patterns.md

Patterns

Notes

Matching is exact by default; for partial matching, surround a pattern with %s. The metacharacter % is a shorthand for .*.

Whitespace is largely ignored; to match a whitespace character, use an escape like \  or \n. All metacharacters, \‑.~[]<>%{}*+?:|&=!( ), must be escaped to be matched literally, even inside character classes.

Character ranges can appear outside character classes. For example, 0‑9+ matches a non-empty sequence of digits. Character classes are complemented by prefixing the opening bracket with ~. For example, ~[abc] matches any character except a or b or c. Single characters and character ranges can be complemented as well. For example, ~\n* matches a sequence of non-newline characters and [aeiou ~a‑z] matches any character except lowercase consonants (insignificant whitespace for clarity).

To match “word” characters (alphanumeric characters plus the underscore), you might use [\m_]. The metacharacter . matches any character, including newlines; to match any character except newlines, you might use ~\n. To match patters like ‘numbers separated by commas’ you might use intercalation: (\d+)*!, (redundant parentheses for clarity). To match patterns like ‘identifiers which are not keywords’ you might use intersection and complementation: \a\m* & !(if|do|for) (insignificant whitespace for clarity).

Supported Syntax

Name	Example	Meaning	Type
Literal Character	a	Symbol consisting of the literal character a	symbol
Metacharacter Escape	\+	Symbol consisting of the metacharacter +	symbol
Simple Escape	\r	Symbol associated with the simple escape \r (see below)	symbol
Hexadecimal Escape	\x41	Symbol with character code 0x41	symbol
Symbol Promotion	any symbol	Singleton set containing the symbol	symbol -> symset
Character Range	a‑z	Set of all characters from a to z inclusively	(symbol, symbol) -> symset
Symset Wildcard	.	Set of all characters	symset
Shorthand	\d	Set of characters in the shorthand \d (see below)	symset
Symset Complement	~u	Set of all characters not in u	symset -> symset
Symset Union	[uv]	Set of characters in u or in v	[symset] -> symset
Symset Intersection	<uv>	Set of characters in u and in v	[symset] -> symset
Symset Promotion	any symset	Length-one words over the symset	symset -> regex
Wildcard	%	All words	regex
Empty Repetition	r{}	Words some 0‑factoring of which consists of rs	regex -> regex
Exact Repetition	r{4}	Words some 4‑factoring of which consists of rs	regex -> regex
Bounded Repetition	r{3,5}	Words some 3–5‑factoring of which consists of rs	regex -> regex
Minimum Repetition	r{3,}	Words some ≥3‑factoring of which consists of rs	regex -> regex
Maximum Repetition	r{,5}	Words some ≤5‑factoring of which consists of rs	regex -> regex
Kleene Star	r*	Words some n‑factoring of which consists of rs	regex -> regex
Kleene Plus	r+	Words some ≥1‑factoring of which consists of rs	regex -> regex
Optional	r?	Words some ≤1‑factoring of which consists of rs	regex -> regex
Dual Empty Repetition	r:{}	Words all 0‑factorings of which contain some r	regex -> regex
Dual Exact Repetition	r:{4}	Words all 4‑factorings of which contain some r	regex -> regex
Dual Bounded Repetition	r:{3,5}	Words all 3–5‑factorings of which contain some r	regex -> regex
Dual Minimum Repetition	r:{3,}	Words all ≥3‑factorings of which contain some r	regex -> regex
Dual Maximum Repetition	r:{,5}	Words all ≤5‑factorings of which contain some r	regex -> regex
Dual Kleene Star	r:*	Words all n‑factorings of which contain some r	regex -> regex
Dual Kleene Plus	r:+	Words all ≥1‑factorings of which contain some r	regex -> regex
Dual Optional	r:?	Words all ≤1‑factorings of which contain some r	regex -> regex
Intercalation	r*!s	Words in r* but with s between consecutive rs	(regex, regex) -> regex
Dual Intercalation	r:*!s	Words in r:* but with s between consecutive rs	(regex, regex) -> regex
Concatenation	rs	Words some 2‑factoring of which has head r and tail s	(regex, regex) -> regex
Dual Concatenation	r:s	Words all 2‑factorings of which have head r or tail s	(regex, regex) -> regex
Complement	!r	Words not in r	regex -> regex
Alternation	r|s	Words in r or in s	(regex, regex) -> regex
Intersection	r&s	Words in r and in s	(regex, regex) -> regex
Biconditional	r=s	Words in r if and only if in s	(regex, regex) -> regex
Grouping	(r)	Words in the subexpression r	regex -> regex

