patt)</code></h3>
<p>
Creates a <em>substitution capture</em>,
which captures the substring of the subject that matches <code>patt</code>,
with <em>substitutions</em>.
For any capture inside <code>patt</code> with a value,
the substring that matched the capture is replaced by the capture value
(which should be a string).
The final captured value is the string resulting from
all replacements.
</p>


<h3><a name="cap-t"></a><code>lpeg.Ct (patt)</code></h3>
<p>
Creates a <em>table capture</em>.
This capture creates a table and puts all values from all anonymous captures
made by <code>patt</code> inside this table in successive integer keys,
starting at 1.
Moreover,
for each named capture group created by <code>patt</code>,
the first value of the group is put into the table
with the group name as its key.
The captured value is only the table.
</p>


<h3><a name="cap-string"></a><code>patt / string</code></h3>
<p>
Creates a <em>string capture</em>.
It creates a capture string based on <code>string</code>.
The captured value is a copy of <code>string</code>,
except that the character <code>%</code> works as an escape character:
any sequence in <code>string</code> of the form <code>%<em>n</em></code>,
with <em>n</em> between 1 and 9,
stands for the match of the <em>n</em>-th capture in <code>patt</code>.
The sequence <code>%0</code> stands for the whole match.
The sequence <code>%%</code> stands for a single&nbsp;<code>%</code>.
</p>


<h3><a name="cap-num"></a><code>patt / number</code></h3>
<p>
Creates a <em>numbered capture</em>.
For a non-zero number,
the captured value is the n-th value
captured by <code>patt</code>. 
When <code>number</code> is zero,
there are no captured values.
</p>


<h3><a name="cap-query"></a><code>patt / table</code></h3>
<p>
Creates a <em>query capture</em>.
It indexes the given table using as key the first value captured by
<code>patt</code>,
or the whole match if <code>patt</code> produced no value.
The value at that index is the final value of the capture.
If the table does not have that key,
there is no captured value.
</p>


<h3><a name="cap-func"></a><code>patt / function</code></h3>
<p>
Creates a <em>function capture</em>.
It calls the given function passing all captures made by
<code>patt</code> as arguments,
or the whole match if <code>patt</code> made no capture.
The values returned by the function
are the final values of the capture.
In particular,
if <code>function</code> returns no value,
there is no captured value.
</p>


<h3><a name="matchtime"></a><code>lpeg.Cmt(patt, function)</code></h3>
<p>
Creates a <em>match-time capture</em>.
Unlike all other captures,
this one is evaluated immediately when a match occurs.
It forces the immediate evaluation of all its nested captures
and then calls <code>function</code>.
</p>

<p>
The given function gets as arguments the entire subject,
the current position (after the match of <code>patt</code>),
plus any capture values produced by <code>patt</code>.
</p>

<p>
The first value returned by <code>function</code>
defines how the match happens.
If the call returns a number,
the match succeeds
and the returned number becomes the new current position.
(Assuming a subject <em>s</em> and current position <em>i</em>,
the returned number must be in the range <em>[i, len(s) + 1]</em>.)
If the call returns <b>true</b>,
the match succeeds without consuming any input.
(So, to return <b>true</b> is equivalent to return <em>i</em>.)
If the call returns <b>false</b>, <b>nil</b>, or no value,
the match fails.
</p>

<p>
Any extra values returned by the function become the
values produced by the capture.
</p>


<h2><a name="ex">Some Examples</a></h2>

<h3>Using a Pattern</h3>
<p>
This example shows a very simple but complete program
that builds and uses a pattern:
</p>
<pre class="example">
local lpeg = require "lpeg"

-- matches a word followed by end-of-string
p = lpeg.R"az"^1 * -1

print(p:match("hello"))        --> 6
print(lpeg.match(p, "hello"))  --> 6
print(p:match("1 hello"))      --> nil
</pre>
<p>
The pattern is simply a sequence of one or more lower-case letters
followed by the end of string (-1).
The program calls <code>match</code> both as a method
and as a function.
In both sucessful cases,
the match returns 
the index of the first character after the match,
which is the string length plus one.
</p>


