CH3.1 CS 345 Dr. Mohamed Ramadan Saady Algebraic Properties of Regular Expressions AXIOMDESCRIPTION...
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CH3.1 CS 345 Dr. Mohamed Ramadan Saady Algebraic Properties of Regular Expressions AXIOM DESCRIPTION r | s = s | r r | (s | t) = (r | s) | t (r s) t = r (s t) r = r r = r r* = ( r | )* r ( s | t ) = r s | r t ( s | t ) r = s r | t r r** = r* | is commutative | is associative concatenation is associative concatenation distributes over | relation between * and Is the identity element for concatenation * is idempotent
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Transcript of CH3.1 CS 345 Dr. Mohamed Ramadan Saady Algebraic Properties of Regular Expressions AXIOMDESCRIPTION...
CH3.1
CS 345
Dr. Mohamed Ramadan Saady
Algebraic Properties of Regular Expressions
AXIOM DESCRIPTION
r | s = s | r
r | (s | t) = (r | s) | t
(r s) t = r (s t)
r = rr = r
r* = ( r | )*
r ( s | t ) = r s | r t( s | t ) r = s r | t r
r** = r*
| is commutative
| is associative
concatenation is associative
concatenation distributes over |
relation between * and
Is the identity element for concatenation
* is idempotent
CH3.2
CS 345
Dr. Mohamed Ramadan Saady
Regular Expression Examples
• All Strings that start with “tab” or end with
“bat”:
tab{A,…,Z,a,...,z}*|{A,…,Z,a,....,z}*bat
• All Strings in Which Digits 1,2,3 exist in
ascending numerical order:
{A,…,Z}*1 {A,…,Z}*2 {A,…,Z}*3 {A,…,Z}*
CH3.3
CS 345
Dr. Mohamed Ramadan Saady
Towards Token Definition
Regular Definitions: Associate names with Regular Expressions
For Example : PASCAL IDs
letter A | B | C | … | Z | a | b | … | zdigit 0 | 1 | 2 | … | 9 id letter ( letter | digit )*
Shorthand Notation: “+” : one or more r* = r+ | & r+ = r r* “?” : zero or one r?=r | [range] : set range of characters (replaces “|” ) [A-Z] = A | B | C | … | Z
Example Using Shorthand : PASCAL IDs
id [A-Za-z][A-Za-z0-9]*
CH3.4
CS 345
Dr. Mohamed Ramadan Saady
Token Recognition
How can we use concepts developed so far to assist in recognizing tokens of a source language ?
Assume Following Tokens:
if, then, else, relop, id, num
What language construct are they used for ?
Given Tokens, What are Patterns ?
if ifthen thenelse elserelop < | <= | > | >= | = | <>id letter ( letter | digit )*num digit + (. digit + ) ? ( E(+ | -) ? digit + ) ?
What does this represent ? What is ?
Grammar:stmt |if expr then stmt
|if expr then stmt else stmt|
expr term relop term | termterm id | num
CH3.5
CS 345
Dr. Mohamed Ramadan Saady
What Else Does Lexical Analyzer Do?
Scan away b, nl, tabs
Can we Define Tokens For These?
blank btab ^Tnewline ^Mdelim blank | tab | newlinews delim +
CH3.6
CS 345
Dr. Mohamed Ramadan Saady
Overall
Regular Expression
Token Attribute-Value
wsifthenelse
idnum
<<==
< >>
>=
-if
thenelseid
numreloprelop reloprelopreloprelop
----
pointer to table entrypointer to table entry
LTLEEQNEGTGE
Note: Each token has a unique token identifier to define category of lexemes
CH3.7
CS 345
Dr. Mohamed Ramadan Saady
Constructing Transition Diagrams for Tokens
• Transition Diagrams (TD) are used to represent the tokens
• As characters are read, the relevant TDs are used to attempt to match lexeme to a pattern
• Each TD has:
• States : Represented by Circles
• Actions : Represented by Arrows between states
• Start State : Beginning of a pattern (Arrowhead)
• Final State(s) : End of pattern (Concentric Circles)
• Each TD is Deterministic - No need to choose between 2 different actions !
CH3.8
CS 345
Dr. Mohamed Ramadan Saady
Example TDs
start
other
=>0 6 7
8 * RTN(G)
RTN(GE)> = :
We’ve accepted “>” and have read other char that must be unread.
CH3.9
CS 345
Dr. Mohamed Ramadan Saady
Example : All RELOPs
start <0
other
=6 7
8
return(relop, LE)
5
4
>
=1 2
3
other
>
=
*
*
return(relop, NE)
return(relop, LT)
return(relop, EQ)
return(relop, GE)
return(relop, GT)
