Rx
**

This document describes Rx.

Copying
*******

Copyright (C) 1996
Tom Lord
Berkeley, CA USA

except portions of "POSIX Regex Functions" which are
Copyright (C) 1995
Free Software Foundation, Inc.

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Overview
********

Nothing to say here, yet.

Posix Basic Regular Expressions
*******************************

The Posix Basic Regular Expression language is a notation for describing textual patterns.  Regexps are typically used by comparing them to a string to see if that string matches the pattern, or by searching within a string for a substring that matches.

This chapter introduces the Posix regexp notation.  This is not a formal or precise definition of Posix regexps -- it is an intuitive and hopefully expository description of them.

An Introduction to Regexps
==========================

In the simplest cases, a regexp is just a literal string that must match exactly.   For example, the pattern:

     regexp

matches the string "regexp" and no others.

Some characters have a special meaning when they occur in a regexp. They aren't matched literally as in the previous example, but instead denote a more general pattern.   For example, the character * is used to indicate that the preceeding element of a regexp may be repeated 0, 1, or more times.  In the pattern:

     smooo*th

the * indicates that the preceeding o can be repeated 0 or more times.   So the pattern matches:

     smooth
     smoooth
     smooooth
     smoooooth
     ...

Suppose you want to write a pattern that literally matches a special character like * -- in other words, you don't want to * to indicate a permissible repetition, but to match * literally.  This is accomplished by quoting the special character with a backslash. The pattern:

     smoo\*th

matches the string:

     smoo*th

and no other strings.

In seven cases, the pattern is reversed -- a backslash makes the character special instead of making a special character normal.  The characters +, ?, |, (, and ) are normal but the sequences \+, \?, \|, \(, \), \{, and \} are special (their meaning is described later).

The remaining sections of this chapter introduce and explain the various special characters that can occur in regexps.

Literal Regexps
===============

A literal regexp is a string which contains no special characters. A literal regexp matches an identical string, but no other characters. For example:

     literally

matches

     literally

and nothing else.

Generally, whitespace characters, numbers, and letters are not special. Some punctuation characters are special and some are not (the syntax summary at the end of this chapter makes a convenient reference for which characters are special and which aren't).

Character Sets
==============

This section introduces the special characters . and [.

. matches any character except the NULL character.  For example:

     p.ck

matches

     pick
     pack
     puck
     pbck
     pcck
     p.ck

     ...

[ begins a character set.  A character set is similar to . in that it matches not a single, literal character, but any of a set of characters.   [ is different from . in that with [, you define the set of characters explicitly.

There are three basic forms a character set can take.

In the first form, the character set is spelled out:

     [<cset-spec>]	-- every character in <cset-spec> is in the set.

In the second form, the character set indicated is the negation of a character set is explicitly spelled out:

     [^<cset-spec>]	-- every character *not* in <cset-spec> is in the set.

A <cset-spec> is more or less an explicit enumeration of a set of characters.  It can be written as a string of individual characters:

     [aeiou]

or as a range of characters:

     [0-9]

These two forms can be mixed:

     [A-za-z0-9_$]

Note that special regexp characters (such as *) are not special within a character set.  -, as illustrated above, is special, except, as illustrated below, when it is the first character mentioned.

This is a four-character set:

     [-+*/]

The third form of a character set makes use of a pre-defined "character class":

     [[:class-name:]] -- every character described by class-name is in the set.

The supported character classes are:

     alnum	- the set of alpha-numeric characters
     alpha	- the set of alphabetic characters
     blank	- tab and space
     cntrl	- the control characters
     digit	- decimal digits
     graph	- all printable characters except space
     lower	- lower case letters
     print	- the "printable" characters
     punct	- punctuation
     space	- whitespace characters
     upper	- upper case letters
     xdigit	- hexidecimal digits

Finally, character class sets can also be inverted:

     [^[:space:]] - all non-whitespace characters

Character sets can be used in a regular expression anywhere a literal character can.

Subexpressions
==============

A subexpression is a regular expression enclosed in \( and \).  A subexpression can be used anywhere a single character or character set can be used.