<h3>Name-value lists</h3>
<p>
This example parses a list of name-value pairs and returns a table
with those pairs:
</p>
<pre class="example">
lpeg.locale(lpeg)   -- adds locale entries into 'lpeg' table

local space = lpeg.space^0
local name = lpeg.C(lpeg.alpha^1) * space
local sep = lpeg.S(",;") * space
local pair = lpeg.Cg(name * "=" * space * name) * sep^-1
local list = lpeg.Cf(lpeg.Ct("") * pair^0, rawset)
t = list:match("a=b, c = hi; next = pi")  --> { a = "b", c = "hi", next = "pi" }
</pre>
<p>
Each pair has the format <code>name = name</code> followed by
an optional separator (a comma or a semicolon).
The <code>pair</code> pattern encloses the pair in a group pattern,
so that the names become the values of a single capture.
The <code>list</code> pattern then folds these captures.
It starts with an empty table,
created by a table capture matching an empty string;
then for each capture (a pair of names) it applies <code>rawset</code>
over the accumulator (the table) and the capture values (the pair of names).
<code>rawset</code> returns the table itself,
so the accumulator is always the table.
</p>

<h3>Splitting a string</h3>
<p>
The following code builds a pattern that
splits a string using a given pattern
<code>sep</code> as a separator:
</p>
<pre class="example">
function split (s, sep)
  sep = lpeg.P(sep)
  local elem = lpeg.C((1 - sep)^0)
  local p = elem * (sep * elem)^0
  return lpeg.match(p, s)
end
</pre>
<p>
First the function ensures that <code>sep</code> is a proper pattern.
The pattern <code>elem</code> is a repetition of zero of more
arbitrary characters as long as there is not a match against
the separator.
It also captures its match.
The pattern <code>p</code> matches a list of elements separated
by <code>sep</code>.
</p>

<p>
If the split results in too many values,
it may overflow the maximum number of values
that can be returned by a Lua function.
In this case,
we can collect these values in a table:
</p>
<pre class="example">
function split (s, sep)
  sep = lpeg.P(sep)
  local elem = lpeg.C((1 - sep)^0)
  local p = lpeg.Ct(elem * (sep * elem)^0)   -- make a table capture
  return lpeg.match(p, s)
end
</pre>


<h3>Searching for a pattern</h3>
<p>
The primitive <code>match</code> works only in anchored mode.
If we want to find a pattern anywhere in a string,
we must write a pattern that matches anywhere.
</p>

<p>
Because patterns are composable,
we can write a function that,
given any arbitrary pattern <code>p</code>,
returns a new pattern that searches for <code>p</code>
anywhere in a string.
There are several ways to do the search.
One way is like this:
</p>
<pre class="example">
function anywhere (p)
  return lpeg.P{ p + 1 * lpeg.V(1) }
end
</pre>
<p>
This grammar has a straight reading:
it matches <code>p</code> or skips one character and tries again.
</p>

<p>
If we want to know where the pattern is in the string
(instead of knowing only that it is there somewhere),
we can add position captures to the pattern:
</p>
<pre class="example">
local I = lpeg.Cp()
function anywhere (p)
  return lpeg.P{ I * p * I + 1 * lpeg.V(1) }
end

print(anywhere("world"):match("hello world!"))   -> 7   12
</pre>

<p>
Another option for the search is like this:
</p>
<pre class="example">
local I = lpeg.Cp()
function anywhere (p)
  return (1 - lpeg.P(p))^0 * I * p * I
end
</pre>
<p>
Again the pattern has a straight reading:
it skips as many characters as possible while not matching <code>p</code>,
and then matches <code>p</code> (plus appropriate captures).
</p>

<p>
If we want to look for a pattern only at word boundaries,
we can use the following transformer:
</p>

<pre class="example">
local t = lpeg.locale()

function atwordboundary (p)
  return lpeg.P{
    [1] = p + t.alpha^0 * (1 - t.alpha)^1 * lpeg.V(1)
  }
end
</pre>


<h3><a name="balanced"></a>Balanced parentheses</h3>
<p>
The following pattern matches only strings with balanced parentheses:
</p>
<pre class="example">
b = lpeg.P{ "(" * ((1 - lpeg.S"()") + lpeg.V(1))^0 * ")" }
</pre>
<p>
Reading the first (and only) rule of the given grammar,
we have that a balanced string is
an open parenthesis,
followed by zero or more repetitions of either
a non-parenthesis character or
a balanced string (<code>lpeg.V(1)</code>),
followed by a closing parenthesis.
</p>


<h3>Global substitution</h3>
<p>
The next example does a job somewhat similar to <code>string.gsub</code>.
It receives a pattern and a replacement value,
and substitutes the replacement value for all occurrences of the pattern
in a given string:
</p>
<pre class="example">
function gsub (s, patt, repl)
  patt = lpeg.P(patt)
  patt = lpeg.Cs((patt / repl + 1)^0)
  return lpeg.match(patt, s)
end
</pre>
<p>
As in <code>string.gsub</code>,
the replacement value can be a string,
a function, or a table.
</p>


