diff options
Diffstat (limited to 'txr.1')
| -rw-r--r-- | txr.1 | 299 |
1 files changed, 188 insertions, 111 deletions
@@ -638,17 +638,33 @@ with a backslash. Two backslashes code for one backslash. So for instance [\e[\e-] means match a [ or - character, [^^] means match any character other than ^, and [\e^\e\e] means match either a ^ or a backslash. +.IP empty +An empty string is a regular expression. It matches the set of texts +consisting of the empty string; i.e. it matches no characters. The empty +string can appear alone as a full regular expression (for instance the +.B txr +syntax @// with nothing between the slashes) +and can also be used as a subexpression term for some operators. The +expression a| means (a|): match either a, or nothing. It's not possible to +pass the empty regex to some operators; for instance (*) is a syntax error, +not the * operator with an empty string on the left. .IP (RE) If RE is a regular expression, then so is (RE). The contents of parentheses denote one regular expression unit, so that for instance in (RE)*, the * operator applies to the entire parenthesized group. +The syntax () is valid and equivalent to the empty regular expression. .IP (RE)? optionally match the preceding regular expression (RE). .IP (RE)+ -match the preceding expression one or more times. +match the preceding expression one or more times, as many times as possible. .IP (RE)* -match the preceding expression zero or more times. This operator -is sometimes called the "Kleene operator". +match the preceding expression zero or more times, as many times + as possible. This operator is sometimes called the "Kleene operator". +.IP (RE1)%(RE2) +match RE1 zero or more times, but not as many times as possible: stop the +match at the first point where RE2 matches, even if repetitions of RE1 can +continue matching. This is called the non-greedy operator. RE2 may be +an empty regular expression, in which case this is equivalent to (RE1)*. .IP ~(RE) match the complement of the preceding expression; i.e. match those texts that (RE) does not match. This operator is called complement, @@ -680,9 +696,16 @@ one-position match of that character itself. Character classes and parentheses have the highest precedence. -The postfix operators ?, + and * have the second highest precedence, and +The postfix operators ?, +, * have the second highest precedence, and associate left to right, so that in A+?*, the * applies to A+?, and the ? -applies to A+. +applies to A+. With respect to the left operand, % has a similar +precedence to these operators. + +The, % operator has a special syntactic behavior: with respect to its +left operand, it has a similar precedence to the ?, + and * operators. +However, it has a lower Prudence. The expression abc*%d*ef means +ab((c*)%(d*ef)). The left argument of % is c*, but the right is +the entire expression d*ef. The unary complement operator has the next lower precedence, so that ~A* means the ~(A*): "match the all text that is not matched by zero @@ -694,8 +717,12 @@ Catenation is on the next lower precedence rung, so that AB? means A(B?), or unit". The latter must be written (AB)? using parentheses to override precedence. -The precedence of intersection (&) is lower than that of catenation, but not as -low as that of union, thus AB +The % operator has the next lower precedence with regard to its right +operand. Thus abc%~def&xyz means (ab(c%def))&xyz. + +The precedence of intersection (&) is lower than that of catenation or the +right operand , but not as low as that of union, thus AB&CD|EF&GH +means (AB&CD)|(EF&GH) The union operator (|) has the lowest precedence, lower than catenation. Thus ABC|DEF means "match ABC, or match DEF". The meaning "match AB, @@ -753,110 +780,8 @@ regular expression matches. The regular expression matches anywhere, including the empty string after the last character, which is the rightmost place. Thus variable A fetches the entire line. -.SS Notes on Exotic Regular Expressions - -Users familiar with regular expressions may not be familiar with the complement -and intersection operators, which are often absent from text processing tools -that support regular expressions. - -Regexp intersection is not essential; it may be obtained from complement and -union as follows, since DeMorgan's law applies to regular expression algebra: -(R1)&(R2) = ~(~(R1)|~(R2)). (The complement of the union of the complements of -R1 and R2 constitutes the intersection. This law works because the regular -expression operators denote set operations in a straightforward way. A regular -expression denotes a set of strings (a potentially infinite one) in a condensed -way. The union of two regular expressions R1 | R2 denotes the union of the set -of texts denoted by R1 and that denoted by R2. Similarly R1 & R2 denotes a set -intersection, and ~R denotes a set complement. Thus algebraic laws -that apply to set operations apply to regular expressions. It's useful to keep -in mind this relationship between regular expressions and sets in understanding -intersection and complement. - -Given a finite set of strings, like the set { "abc", "def" }, which corresponds -to the regular expression (abc|def), the complement is set which contains an -infinite number of strings: it consists of all possible strings except "abc" -and "def". It includes the empty string, all strings of length 1, all strings -of length 2, all strings of length 3 other than "abc" and "def", all strings of -length 4, etc. This means that a "harmless looking" expression like -~(abc|def) can actually match arbitrarily long inputs. - -How about matching only three-character-long strings other than "abc" or "def"? -To express this, regex intersection can be used: these strings are the -intersection of the set of all three-character strings, and the set of all -strings which are not "abc" or "def". The straightforward set-based reasoning -leads us to this: ...