![Extensions
One or more instances: (r)+
Zero of one instances: r?
Character classes: [abc]
Example:
letter_ -> [A-Za-z_]
digit -> [0-9]
id -> letter_(letter|digit)*](https://image.slidesharecdn.com/lecture1-lexicalanalysis-230223081625-71955661/85/Lecture-1-Lexical-Analysis-ppt-17-320.jpg)
![Recognition of tokens (cont.)
The next step is to formalize the patterns:
digit -> [0-9]
Digits -> digit+
number -> digit(.digits)? (E[+-]? Digit)?
letter -> [A-Za-z_]
id -> letter (letter|digit)*
If -> if
Then -> then
Else -> else
Relop -> < | > | <= | >= | = | <>
We also need to handle whitespaces:
ws -> (blank | tab | newline)+](https://image.slidesharecdn.com/lecture1-lexicalanalysis-230223081625-71955661/85/Lecture-1-Lexical-Analysis-ppt-19-320.jpg)
![Example
%{
/* definitions of manifest constants
LT, LE, EQ, NE, GT, GE,
IF, THEN, ELSE, ID, NUMBER, RELOP */
%}
/* regular definitions
delim [ tn]
ws {delim}+
letter [A-Za-z]
digit [0-9]
id {letter}({letter}|{digit})*
number {digit}+(.{digit}+)?(E[+-]?{digit}+)?
%%
{ws} {/* no action and no return */}
if {return(IF);}
then {return(THEN);}
else {return(ELSE);}
{id} {yylval = (int) installID(); return(ID); }
{number} {yylval = (int) installNum(); return(NUMBER);}
…
Int installID() {/* funtion to install the
lexeme, whose first character is
pointed to by yytext, and whose
length is yyleng, into the symbol
table and return a pointer thereto
*/
}
Int installNum() { /* similar to
installID, but puts numerical
constants into a separate table */
}](https://image.slidesharecdn.com/lecture1-lexicalanalysis-230223081625-71955661/85/Lecture-1-Lexical-Analysis-ppt-27-320.jpg)
![50
Implementation
A DFA can be implemented by a 2D table T
One dimension is “states”
Other dimension is “input symbols”
For every transition Si a Sk define T[i,a] = k
DFA “execution”
If in state Si and input a, read T[i,a] = k and skip to state
Sk
Very efficient](https://image.slidesharecdn.com/lecture1-lexicalanalysis-230223081625-71955661/85/Lecture-1-Lexical-Analysis-ppt-50-320.jpg)
Lecture 1 - Lexical Analysis.ppt
- 2. Outline Role of lexical analyzer Specification of tokens Recognition of tokens Lexical analyzer generator Finite automata Design of lexical analyzer generator
- 3. The role of lexical analyzer The main task of the lexical analyzer is to read the input characters of the source program group them into lexemes and produce as output a sequence of tokens for each lexeme in the source program. If a lexeme has an identifier, that lexeme is entered into the symbol table. The lexical analyzer not only identifies the lexemes but also pre-processes the source text like removing comments, white spaces, etc.
- 4. The role of lexical analyzer Lexical Analyzer Parser Source program token getNextToken Symbol table To semantic analysis
- 5. Why to separate Lexical analysis and parsing 1. Simplicity of design 2. Improving compiler efficiency 3. Enhancing compiler portability
- 6. Lexical analysis Lexical analyzers are divided into a cascade of two processes: Scanning - It consists of simple processes that do not require the tokenization of the input such as deletion of comments, compaction of consecutive white space characters into one. Lexical Analysis- This is the more complex portion where the scanner produces sequence of tokens as output.