<h3><a name="CSV"></a>Comma-Separated Values (CSV)</h3>
<p>
This example breaks a string into comma-separated values,
returning all fields:
</p>
<pre class="example">
local field = '"' * lpeg.Cs(((lpeg.P(1) - '"') + lpeg.P'""' / '"')^0) * '"' +
                    lpeg.C((1 - lpeg.S',\n"')^0)

local record = field * (',' * field)^0 * (lpeg.P'\n' + -1)

function csv (s)
  return lpeg.match(record, s)
end
</pre>
<p>
A field is either a quoted field
(which may contain any character except an individual quote,
which may be written as two quotes that are replaced by one)
or an unquoted field
(which cannot contain commas, newlines, or quotes).
A record is a list of fields separated by commas,
ending with a newline or the string end (-1).
</p>

<p>
As it is,
the previous pattern returns each field as a separated result.
If we add a table capture in the definition of <code>record</code>,
the pattern will return instead a single table
containing all fields:
</p>
<pre>
local record = lpeg.Ct(field * (',' * field)^0) * (lpeg.P'\n' + -1)
</pre>


<h3>UTF-8 and Latin 1</h3>
<p>
It is not difficult to use LPeg to convert a string from
UTF-8 encoding to Latin 1 (ISO 8859-1):
</p>

<pre class="example">
-- convert a two-byte UTF-8 sequence to a Latin 1 character
local function f2 (s)
  local c1, c2 = string.byte(s, 1, 2)
  return string.char(c1 * 64 + c2 - 12416)
end

local utf8 = lpeg.R("\0\127")
           + lpeg.R("\194\195") * lpeg.R("\128\191") / f2

local decode_pattern = lpeg.Cs(utf8^0) * -1
</pre>
<p>
In this code,
the definition of UTF-8 is already restricted to the
Latin 1 range (from 0 to 255).
Any encoding outside this range (as well as any invalid encoding)
will not match that pattern.
</p>

<p>
As the definition of <code>decode_pattern</code> demands that
the pattern matches the whole input (because of the -1 at its end),
any invalid string will simply fail to match,
without any useful information about the problem.
We can improve this situation redefining <code>decode_pattern</code>
as follows:
</p>
<pre class="example">
local function er (_, i) error("invalid encoding at position " .. i) end

local decode_pattern = lpeg.Cs(utf8^0) * (-1 + lpeg.P(er))
</pre>
<p>
Now, if the pattern <code>utf8^0</code> stops
before the end of the string,
an appropriate error function is called.
</p>


<h3>UTF-8 and Unicode</h3>
<p>
We can extend the previous patterns to handle all Unicode code points.
Of course,
we cannot translate them to Latin 1 or any other one-byte encoding.
Instead, our translation results in a array with the code points
represented as numbers.
The full code is here:
</p>
<pre class="example">
-- decode a two-byte UTF-8 sequence
local function f2 (s)
  local c1, c2 = string.byte(s, 1, 2)
  return c1 * 64 + c2 - 12416
end

-- decode a three-byte UTF-8 sequence
local function f3 (s)
  local c1, c2, c3 = string.byte(s, 1, 3)
  return (c1 * 64 + c2) * 64 + c3 - 925824
end

-- decode a four-byte UTF-8 sequence
local function f4 (s)
  local c1, c2, c3, c4 = string.byte(s, 1, 4)
  return ((c1 * 64 + c2) * 64 + c3) * 64 + c4 - 63447168
end

local cont = lpeg.R("\128\191")   -- continuation byte

local utf8 = lpeg.R("\0\127") / string.byte
           + lpeg.R("\194\223") * cont / f2
           + lpeg.R("\224\239") * cont * cont / f3
           + lpeg.R("\240\244") * cont * cont * cont / f4

local decode_pattern = lpeg.Ct(utf8^0) * -1
</pre>


<h3>Lua's long strings</h3>
<p>
A long string in Lua starts with the pattern <code>[=*[</code>
and ends at the first occurrence of <code>]=*]</code> with
exactly the same number of equal signs.
If the opening brackets are followed by a newline,
this newline is discarded
(that is, it is not part of the string).
</p>

<p>
To match a long string in Lua,
the pattern must capture the first repetition of equal signs and then,
whenever it finds a candidate for closing the string,
check whether it has the same number of equal signs.
</p>

<pre class="example">
equals = lpeg.P"="^0
open = "[" * lpeg.Cg(equals, "init") * "[" * lpeg.P"\n"^-1
close = "]" * lpeg.C(equals) * "]"
closeeq = lpeg.Cmt(close * lpeg.Cb("init"), function (s, i, a, b) return a == b end)
string = open * lpeg.C((lpeg.P(1) - closeeq)^0) * close / 1
</pre>