Subexpressions are useful for grouping regexp constructs.  For example, the repeat operator, *, usually applies to just the preceeding character.   Recall that:

     smooo*th

matches

     smooth
     smoooth
     ...

Using a subexpression, we can apply * to a longer string:

     banan\(an\)*a

matches

     banana
     bananana
     banananana
     ...

Subexpressions also have a special meaning with regard to backreferences and substitutions (see Backreferences).

Repeated Subexpressions
=======================

* is the repeat operator.  It applies to the preceeding character, character set, subexpression or backreference.  It indicates that the preceeding element can be matched 0 or more times:

     bana\(na\)*

matches

     bana
     banana
     bananana
     banananana
     ...

\+ is similar to * except that \+ requires the preceeding element to be matched at least once.  So while:

     bana\(na\)*

matches

     bana

     bana(na\)\+

does not.   Both match

     banana
     bananana
     banananana
     ...

Thus, bana\(na\)+ is short-hand for banana\(na\)*.

Optional Subexpressions
=======================

\? indicates that the preceeding character, character set, or subexpression is optional.  It is permitted to match, or to be skipped:

     CSNY\?

matches both

     CSN

and

     CSNY

Counted Subexpressions
======================

An interval expression, \{m,n\} where m and n are non-negative integers with n >= m, applies to the preceeding character, character set, subexpression or backreference.  It indicates that the preceeding element must match at least m times and may match as many as n times.

For example:

     c\([ad]\)\{1,4\}

matches

     car
     cdr
     caar
     cdar
     ...
     caaar
     cdaar
     ...
     cadddr
     cddddr

Alternative Subexpressions
==========================

An alternative is written:

     regexp-1\|regexp-2\|regexp-3\|...

It matches anything matched by some regexp-n.  For example:

     Crosby, Stills, \(and Nash\|Nash, and Young\)

matches

     Crosby, Stills, and Nash

and

     Crosby, Stills, Nash, and Young

Backreferences, Extractions and Substitutions
=============================================

A backreference is written \n where n is some single digit other than 0.  To be a valid backreference, there must be at least n parenthesized subexpressions in the pattern prior to the backreference.

A backreference matches a literal copy of whatever was matched by the corresponding subexpression.  For example,

     \(.*\)-\1

matches:

     go-go
     ha-ha
     wakka-wakka
     ...

In some applications, subexpressions are used to extract substrings. For example, Emacs has the functions match-beginnning and match-end which report the positions of strings matched by subexpressions.  These functions use the same numbering scheme for subexpressions as backreferences, with the additional rule that subexpression 0 is defined to be the whole regexp.

In some applications, subexpressions are used in string substitution. This again uses the backreference numbering scheme. For example, this sed command:

     s/From:.*<\(.*\)>/To: \1/

first matches the line:

     From: Joe Schmoe <schmoe@uspringfield.edu>

when it does, subexpression 1 matches "schmoe@uspringfield.edu". The command replaces the matched line with "To: \1" after doing subexpression substitution on it to get:

     To: schmoe@uspringfield.edu

A Summary of Regexp Syntax
==========================

In summary, regexps can be:

abcd -- matching a string literally

. -- matching everything except NULL

[a-z_?], ^[a-z_?], [[:alpha:]] and [^[:alpha:]] -- matching character sets

\(subexp\) -- grouping an expression into a subexpression.

\n -- match a copy of whatever was matched by the nth subexpression.

The following special characters and sequences can be applied to a character, character set, subexpression, or backreference:

* -- repeat the preceeding element 0 or more times.

\+ -- repeat the preceeding element 1 or more times.

\? -- match the preceeding element 0 or 1 time.

{m,n} -- match the preceeding element at least m, and as many as n times.

regexp-1\|regexp-2\|.. -- match any regexp-n.

A special character, like . or * can be made into a literal character by prefixing it with \.

A special sequence, like \+ or \? can be made into a literal character by dropping the \.