- 7. Tokens, Patterns and Lexemes A token is a pair a token name and an optional token value A pattern is a description of the form that the lexemes of a token may take Specification of Tokens: Regular expressions are important part in specifying lexeme patterns. While they cannot express all possible patterns, they are very effective in specifying those type of patterns that we actually need for tokens. A lexeme is a sequence of characters in the source program that matches the pattern for a token
- 8. Example Token Informal description Sample lexemes if else comparison id number literal Characters i, f Characters e, l, s, e < or > or <= or >= or == or != Letter followed by letter and digits Any numeric constant Anything but “ sorrounded by “ if else <=, != pi, score, D2 3.14159, 0, 6.02e23 “core dumped” printf(“total = %dn”, score);
- 9. Attributes for tokens E = M * C ** 2 <id, pointer to symbol table entry for E> <assign-op> <id, pointer to symbol table entry for M> <mult-op> <id, pointer to symbol table entry for C> <exp-op> <number, integer value 2>
- 10. Lexical errors Some errors are out of power of lexical analyzer to recognize: fi (a == f(x)) … However it may be able to recognize errors like: d = 2r Such errors are recognized when no pattern for tokens matches a character sequence
- 11. Error recovery Panic mode: successive characters are ignored until we reach to a well formed token Delete one character from the remaining input Insert a missing character into the remaining input Replace a character by another character Transpose two adjacent characters
- 12. Input buffering Sometimes lexical analyzer needs to look ahead some symbols to decide about the token to return In C language: we need to look after -, = or < to decide what token to return We need to introduce a two buffer scheme to handle large look-aheads safely E = M * C * * 2 eof
- 13. Sentinels Switch (*forward++) { case eof: if (forward is at end of first buffer) { reload second buffer; forward = beginning of second buffer; } else if {forward is at end of second buffer) { reload first buffer; forward = beginning of first buffer; } else /* eof within a buffer marks the end of input */ terminate lexical analysis; break; cases for the other characters; } E = M eof * C * * 2 eof eof
- 14. Specification of tokens In theory of compilation regular expressions are used to formalize the specification of tokens Regular expressions are means for specifying regular languages Example: Letter_(letter_ | digit)* Each regular expression is a pattern specifying the form of strings
- 15. Regular expressions Ɛ is a regular expression, L(Ɛ) = {Ɛ} If a is a symbol in ∑then a is a regular expression, L(a) = {a} (r) | (s) is a regular expression denoting the language L(r) ∪ L(s) (r)(s) is a regular expression denoting the language L(r)L(s) (r)* is a regular expression denoting (L(r))* (r) is a regular expression denoting L(r)
- 16. Regular definitions d1 -> r1 d2 -> r2 … dn -> rn Example: letter_ -> A | B | … | Z | a | b | … | Z | _ digit -> 0 | 1 | … | 9 id -> letter_ (letter_ | digit)*
- 17. Extensions One or more instances: (r)+ Zero of one instances: r? Character classes: [abc] Example: letter_ -> [A-Za-z_] digit -> [0-9] id -> letter_(letter|digit)*
- 18. Recognition of tokens Starting point is the language grammar to understand the tokens: stmt -> if expr then stmt | if expr then stmt else stmt | Ɛ expr -> term relop term | term term -> id | number
- 19. Recognition of tokens (cont.) The next step is to formalize the patterns: digit -> [0-9] Digits -> digit+ number -> digit(.digits)? (E[+-]? Digit)? letter -> [A-Za-z_] id -> letter (letter|digit)* If -> if Then -> then Else -> else Relop -> < | > | <= | >= | = | <> We also need to handle whitespaces: ws -> (blank | tab | newline)+
- 20. Transition diagrams Transition diagram for relop
- 21. Transition diagrams (cont.) Transition diagram for reserved words and identifiers
- 22. Transition diagrams (cont.) Transition diagram for unsigned numbers
- 23. Transition diagrams (cont.) Transition diagram for whitespace
- 24. Architecture of a transition- diagram-based lexical analyzer TOKEN getRelop() { TOKEN retToken = new (RELOP) while (1) { /* repeat character processing until a return or failure occurs */ switch(state) { case 0: c= nextchar(); if (c == ‘<‘) state = 1; else if (c == ‘=‘) state = 5; else if (c == ‘>’) state = 6; else fail(); /* lexeme is not a relop */ break; case 1: … … case 8: retract(); retToken.attribute = GT; return(retToken); }
- 25. Lexical Analyzer Generator - Lex Lexical Compiler Lex Source program lex.l lex.yy.c C compiler lex.yy.c a.out a.out Input stream Sequence of tokens
- 26. Structure of Lex programs declarations %% translation rules %% auxiliary functions Pattern {Action}