&~(abc|def). This A&~B idiom is also called set -difference, sometimes notated with a minus sign: A-B (which is not -supported in -.B txr -regular expression syntax). Elements which are in the set A, but not B, are -those elements which are in the intersection of A with the complement of B. -This is similar to the arithmetic rule A - B = A + -B: subtraction is -equivalent to addition of the additive inverse. Set difference is a useful -tool: it enables us to write a positive match which captures a more general set -than what is intended (but one whose regular expression is far simpler -than a positive match for the exact set we want), then we can intersect -intersect this over-generalized set with the complemented set of -another regular expression which matches the particulars that we wish excluded. - -It is important to understand that any regular expression which uses the -complement or intersection operator can be replaced by an expression which -matches the same texts without using these operators. But such equivalent -expressions are often much more complicated, cumbersome, and difficult to -develop, debug and understand. Such equivalent expressions do not actually -. B express -the concept of what they match; they merely capture the equivalent set. -The use of complement and intersection can lead to natural expressions. - -For instance, using complement, we can write a straightforward regular -expression which matches C language comments. A C language -comment is the digraph /*, followed by any string which does not contain the -Examples of valid comments are /**/, /* abc */ or /***/. But C -comments do not nest (cannot contain comments), so that -/* /* nested */ */ actually consists of the comment /* /* nested */, -which is followed by the trailing junk */. -Our simple characterization of interior part of a C comment as a string -which does not contain the terminating digraph makes use of the -complement, and can be expressed using the complemented regular expression like -this: (~.*[*][/].*). That is to say, strings which contain */ are matched by -the expression .*[*][/].*: zero or more arbitrary characters, followed by -*/, followed by zero or more arbitrary characters. Therefore, the complement of this expression matches all other strings: those which do not contain */. -These strings up the inside of a C comment between the /* and */. - -The equivalent simple regex is much more complicated. -Without complement, we must somehow write a positive match for all strings such -that we avoid matching */. Obviously, sequences of characters other than * -are included: [^*]*. Occurrences of * are also allowed, but only if followed -by something other than a slash, so let's include this via union: -([^*]|[*][^/])*. Alas, already, we have a bug in this expression. The -subexpression [*][^/] can match "**", since a * is not a /. If the next -character in the input is /, we missed a comment close. To fix the problem we -revise to this: ([^*]|[*][^*/])* (the interior of a C language comment is a any -mixture of zero or more non-asterisks, or digraphs consisting of an asterisk -followed by something other than a slash or another asterisk). Oops, now we -have a problem again. What if two asterisks occur in a comment? They are not -matched by [^*], and they are not matched by [*][^*/]. Actually, our regex must -not simply match asterisk-non-asterisk digraphs, but rather sequences of one or -more asterisks followed by a non-asterisk: ([^*]|[*]*[^*/])*. This is still -not right, because, for instance, it fails to match the interior of a comment -which is terminated by asterisks, including the simple test cases where -the comment interior is nothing but asterisks. We have no provision in our -expression for this case; the expression requires all runs of asterisks to be -followed by something which is not a slash or asterisk. The way to fix this is -to add on a subexpression which optionally matches a run of zero or more -interior asterisks before the comment close: ([^*]|[*]*[^*/])*[*]*. Thus the -semi-final regular expression is: [/][*]([^*]|[*]*[^*/])*[*]*[*][/]. (A C -comment is an interior string enclosed in /* */, where this interior part -consists of a mixture of non-asterisk characters, as well as runs of asterisk -characters which are terminated by a character other than a slash, except -for possibly one rightmost run of asterisks which extends to the end of the -interior, touching