Ambiguous Patterns
==================

Sometimes a regular expression appears to be ambiguous.  For example, suppose we compare the pattern:

     begin\|beginning

to the string

     beginning

either just the first 5 characters will match, or the whole string will match.

In every case like this, the longer match is preferred.  The whole string will match.

Sometimes there is ambiguity not about how many characters to match, but where the subexpressions occur within the match.  This can effect extraction functions like Emacs' match-beginning or rewrite functions like sed's s command.  For example, consider matching the pattern:

     b\(\[^q]*\)\(ing\)?

against the string

     beginning

One possibility is that the first subexpression matches "eginning" and the second is skipped.  Another possibility is that the first subexpression matches "eginn" and the second matches "ing".

The rule is that consistant with matching as many characters as possible, the length of lower numbered subexpressions is maximized in preference to maximizing the length of later subexpressions.

In the case of the above example, the two possible matches are equal in overall length.  Therefore, it comes down to maximizing the lower-numbered subexpression, \1.  The correct answer is that \1 matches "eginning" and \2 is skipped.

Posix Entry Points
******************

This section is excerpted from The GNU C Library reference manual by Sandra Loosemore with Richard M. Stallman, Roland McGrath, and Andrew Oram.

The GNU C library supports the standard POSIX.2 interface.  Programs using this interface should include the header file rxposix.h.

POSIX Regular Expression Compilation
====================================

Before you can actually match a regular expression, you must compile it.  This is not true compilation---it produces a special data structure, not machine instructions.  But it is like ordinary compilation in that its purpose is to enable you to ``execute'' the pattern fast.  (see Matching POSIX Regexps, for how to use the compiled regular expression for matching.)

There is a special data type for compiled regular expressions:

 -- Data Type: regex_t
     This type of object holds a compiled regular expression. It is actually a structure.  It has just one field that your programs should look at:

     re_nsub
          This field holds the number of parenthetical subexpressions in the regular expression that was compiled.

     There are several other fields, but we don't describe them here, because only the functions in the library should use them.

After you create a regex_t object, you can compile a regular expression into it by calling regcomp.

 -- Function: int regcomp (regex_t *COMPILED, const char *PATTERN, int CFLAGS)
 -- Function: int regncomp (regex_t *COMPILED, const char *PATTERN, int LEN, int CFLAGS)
     The function regcomp ``compiles'' a regular expression into a data structure that you can use with regexec to match against a string.  The compiled regular expression format is designed for efficient matching.  regcomp stores it into *COMPILED.

     The parameter PATTERN points to the regular expression to be compiled.  When using regcomp, PATTERN must be 0-terminated.  When using regncomp, PATTERN must be LEN characters long.

     regncomp is not a standard function;  strictly POSIX programs should avoid using it.

     It's up to you to allocate an object of type regex_t and pass its address to regcomp.

     Before freeing the object of type regex_t You must pass it to regfree.  Not doing so may cause subsequent calls to Rx functions to behave strangely.

     The argument CFLAGS lets you specify various options that control the syntax and semantics of regular expressions.  See Flags for POSIX Regexps.

     If you use the flag REG_NOSUB, then regcomp omits from the compiled regular expression the information necessary to record how subexpressions actually match.  In this case, you might as well pass 0 for the MATCHPTR and NMATCH arguments when you call regexec.

     If you don't use REG_NOSUB, then the compiled regular expression does have the capacity to record how subexpressions match.  Also, regcomp tells you how many subexpressions PATTERN has, by storing the number in COMPILED->re_nsub.  You can use that value to decide how long an array to allocate to hold information about subexpression matches.

     regcomp returns 0 if it succeeds in compiling the regular expression; otherwise, it returns a nonzero error code (see the table below).  You can use regerror to produce an error message string describing the reason for a nonzero value; see Regexp Cleanup.

Here are the possible nonzero values that regcomp can return:

REG_BADBR
     There was an invalid \{...\} construct in the regular expression.  A valid \{...\} construct must contain either a single number, or two numbers in increasing order separated by a comma.

