## 9.4. ` `Values of Regular expressions

Expressions in any algebra have values of a certain type.` `

For arithmetic expressions, values are integers,
reals or whatever type of numbers with which
we are working.` `

5 + 8 / 16 * 7 + 3 =

For regular expressions,
the value of each expression is pattern consisting
of a set of strings often called a language.` `

The language denoted by regular expressions
E will be referred to as
*L(E)*,
or the language of E.` `
The languages of the atomic operands are defined
as follows:

1. IF x is any character, then the regular expres
sion x stands for the language {x}; that is
L(x) = { x }. Note that this language is a set
that contains one string, the string is the
length 1, and the first position of that string
has the character x
2. L() = { }. The special symbol as a regular
expression denotes the set whose only string is
the empty string, or string of length 0.
3. L() = { }. The special symbol as a regular
expression denotes the empty set of strings.

Note that we do not define a value from an atomic
operand that is a variable.` `
Such an operand only takes an value when we replace
the variable by a concrete expression,
and its value is whatever value that expression has.` `

Created by *unroff & hp-tools.*
© by Hans-Peter Bischof. All Rights Reserved (1998).
Last modified: 27/July/98 (12:14)