- 27. Example %{ /* definitions of manifest constants LT, LE, EQ, NE, GT, GE, IF, THEN, ELSE, ID, NUMBER, RELOP */ %} /* regular definitions delim [ tn] ws {delim}+ letter [A-Za-z] digit [0-9] id {letter}({letter}|{digit})* number {digit}+(.{digit}+)?(E[+-]?{digit}+)? %% {ws} {/* no action and no return */} if {return(IF);} then {return(THEN);} else {return(ELSE);} {id} {yylval = (int) installID(); return(ID); } {number} {yylval = (int) installNum(); return(NUMBER);} … Int installID() {/* funtion to install the lexeme, whose first character is pointed to by yytext, and whose length is yyleng, into the symbol table and return a pointer thereto */ } Int installNum() { /* similar to installID, but puts numerical constants into a separate table */ }
- 28. 28 Finite Automata Regular expressions = specification Finite automata = implementation A finite automaton consists of An input alphabet A set of states S A start state n A set of accepting states F S A set of transitions state input state
- 29. 29 Finite Automata Transition s1 a s2 Is read In state s1 on input “a” go to state s2 If end of input If in accepting state => accept, othewise => reject If no transition possible => reject
- 30. 30 Finite Automata State Graphs A state • The start state • An accepting state • A transition a
- 31. 31 A Simple Example A finite automaton that accepts only “1” A finite automaton accepts a string if we can follow transitions labeled with the characters in the string from the start to some accepting state 1
- 32. 32 Another Simple Example A finite automaton accepting any number of 1’s followed by a single 0 Alphabet: {0,1} Check that “1110” is accepted but “110…” is not 0 1
- 33. 33 And Another Example Alphabet {0,1} What language does this recognize? 0 1 0 1 0 1
- 34. 34 And Another Example Alphabet still { 0, 1 } The operation of the automaton is not completely defined by the input On input “11” the automaton could be in either state 1 1
- 35. 35 Epsilon Moves Another kind of transition: -moves • Machine can move from state A to state B without reading input A B
- 36. 36 Deterministic and Nondeterministic Automata Deterministic Finite Automata (DFA) One transition per input per state No -moves Nondeterministic Finite Automata (NFA) Can have multiple transitions for one input in a given state Can have -moves Finite automata have finite memory Need only to encode the current state
- 37. 37 Execution of Finite Automata A DFA can take only one path through the state graph Completely determined by input NFAs can choose Whether to make -moves Which of multiple transitions for a single input to take
- 38. 38 Acceptance of NFAs An NFA can get into multiple states • Input: 0 1 1 0 1 0 1 • Rule: NFA accepts if it can get in a final state
- 39. 39 NFA vs. DFA (1) NFAs and DFAs recognize the same set of languages (regular languages) DFAs are easier to implement There are no choices to consider
- 40. 40 NFA vs. DFA (2) For a given language the NFA can be simpler than the DFA 0 1 0 0 0 1 0 1 0 1 NFA DFA • DFA can be exponentially larger than NFA
- 41. 41 Regular Expressions to Finite Automata High-level sketch Regular expressions NFA DFA Lexical Specification Table-driven Implementation of DFA
- 42. 42 Regular Expressions to NFA (1) For each kind of rexp, define an NFA Notation: NFA for rexp A A • For • For input a a
- 43. 43 Regular Expressions to NFA (2) For AB A B • For A | B A B
- 44. 44 Regular Expressions to NFA (3) For A* A
- 45. 45 Example of RegExp -> NFA conversion Consider the regular expression (1 | 0)*1 The NFA is 1 C E 0 D F B G A H 1 I J
- 47. 47 NFA to DFA. The Trick Simulate the NFA Each state of resulting DFA = a non-empty subset of states of the NFA Start state = the set of NFA states reachable through -moves from NFA start state Add a transition S a S’ to DFA iff S’ is the set of NFA states reachable from the states in S after seeing the input a considering -moves as well
- 48. 48 NFA -> DFA Example 1 0 1 A B C D E F G H I J ABCDHI FGABCDHI EJGABCDHI 0 1 0 1 0 1
- 49. 49 NFA to DFA. Remark An NFA may be in many states at any time How many different states ? If there are N states, the NFA must be in some subset of those N states How many non-empty subsets are there? 2N - 1 = finitely many, but exponentially many
- 50. 50 Implementation A DFA can be implemented by a 2D table T One dimension is “states” Other dimension is “input symbols” For every transition Si a Sk define T[i,a] = k DFA “execution” If in state Si and input a, read T[i,a] = k and skip to state Sk Very efficient
- 51. 51 Table Implementation of a DFA S T U 0 1 0 1 0 1 0 1 S T U T T U U T U
- 52. 52 Implementation (Cont.) NFA -> DFA conversion is at the heart of tools such as flex or jflex But, DFAs can be huge In practice, flex-like tools trade off speed for space in the choice of NFA and DFA representations