REG_BADPAT
     There was a syntax error in the regular expression.

REG_BADRPT
     A repetition operator such as ? or * appeared in a bad position (with no preceding subexpression to act on).

REG_ECOLLATE
     The regular expression referred to an invalid collating element (one not defined in the current locale for string collation).

REG_ECTYPE
     The regular expression referred to an invalid character class name.

REG_EESCAPE
     The regular expression ended with \.

REG_ESUBREG
     There was an invalid number in the \DIGIT construct.

REG_EBRACK
     There were unbalanced square brackets in the regular expression.

REG_EPAREN
     An extended regular expression had unbalanced parentheses, or a basic regular expression had unbalanced \( and \).

REG_EBRACE
     The regular expression had unbalanced \{ and \}.

REG_ERANGE
     One of the endpoints in a range expression was invalid.

REG_ESPACE
     regcomp ran out of memory.

Flags for POSIX Regular Expressions
===================================

These are the bit flags that you can use in the CFLAGS operand when compiling a regular expression with regcomp.

REG_EXTENDED
     Treat the pattern as an extended regular expression, rather than as a basic regular expression.

REG_ICASE
     Ignore case when matching letters.

REG_NOSUB
     Don't bother storing the contents of the MATCHES-PTR array.

REG_NEWLINE
     Treat a newline in STRING as dividing STRING into multiple lines, so that $ can match before the newline and ^ can match after.  Also, don't permit . to match a newline, and don't permit [^...] to match a newline.

     Otherwise, newline acts like any other ordinary character.

Matching a Compiled POSIX Regular Expression
============================================

Once you have compiled a regular expression, as described in POSIX Regexp Compilation, you can match it against strings using regexec.  A match anywhere inside the string counts as success, unless the regular expression contains anchor characters (^ or $).

 -- Function: int regexec (regex_t *COMPILED, char *STRING, size_t NMATCH, regmatch_t MATCHPTR [], int EFLAGS)
 -- Function: int regnexec (regex_t *COMPILED, char *STRING, int LEN, size_t NMATCH, regmatch_t MATCHPTR [], int EFLAGS)
     This function tries to match the compiled regular expression *COMPILED against STRING.

     regexec returns 0 if the regular expression matches; otherwise, it returns a nonzero value.  See the table below for what nonzero values mean.  You can use regerror to produce an error message string describing the reason for a nonzero value; see Regexp Cleanup.

     The parameter STRING points to the text to search.  When using regexec, STRING must be 0-terminated.  When using regnexec, STRING must be LEN characters long.

     regnexec is not a standard function;  strictly POSIX programs should avoid using it.

     The argument EFLAGS is a word of bit flags that enable various options.

     If you want to get information about what part of STRING actually matched the regular expression or its subexpressions, use the arguments MATCHPTR and NMATCH.  Otherwise, pass 0 for NMATCH, and NULL for MATCHPTR.  See Regexp Subexpressions.

You must match the regular expression with the same set of current locales that were in effect when you compiled the regular expression.

The function regexec accepts the following flags in the EFLAGS argument:

REG_NOTBOL
     Do not regard the beginning of the specified string as the beginning of a line; more generally, don't make any assumptions about what text might precede it.

REG_NOTEOL
     Do not regard the end of the specified string as the end of a line; more generally, don't make any assumptions about what text might follow it.

Here are the possible nonzero values that regexec can return:

REG_NOMATCH
     The pattern didn't match the string.  This isn't really an error.

REG_ESPACE
     regexec ran out of memory.

Match Results with Subexpressions
=================================

When regexec matches parenthetical subexpressions of PATTERN, it records which parts of STRING they match.  It returns that information by storing the offsets into an array whose elements are structures of type regmatch_t.  The first element of the array (index 0) records the part of the string that matched the entire regular expression.  Each other element of the array records the beginning and end of the part that matched a single parenthetical subexpression.

 -- Data Type: regmatch_t
     This is the data type of the MATCHARRAY array that you pass to regexec.  It containes two structure fields, as follows:

     rm_so
          The offset in STRING of the beginning of a substring.  Add this value to STRING to get the address of that part.

     rm_eo
          The offset in STRING of the end of the substring.