<p>
The <code>open</code> pattern matches <code>[=*[</code>,
capturing the repetitions of equal signs in a group named <code>init</code>;
it also discharges an optional newline, if present.
The <code>close</code> pattern matches <code>]=*]</code>,
also capturing the repetitions of equal signs.
The <code>closeeq</code> pattern first matches <code>close</code>;
then it uses a back capture to recover the capture made
by the previous <code>open</code>,
which is named <code>init</code>;
finally it uses a match-time capture to check
whether both captures are equal.
The <code>string</code> pattern starts with an <code>open</code>,
then it goes as far as possible until matching <code>closeeq</code>,
and then matches the final <code>close</code>.
The final numbered capture simply discards
the capture made by <code>close</code>.
</p>


<h3>Arithmetic expressions</h3>
<p>
This example is a complete parser and evaluator for simple
arithmetic expressions.
We write it in two styles.
The first approach first builds a syntax tree and then
traverses this tree to compute the expression value:
</p>
<pre class="example">
-- Lexical Elements
local Space = lpeg.S(" \n\t")^0
local Number = lpeg.C(lpeg.P"-"^-1 * lpeg.R("09")^1) * Space
local TermOp = lpeg.C(lpeg.S("+-")) * Space
local FactorOp = lpeg.C(lpeg.S("*/")) * Space
local Open = "(" * Space
local Close = ")" * Space

-- Grammar
local Exp, Term, Factor = lpeg.V"Exp", lpeg.V"Term", lpeg.V"Factor"
G = lpeg.P{ Exp,
  Exp = lpeg.Ct(Term * (TermOp * Term)^0);
  Term = lpeg.Ct(Factor * (FactorOp * Factor)^0);
  Factor = Number + Open * Exp * Close;
}

G = Space * G * -1

-- Evaluator
function eval (x)
  if type(x) == "string" then
    return tonumber(x)
  else
    local op1 = eval(x[1])
    for i = 2, #x, 2 do
      local op = x[i]
      local op2 = eval(x[i + 1])
      if (op == "+") then op1 = op1 + op2
      elseif (op == "-") then op1 = op1 - op2
      elseif (op == "*") then op1 = op1 * op2
      elseif (op == "/") then op1 = op1 / op2
      end
    end
    return op1
  end
end

-- Parser/Evaluator
function evalExp (s)
  local t = lpeg.match(G, s)
  if not t then error("syntax error", 2) end
  return eval(t)
end

-- small example
print(evalExp"3 + 5*9 / (1+1) - 12")   --> 13.5
</pre>

<p>
The second style computes the expression value on the fly,
without building the syntax tree.
The following grammar takes this approach.
(It assumes the same lexical elements as before.)
</p>
<pre class="example">
-- Auxiliary function
function eval (v1, op, v2)
  if (op == "+") then return v1 + v2
  elseif (op == "-") then return v1 - v2
  elseif (op == "*") then return v1 * v2
  elseif (op == "/") then return v1 / v2
  end
end

-- Grammar
local V = lpeg.V
G = lpeg.P{ "Exp",
  Exp = lpeg.Cf(V"Term" * lpeg.Cg(TermOp * V"Term")^0, eval);
  Term = lpeg.Cf(V"Factor" * lpeg.Cg(FactorOp * V"Factor")^0, eval);
  Factor = Number / tonumber + Open * V"Exp" * Close;
}

-- small example
print(lpeg.match(G, "3 + 5*9 / (1+1) - 12"))   --> 13.5
</pre>
<p>
Note the use of the fold (accumulator) capture.
To compute the value of an expression,
the accumulator starts with the value of the first term,
and then applies <code>eval</code> over
the accumulator, the operator,
and the new term for each repetition.
</p>


<h2><a name="download"></a>Download</h2>

<p>LPeg 
<a href="http://www.inf.puc-rio.br/~roberto/lpeg/lpeg-0.12.tar.gz">source code</a>.</p>


<h2><a name="license">License</a></h2>

<p>
Copyright &copy; 2013 Lua.org, PUC-Rio.
</p>
<p>
Permission is hereby granted, free of charge,
to any person obtaining a copy of this software and
associated documentation files (the "Software"),
to deal in the Software without restriction,
including without limitation the rights to use,
copy, modify, merge, publish, distribute, sublicense,
and/or sell copies of the Software,
and to permit persons to whom the Software is
furnished to do so,
subject to the following conditions:
</p>

<p>
The above copyright notice and this permission notice
shall be included in all copies or substantial portions of the Software.
</p>

<p>
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED,
INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
</p>

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