the comment close. Phew!) One final simplification is -possible: the tail part [*]*[*][/] can be reduced to [*]+[/] such that the -final run of asterisks is regarded as part of an extended comment terminator -which consists of one or more asterisks followed by a slash. Clearly, working -without regular expression complement is not impossible, but difficult and -error-prone. Complemented matches without complement may require regex -experience combined with cunning, perseverance and possibly multiple cycles of -trial-and-error involving numerous test cases. +For additional information about the advanced regular expression +operators, NOTES ON EXOTIC REGULAR EXPRESSIONS below. .SS Directives @@ -2925,6 +2850,158 @@ definitions are in error: @(defex x y) @(defex y x)@# error: circularity; y is already a supertype of x. +.SS NOTES ON EXOTIC REGULAR EXPRESSIONS + +Users familiar with regular expressions may not be familiar with the complement +and intersection operators, which are often absent from text processing tools +that support regular expressions. The following remarks may be of use +as introductory material. + +.SS Equivalence to Sets + +Regexp intersection is not essential; it may be obtained from complement and +union as follows, since DeMorgan's law applies to regular expression algebra: +(R1)&(R2) = ~(~(R1)|~(R2)). (The complement of the union of the complements of +R1 and R2 constitutes the intersection. This law works because the regular +expression operators denote set operations in a straightforward way. A regular +expression denotes a set of strings (a potentially infinite one) in a condensed +way. The union of two regular expressions R1 | R2 denotes the union of the set +of texts denoted by R1 and that denoted by R2. Similarly R1 & R2 denotes a set +intersection, and ~R denotes a set complement. Thus algebraic laws +that apply to set operations apply to regular expressions. It's useful to keep +in mind this relationship between regular expressions and sets in understanding +intersection and complement. + +Given a finite set of strings, like the set { "abc", "def" }, which corresponds +to the regular expression (abc|def), the complement is set which contains an +infinite number of strings: it consists of all possible strings except "abc" +and "def". It includes the empty string, all strings of length 1, all strings +of length 2, all strings of length 3 other than "abc" and "def", all strings of +length 4, etc. This means that a "harmless looking" expression like +~(abc|def) can actually match arbitrarily long inputs. + +.SS Set Difference + +How about matching only three-character-long strings other than "abc" or "def"? +To express this, regex intersection can be used: these strings are the +intersection of the set of all three-character strings, and the set of all +strings which are not "abc" or "def". The straightforward set-based reasoning +leads us to this: ...&~(abc|def). This A&~B idiom is also called set +difference, sometimes notated with a minus sign: A-B (which is not +supported in +.B txr +regular expression syntax). Elements which are in the set A, but not B, are +those elements which are in the intersection of A with the complement of B. +This is similar to the arithmetic rule A - B = A + -B: subtraction is +equivalent to addition of the additive inverse. Set difference is a useful +tool: it enables us to write a positive match which captures a more general set +than what is intended (but one whose regular expression is far simpler +than a positive match for the exact set we want), then we can intersect +intersect this over-generalized set with the complemented set of +another regular expression which matches the particulars that we wish excluded. + +.SS Expressivity versus Power + +It is important to understand that any regular expression which uses the +complement or intersection operator can be replaced by an expression which +matches the same texts without using these operators. This is a departure +from set operations, which are distinctly less powerful without the complement +operator: we cannot express the complement of a formula which combines +sets if we do not have the set complement operator. + +But, though they exist, such equivalent regular expressions are often much more +complicated, cumbersome, and difficult to develop, debug and understand. Such +equivalent expressions do not actually +. B express +the concept of what they match; they merely capture the equivalent set (they +have the theoretical matching power). +The use of complement and intersection can lead to natural expressions, which +not only demonstrate the power to carry out an operation, but also express, in +some sense, the concept associated with that power. + +.SS Example: Matching C Language Comments. + +For instance, using complement, we can write a straightforward regular +expression which matches C language comments. A C language +comment is the digraph /*, followed by any string which does not contain the +Examples of valid comments are /**/, /* abc */ or /***/. But C +comments do not nest (cannot contain comments), so that +/* /* nested */ */ actually consists of the comment /* /* nested */, +which is followed by the trailing junk */. +Our simple characterization of interior part of a C comment as a string +which does not contain the terminating digraph makes use of the +complement, and can be expressed using the complemented regular expression like +this: (~.