 -- Data Type: regoff_t
     regoff_t is an alias for another signed integer type. The fields of regmatch_t have type regoff_t.

The regmatch_t elements correspond to subexpressions positionally; the first element (index 1) records where the first subexpression matched, the second element records the second subexpression, and so on.  The order of the subexpressions is the order in which they begin.

When you call regexec, you specify how long the MATCHPTR array is, with the NMATCH argument.  This tells regexec how many elements to store.  If the actual regular expression has more than NMATCH subexpressions, then you won't get offset information about the rest of them.  But this doesn't alter whether the pattern matches a particular string or not.

If you don't want regexec to return any information about where the subexpressions matched, you can either supply 0 for NMATCH, or use the flag REG_NOSUB when you compile the pattern with regcomp.

Complications in Subexpression Matching
=======================================

Sometimes a subexpression matches a substring of no characters.  This happens when f\(o*\) matches the string fum.  (It really matches just the f.)  In this case, both of the offsets identify the point in the string where the null substring was found.  In this example, the offsets are both 1.

Sometimes the entire regular expression can match without using some of its subexpressions at all---for example, when ba\(na\)* matches the string ba, the parenthetical subexpression is not used.  When this happens, regexec stores -1 in both fields of the element for that subexpression.

Sometimes matching the entire regular expression can match a particular subexpression more than once---for example, when ba\(na\)* matches the string bananana, the parenthetical subexpression matches three times.  When this happens, regexec usually stores the offsets of the last part of the string that matched the subexpression.  In the case of bananana, these offsets are 6 and 8.

But the last match is not always the one that is chosen.  It's more accurate to say that the last opportunity to match is the one that takes precedence.  What this means is that when one subexpression appears within another, then the results reported for the inner subexpression reflect whatever happened on the last match of the outer subexpression.  For an example, consider \(ba\(na\)*s \)* matching the string bananas bas .  The last time the inner expression actually matches is near the end of the first word.  But it is considered again in the second word, and fails to match there. regexec reports nonuse of the ``na'' subexpression.

Another place where this rule applies is when the regular expression \(ba\(na\)*s \|nefer\(ti\)* \)* matches bananas nefertiti. The ``na'' subexpression does match in the first word, but it doesn't match in the second word because the other alternative is used there. Once again, the second repetition of the outer subexpression overrides the first, and within that second repetition, the ``na'' subexpression is not used.  So regexec reports nonuse of the ``na'' subexpression.

POSIX Regexp Matching Cleanup
=============================

When you are finished using a compiled regular expression, you must free the storage it uses by calling regfree.

 -- Function: void regfree (regex_t *COMPILED)
     Calling regfree frees all the storage that *COMPILED points to.  This includes various internal fields of the regex_t structure that aren't documented in this manual.

     regfree does not free the object *COMPILED itself.

You should always free the space in a regex_t structure with regfree before using the structure to compile another regular expression.

When regcomp or regexec reports an error, you can use the function regerror to turn it into an error message string.

 -- Function: size_t regerror (int ERRCODE, regex_t *COMPILED, char *BUFFER, size_t LENGTH)
     This function produces an error message string for the error code ERRCODE, and stores the string in LENGTH bytes of memory starting at BUFFER.  For the COMPILED argument, supply the same compiled regular expression structure that regcomp or regexec was working with when it got the error.  Alternatively, you can supply NULL for COMPILED; you will still get a meaningful error message, but it might not be as detailed.

     If the error message can't fit in LENGTH bytes (including a terminating null character), then regerror truncates it. The string that regerror stores is always null-terminated even if it has been truncated.

     The return value of regerror is the minimum length needed to store the entire error message.  If this is less than LENGTH, then the error message was not truncated, and you can use it.  Otherwise, you should call regerror again with a larger buffer.

