REGULAR EXPRESSIONS

1. REGULAR EXPRESSIONS

2. Lexical Analysis Lexical analysers can be constructed by programs such as LEX These programs employ as input a description of the tokens that can occur in the language This description is made by means of regular expressions, as defined on the next slide. Regular expressions define patterns of characters.

3. Basics of Regular Expressions 1. Any character (or string of characters) except those (called metacharacters) which have a special interpretation, such as () [] {} + * ? | etc. For instance the string “if” in a regular expression will match the identical string in the source code.

4. 2. The period symbol “.” is used to match any single character in the source code except the new line indicator "\n".

5. 3.Square brackets are used to define a character class.  Either a sequence of symbols or a range denoted using the hyphen can be employed,e.g.: [01a-z] A character class matches a single symbol in the source code that is a member of the class. For instance [01a-z] matches the character 0 or 1 or any lower case alphabetic character

6. 4. The "+" symbol following a regular expression denotes 1 or more occurrences of that expression. For instance [0-9]+ matches any sequence of digits in the source code.

7. Similarly: 5. A "*" following a regular expression denotes 0 or more occurrences of that expression. 6. A “?" following a regular expression denotes 0 or 1 occurrence of that expression.

8. 7. The symbol “|”  is used as an OR operator to identify alternate choices. For instance [a-z]+|9 matches either a lower case alphabetic or the digit “9”.

9. 8. Parentheses can be freely used. For example: (a|b)+ matches e.g. abba while a|b+ match a or a string of b’s.

10. 9. Regular expressions can be concatenated For instance: [a-zA-Z]*[0-9]+[a-zA-Z] matches any sequence of 0 or more letters, followed by 1 or more digits, followed by 1 letter

11. As has been shown, symbols such as +, *, ?, ., (, ), [,]have special meanings in regular expressions. 10. If you want to include one of these symbols in a regular expression simply as a character, you can either use the c escape symbol “\” or double quotes. For example: [0-9]”+”[0-9] or [0-9]\+[0-9] match a digit followed by a plus sign, followed by a digit

12. Examples Given: R = ( abb | cd ) and S = abc RS = ( abbabc | cdabc ) is a regular expression. SR = ( abcabb | abccd ) is a regular expression. The following strings are matched by R*: abbcdcdcdcd e cdabbcdabbabbcd abb cd cdcdcdcdcdcdcd and so forth.

13. What kinds of strings can be matched by the regular • expression: ( a | c )* b ( a | c )* • ( a | c )* is a regular expression that can match the empty string e, or any string containing only a's and c's. • b is a regular expression that can match a single occurrence • of the symbol "b". • ( a | c )* is the same as the first regular expression. • So, the entire expression: ( a | c )* b ( a | c )* can match any • string made up of a possibly empty string of a's and c's, followed by a single b, followed by a possibly empty string of a’s and c’s • In other words the regular expression can match any string on • the alphabet {a,b,c} that contains exactly one b.

14. What kinds of strings can be matched by the regular • expression: ( a | c )* ( b | e ) ( a | c )* • This is the same as the previous example, except that the • regular expression in the center is now: ( b | e ) • ( b | e ) can match either an occurrence of a single b, or the • empty string which contains no characters • So the entire expression ( a | c )* ( b | e ) ( a | c )* can match any string over the alphabet {a,b,c} that contains either 0 or 1 b's.

15. Precedence of Operations in Regular Expressions From highest to lowest Concatenation Closure (*) Alternation ( OR ) Examples: a | bcf means the symbol a OR the string bcf a( bcf* ) is the string abc followed by 0 or more repetitions of the symbol f. Note: this is the same as (abcf*)

16. GRAMMARS vs REGULAR EXPRESSIONS Consider the set of strings (ie. language) {an b an | n > 0} A grammar that generates this language is: S -> b b -> a b a However, as can be shown, it is not possible to construct a regular expression that recognizes this language.

17. In the Lex definition file one can assign macro names to regular expressions e.g.: • digit 0|1|2|...|9 assigns the macro name digit • integer {digit}+ assigns the macro name integer to 1 ormore repetitions of digit NOTE. when using a macro name as part of a regular expression, you need to enclose the name in curly parentheses {}. • Signed_int (+|-)?{integer} assigns macro name signed_int to an optional sign followedby an integer • number{signed_int}(\.{integer})?(E{signed_int})? assigns the macro name number to a signed_int followed by an optional fractional part followed by an optional exponent part

18. alpha [a-zA-Z] assigns the macro name alpha to the character class given by a-z and A-Z • identifier {alpha}({alpha}|{digit})* assigns the macro name identifier to an alpha character followed by the alternation of either alpha characters or digits, with 0 or more repetitions.

19. RULE Using the regular expression for an identifier on the previous slide, what would be the first token of the following string? MAX23= Z29 + 8 Lex picks as the "next" token, the longest string that can be matched by one of it regular expressions. In this case, MAX23 would be matched as an identifier, not just M or MA or MAX