Regular Expression in Compiler design
- 1. A sequence of symbols and characters expressing a string or pattern to be searched for within a longer piece of text. Regular Expressions
- 2. Regular Expressions we were able to describe identifiers by giving names to sets of letters and digits and using the language operators union, concatenation, and closure. This process is so useful that a notation called regular expressions has come into common use for describing all the languages that can be built from these operators applied to the symbols of some alphabet. In this notation, if letter- is established to stand for any letter or the underscore, and digit- is established to stand for any digit.
- 3. Regular Expressions The regular expressions are built recursively out of smaller regular expres- sions, using the rules described below. Each regular expression r denotes a language L(r), which is also defined recursively from the languages denoted by r's subexpressions. Here are the rules that define the regular expressions over some alphabet C and the languages that those expressions denote.
- 4. BASIS 1. E is a regular expression, and L (E) is {E) , that is, the language whose sole member is the empty string. 2. If a is a symbol in C, then a is a regular expression, and L(a) = {a), that is, the language with one string, of length one, with a in its one position. Note that by convention, we use italics for symbols, and boldface for their corresponding regular expression.
- 5. INDUCTION 1. (r) 1 (9) is a regular expression denoting the language L(r) U L(s). 2. (r) (s) is a regular expression denoting the language L(r) L(s) . 3. (r) * is a regular expression denoting (L (r)) * . 4. (r) is a regular expression denoting L(r). This last rule says that we can add additional pairs of parentheses around expressions without changing the language they denote
- 6. Precedence As defined, regular expressions often contain unnecessary pairs of paren- theses. We may drop certain pairs of parentheses if we adopt the conventions that: a) The unary operator * has highest precedence and is left associative. b) Concatenation has second highest precedence and is left associative. c) I has lowest precedence and is left associative.
- 7. Precedence Under these conventions, for example, we may replace the regular expression (a) I ((b) * (c)) by a/ b*c. Both expressions denote the set of strings that are either a single a or are zero or more b's followed by one c.
- 8. Let C = {a, b}. 1. The regular expression a1 b denotes the language {a, b}. 2. (a1 b) (alb) denotes {aa, ab, ba, bb), the language of all strings of length two over the alphabet C. Another regular expression for the same language is aalablbal bb. 3. a* denotes the language consisting of all strings of zero or more a's, that is, {E, a, aa, aaa, . . . }.
- 9. Let C = {a, b} 4. (alb)* denotes the set of all strings consisting of zero or more instances of a or b, that is, all strings of a's and b's: {e, a, b, aa, ab, ba, bb, aaa, . . .}. Another regular expression for the same language is (a*b*)*. 5. ala*b denotes the language {a, b, ab, aab,aaab,. . .), that is, the string a and all strings consisting of zero or more a's and ending in b.