     Here is a function which uses regerror, but always dynamically allocates a buffer for the error message:

          char *get_regerror (int errcode, regex_t *compiled)
          {
            size_t length = regerror (errcode, compiled, NULL, 0);
            char *buffer = xmalloc (length);
            (void) regerror (errcode, compiled, buffer, length);
            return buffer;
          }

Beyond POSIX
************

This section is not finished documentation, but rather a collection of pointers towards some of the interesting, non-standard features of Rx.

New Regexp Operators
====================

Rx supports some unusual regexp syntax.

[[:cut N:]] sets pmatch[0].final_tag to N and causes the matching to stop instantly.  If N is 0, the overall match fails, otherwise it succeeds.

[[:(:]] ... [[:):]] is just like \( ... \) except that in the first case, no pmatch entries are changed, and the subexpression is not counted in the numbering of parenthesized subexpressions.

[[:(:]] ... [[:):]] can be used when you do not need to know where a subexpression matched but are only using parentheses to effect the parsing of the regexp.

There are two reasons to use [[:(:]] ... [[:):]]:

1. regexec will run faster.

2. Currently, only 8 backreferencable subexpressions are supported: \1 .. \9.  Using [[:(:]] ... [[:):]] is a way to conserve backreferencable subexpression names in an expression with many parentheses.

New POSIX Functions
===================

regncomp and regnexec are non-standard generalizations of regcomp and regexec.

Tuning POSIX performance
========================

Two mysterious parmaters can be used to trade-off performance and memory use.

At compile-time they are RX_DEFAULT_DFA_CACHE_SIZE and RX_DEFAULT_NFA_DELAY.

If you want to mess with these (I generally don't advise it), I suggest experimenting for your particular application/memory situation; frob these by powers of two and try out the results on what you expect will be typical regexp workloads.

You can also set those parameters at run-time (before calling any regexp functions) by tweaking the corresponding variables:

rx_default_cache->bytes_allowed

and

rx_basic_unfaniverse_delay

POSIX stream-style interface
============================

rx_make_solutions, rx_next_solution, and rx_free_solutions are a lower level alternative to the posix functions.  Using those functions, you can compare a compiled regexp to a string that is not contiguous in memory or even a string that is not entirely in memory at any one time.

The code in rxposix.c points out how those functions are used.

DFAs Directly
=============

If you are only interested in pure regular expressions (no pmatch data, no backreferences, and no counted subexpressions), you can parse a regexp using rx_parse, convert it to an nfa using rx_unfa, and run the dfa using rx_init_system, rx_advance_to_final, and rx_terminate_system.  The dfa Scheme primitives in rgx.c may provide some guide.

Rx Theory
*********

There are two match algorithms.  One is for truly regular regexps (those that can be reduced to a dfa).  The other is for non-regular regexps.

The dfa algorithm implements the idea suggested in Compilers by Aho, Sethi and Ullman:

     [One] approach [to pattern matching regular expressions] is to use a DFA, but avoid constructing all of the transition table by using a technique called "lazy transition evaluation".  Here, transitions are computed at run time [when] actually needed. [T]ransitions are stored in a cache. [....] If the cache becomes full, we can erase some previously computed transition to make room for the new transition.

The implementation in Rx is generalized from that, but the above description covers what is used for Posix patterns.

The non-dfa algorithm implements a "recursive decomposition" technique described in email by Henry Spencer.  For a given pattern, this algorithm first checks to see if a simpler, superset language, DFA-pattern matches.  If it does, then this algorithm does the detail-work to see if the non-DFA pattern matches.

The detail work usually involves recursing on subpatterns.  For example, a concatentation of two subexpressions matches a string if the string can be divided into two parts, each matching one subexpression, in the right order.  More than one solution is often possible for a given pattern.  This ambiguity is the subject of the "leftmost longest" rules in the spec, and the back-tracking oriented stream-of-solution functions rx_make_solutions, rx_next_solution and rx_free_solutions.

     rxspencer.[ch]	 			-- The non-DFA algorithm
     rxanal.[ch] rxsuper.[ch] rxnfa.[ch]	-- The DFA algorithm