1. Lexical Analyzer (Checker)

2. lec01-lexicalanalyzer
April 23, 2017
Lexical Analyzer
Lexical Analyzer reads the source program character by character to produce tokens.
Normally a lexical analyzer doesn’t return a list of tokens at one shot, it returns a token when the parser asks a token from it.

3. Tokens, Lexemes, and Patterns
Tokens include keywords, operators, identifiers, constants, literal strings, punctuation symbols
e.g: identifier, number, addop, assgop
A lexeme is a sequence of characters in the source program representing a token
e.g: newval, oldval
A pattern is a rule describing a set of lexemes that can represent a particular token
e.g: Identifier represents a set of strings which start with a letter continues with letters and digits
Regular expressions are widely used to specify patterns.

4. Attributes
Since a token can represent more than one lexeme, attributes provide additional information about tokens
For simplicity, a token may have a single attribute.
For an identifier, attribute is a pointer to the symbol table
Examples of some attributes:
<id,attr> where attr is pointer to the symbol table
<assgop,_> no attribute is needed (only one assignment operator)
<num,val> where val is the actual value of the number.
Token and its attribute uniquely identifies a lexeme.

5. Strings and Languages
Alphabet – any finite set of symbols (e.g. ASCII, binary alphabet, or a set of tokens)
String – A finite sequence of symbols drawn from an alphabet
Language – A set of strings over a fixed alphabet

6. Operations on Languages
Union:
Concatenation:
Kleene closure:
Zero or more concatenations
Positive closure:
One or more concatenations

7. Regular Expressions Can give “names” to regular expressions
Convention: names in boldface (to distinguish them from symbols)
letter  A|B|…|Z|a|b|…|z
digit  0|1|…|9
id  letter (letter | digit)*

8. Notational Shorthands
One or more instances: r+ denotes rr*
Zero or one Instance: r? denotes r|ε
Character classes: [a-z] denotes [a|b|…|z]
digit  [0-9]
digits  digit+
optional_fraction  (. digits )?
num  digits optional_fraction

9. Limitations Can not describe balanced or nested constructs
Example, all valid strings of balanced parentheses
This can be done with Context Free Grammar ( CFG)

10. Grammar Fragment (Pascal)
stmt  if expr then stmt
| if expr then stmt else stmt
| ε
expr  term relop term
| term
term  id | num

11. Related Regular Expression Definitions
if  if
then  then
else  else
relop  < | <= | = | <> | > | >=
id  letter ( letter | digit )*
num  digit+ (. digit+ )?
ws  delim+
delim  blank | tab | newline

12. Tokens and Attributes Regular Expression Token Attribute Value ws - if
then
else id
pointer to entry
num
<
relop LT
<= LE = EQ
<> NE
> GT
=> GE

13. Transition Diagrams A stylized flowchart
Transition diagrams consist of states connected by edges
Edges leaving a state s are labeled with input characters that may occur after reaching state s
Assumed to be deterministic
There is one start state and at least one accepting (final) state

14. Transition Diagram for “relop”

15. Identifiers and Keywords
Share a transition diagram
After reaching accepting state, code determines if lexeme is keyword or identifier

16. Numbers

17. Finding the Next Token token nexttoken(void) { while (1) {
switch (state) {
case 0:
c = nextchar();
if (c == ' ' || c=='\t' || c == '\n') {
state = 0;
lexeme_beginning++; }
else if (c == '<') state = 1;
else if (c == '=') state = 5
else if (c == '>') state = 6
else state = next_td();
break;
… /* other cases here */

18. Trying Transition Diagrams
int next_td(void) {
switch (start) {
case 0: start = 9; break;
case 9: start = 20; break;
case 20: start = 25; break;
case 25: recover(); break;
default: error("invalid start state"); }
/* Possibly additional actions here */
return start;

19. Finite Automata
Generalized transition diagrams that act as “recognizer” for a language
Can be nondeterministic (NFA) or deterministic (DFA)
NFAs can have ε-transitions, DFAs can not
NFAs can have multiple edges with same symbol leaving a state, DFAs can not
Both can recognize exactly what regular expressions can denote

20. NFAs A set of states S A set of input symbols Σ (input alphabet)
A transition function move that maps state, symbol pairs to a set of states
A single start state s0
A set of accepting (or final) states F
An NFA accepts a string s if and only if there exists a path from the start state to an accepting state such that the edge labels spell out s

21. NFA (Example) The language recognized by this NFA is (a|b) * ab1 2 a b
start
0 is the start state s0
{2} is the set of final states F
= {a,b}
S = {0,1,2}
Transition graph of the NFA
The language recognized by this NFA is (a|b) * ab

22. Transition Tables
State
Input Symbol a b
{0,1}
{0} 1
---
{2} 2
{3}

23. DFAs No state has an ε-transition
For each state s and input symbol a, there as at most one edge labeled a leaving s

24. Example: r = (a|b)*abb

25. Functions ε-closure and move
ε-closure(s) is the set of NFA states reachable from NFA state s on ε-transitions alone
move(T,a) is the set of NFA states to which there is a transition on input a from any NFA state s in T

26. Constructed DFA

27. Simulating a DFA s := s0 c := nextchar while c != eof do
s := move(s, c)
end
if s is in F then
return “yes”
else
return “no”

28. Simulating an NFA S := ε-closure({s0}) a := nextchar while a != eof do
S := ε-closure(move(S,a))
if S ∩ F != Ø
return “yes”
else
return “no”

29. Space/Time Tradeoff (Worst Case)
NFA
O(|r|)
O(|r|*|x|)
DFA
O(2|r|)
O(|x|)

30. Simulating a Regular Expression
First use Thompson’s Construction to convert RE to NFA
Then there are two choices:
Use subset construction to convert NFA to DFA, then simulate the DFA
Simulate the NFA directly

31. Some Other Issues in Lexical Analyzer
The lexical analyzer has to recognize the longest possible string.
Ex: identifier newval n ne new newv newva newval
What is the end of a token? Is there any character which marks the end of a token?

32. Some Other Issues in Lexical Analyzer (cont.)
Skipping comments
Normally we don’t return a comment as a token.
So, the comments are only processed by the lexical analyzer, and don’t complicate the syntax of the language.
Symbol table interface
symbol table holds information about tokens (at least lexeme of identifiers)
how to implement the symbol table, and what kind of operations.
hash table – open addressing, chaining
putting into the hash table, finding the position of a token from its lexeme.
Positions of the tokens in the file (for the error handling).