Literal characters include any printable character that’s not a metacharacter. Metacharacter escapes work for any metacharacter, \‑.~[]<>%{}*+?:|&=!( ). Hexadecimal escapes take exactly two digits. Character ranges support wraparound; for example, z‑a means ~b‑y. Intercalation may be defined as r{m+1,n+1}!s ⊢ r(sr){m,n}, r{,n+1}!s ⊢ |r(sr){,n}, r{}!s ⊢ (); and dual intercalation may be defined as r:{m+1,n+1}!s ⊢ r:(s:r):{m,n}, r:{,n+1}!s ⊢ !&r:(s:r):{,n}, r:{}!s ⊢ (!). Intercalation and dual intercalation work for any quantifier, {}*+?. At most one complement may be applied per grouping level, and at most one symset complement may be applied per symset union/intersection level.

An n‑factoring of a word is an n‑tuple of strings whose concatenation is that word. The empty word has a unique 0‑factoring, namely the 0‑tuple; no other word has 0‑factorings.

Insignificant whitespace can appear anywhere except within escapes, character ranges, shorthands, quantifiers, and intercalators.

Dual operators are dual with respect to complementation. For example, r:s means !(!r)(!s) and r:* means !(!r)* .

Precedence

In decreasing order, and otherwise right associative:

• Escapes \+ \r \x41;
• Character ranges a‑z, shorthands \d;
• Symset complements ~u;
• Quantification r{3,5} r* r+ r?, dual quantification r:{3,5} r:* r:+ r:?;
• Intercalation r*!s, dual intercalation r:*!s;
• Concatenation rs;
• Dual concatenation r:s;
• Complements !r;
• Alternation r|s, intersection r&s, biconditionals r=s.

Simple Escapes

Simple Escape	Definition	Character Name
\b	\x08	BACKSPACE
\f	\x0c	FORM FEED
\n	\x0a	LINE FEED
\r	\x0d	CARRIAGE RETURN
\t	\x09	HORIZONTAL TABULATION
\v	\x0b	VERTICAL TABULATION
\e	\x1b	ESCAPE

Shorthands

Shorthand	Definition	Equivalents	libc Analogue
\m, ~\M	[0‑9A‑Za‑z]	[\d\a], <\g\Q>	isalnum (C89)
\a, ~\A	[A‑Za‑z]	[\u\l], <\m\D>	isalpha (C89)
\k, ~\K	[\t\ ]	<\s~\n‑\r>	isblank (C99)
\c, ~\C	[\x00‑\x1f\x7f]	<\z\P>	iscntrl (C89)
\d, ~\D	0‑9	<\m\A>	isdigit (C89)
\g, ~\G	\!‑\~	[\q\m], <\p~\ >	isgraph (C89)
\l, ~\L	a‑z	<\a\U>	islower (C89)
\p, ~\P	\ ‑\~	[\g\ ], <\z\C>	isprint (C89)
\q, ~\Q	[\!‑/\:‑@\[‑`\{‑\~]	<\g\M>	ispunct (C89)
\s, ~\S	[\t‑\r\ ]	[\k\n‑\r]	isspace (C89)
\u, ~\U	A‑Z	<\a\L>	isupper (C89)
\h, ~\H	[0‑9A‑Fa‑f]		isxdigit (C89)
\z, ~\Z	\x00‑\x7f	[\c\p]	isascii (BSD)