*[*][/].*). That is to say, strings which contain */ are matched by +the expression .*[*][/].*: zero or more arbitrary characters, followed by +*/, followed by zero or more arbitrary characters. Therefore, the complement of this expression matches all other strings: those which do not contain */. +These strings up the inside of a C comment between the /* and */. + +The equivalent simple regex is much more complicated. +Without complement, we must somehow write a positive match for all strings such +that we avoid matching */. Obviously, sequences of characters other than * +are included: [^*]*. Occurrences of * are also allowed, but only if followed +by something other than a slash, so let's include this via union: +([^*]|[*][^/])*. Alas, already, we have a bug in this expression. The +subexpression [*][^/] can match "**", since a * is not a /. If the next +character in the input is /, we missed a comment close. To fix the problem we +revise to this: ([^*]|[*][^*/])* (the interior of a C language comment is a any +mixture of zero or more non-asterisks, or digraphs consisting of an asterisk +followed by something other than a slash or another asterisk). Oops, now we +have a problem again. What if two asterisks occur in a comment? They are not +matched by [^*], and they are not matched by [*][^*/]. Actually, our regex must +not simply match asterisk-non-asterisk digraphs, but rather sequences of one or +more asterisks followed by a non-asterisk: ([^*]|[*]*[^*/])*. This is still +not right, because, for instance, it fails to match the interior of a comment +which is terminated by asterisks, including the simple test cases where +the comment interior is nothing but asterisks. We have no provision in our +expression for this case; the expression requires all runs of asterisks to be +followed by something which is not a slash or asterisk. The way to fix this is +to add on a subexpression which optionally matches a run of zero or more +interior asterisks before the comment close: ([^*]|[*]*[^*/])*[*]*. Thus the +semi-final regular expression is: [/][*]([^*]|[*]*[^*/])*[*]*[*][/]. (A C +comment is an interior string enclosed in /* */, where this interior part +consists of a mixture of non-asterisk characters, as well as runs of asterisk +characters which are terminated by a character other than a slash, except +for possibly one rightmost run of asterisks which extends to the end of the +interior, touching the comment close. Phew!) One final simplification is +possible: the tail part [*]*[*][/] can be reduced to [*]+[/] such that the +final run of asterisks is regarded as part of an extended comment terminator +which consists of one or more asterisks followed by a slash. Clearly, working +without regular expression complement is not impossible, but difficult and +error-prone. Complemented matches without complement may require regex +experience combined with cunning, perseverance and possibly multiple cycles of +trial-and-error involving numerous test cases. + +.SS The Non-Greedy Operator + +The non-greedy operator % is actually defined in terms of a set difference, +based on intersection and complement. The uninteresting case (R%) where the +right operand is empty reduces to (R*): if there is no trailing context, the +non-greedy operator matches R as far as possible, possibly to the end of the +input, exactly like the greedy Kleene. The interesting case (R%T) is defined +as a "syntactic sugar" for the equivalent expression ((R*)&(~.*T.*))T which +means: match the longest string which is matched by R*, but which does +not contain T; then, match T. This is a useful and expressive notation. With +it, we can write the regular expression for matching C language comments simply +like this: [/][*].%[*][/] (match the opening sequence /*, then match a sequence +of zero or more characters non-greedily, and then the closing sequence */. +Non-greediness is expressive, but it may be deceptively simple. +The non-greedy operator looks as if it works "magically" by itself; "somehow" +this .% "knows" only to consume enough characters so that it doesn't swallow an +occurrence of the trailing context. Care must be taken that the trailing context is really the desired one. For instance, take the expression .%abc. +If you intend the trailing context to be merely a, you must be careful to write +(.%a)bc. Otherwise the trailing context is abc, and this means that +the .% match will consume the longest string that does not contain "abc", +when in fact what was intended was to consume the longest string that +does not contain a. For single-character trailing contexts, it may be a +good idea to use a complemented character class instead. That is to say, +rather than (.%a)bc, how about [^a]*bc. The set of strings which don't contain +the character a is adequately expressed by [^a]*. + +.% will + +[/][*].%[*][/] ( + .SH NOTES ON FALSE The reason for printing the word |