Type 3 languages. Regular grammars Finite automata. Regular expressions. Deterministic Nondeterministic. a, a, ε, E 1.E 2, E 1 E 2, E 1*, (E 1 )

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1 Course 7 1

2 Type 3 languages Regular grammars Finite automata Deterministic Nondeterministic Regular expressions a, a, ε, E 1.E 2, E 1 E 2, E 1*, (E 1 ) 2

3 Brief history of programming Stages of compilation Lexical analysis Lexical description Interpretation Right oriented interpretation Well formed lexical description Lex 3

4 1957 Fortran: first compiler (arithmetic expressions, instructions, subroutines) 1960 Algol: first use of formal definitions (grammars, BNF, blocks, recursion) 1970 Pascal: user defined types, virtual machines (P-code) 1972 C: dynamic variables, multitasking, interrupt management 1983 ADA: first standardized language 1985 C++: object oriented, exceptions, design patterns 1995 Java: just-in-time compilation 2000 C#:.NET 4

5 Source code Characters Lexical analyzer Lexemes Syntactic analyzer Syntactic tree Semantic analyzer Processor code Decorated syntactic tree Code generator Intermediary code Assembler Interpreter 5

6 Def. 1 Let Σ be an alphabet (of a programming language). A lexical description over is a regular expression E = (E 1 E 2 E n ) +, whre n is the number of lexical units, and E i describes a lexical unit, 1 i n. Def. 2 Let E be a lexical description over Σ which contains n lexical units and w +. The word w isccorrect relative to the description E if w L(E). An interpretation of the word w L(E) is a sequence of pairs (u 1, k 1 ), (u 2, k 2 ),, (u m, k m ), where w = u 1 u 2 u m, u i L(E ki ) 1 i m, 1 ki n. 6

7 w = alpha := beta = 542 Interpretations for the word w: (alpha, Id), (:=, Assign), (beta, Id), (=, Equal), (542, Integer) (alp, Id), (ha, Id), (:=, Assign), (beta, Id), (=, Equal), (542, Integer) (alpha, Id), (:, Colon), ( =, Equal), (beta, Id), (=, Equal), (542, Integer) 7

8 Def. 3 Let E be a lexical description over and w L(E). An interpretation of the word w, (u 1, k 1 )(u 2, k 2 ), (u m, k m ), is a right-oriented interpretation if ( i) 1 i m: u i = max{ v, v L(E 1 E 2 E n ) Pref(u i u i+1 u m )}. (where Pref(w) is the set of prefixes for the word w ). There are some lexical descriptions E in which not every word of L(E) allows for a right-oriented interpretation. E = (a ab bc) + şi w = abc. 8

9 Def. 4 A lexical description E is well-formed if every word w L(E) has exactly one rightoriented interpretation. Theorem Given a lexical description E, it can be determined if it is well-formed. Def. 5 Let E be a well-formed lexical description over. A lexical analyzer (scanner) for E is a program that recognizes the language L(E) and determines, for each w L(E), its right-oriented interpretation. 9

10 Let E be a lexical description over Σ. To produce a lexical analyzer for E means to: 1. Build the finite automaton A, equivalent to E 2. From A, obtain the deterministic automaton equivalent to E, A. 3. (Optional) Obtain the minimal automaton equivalent to A. 4. Implement the automaton A. 10

11 Lexical description: letter a b z digit identifier letter (letter digit)* sign + - number (sign ε) digit+ operator + - * / < > <= >= < > assign := Colon : reserved_words if then else parenthesis ) ( 11

12 A i A n A o q 0 A a A : A r A p 12

13 letter, digit letter 1 # i or # r digit 2 digit # n +,- 3 digit # o operator {+,-} 4 # o : ),( = # a # : # p 0 13

14 Bell Laboratories 1975 M.E. Lesk şi E. Schmidt Standard in UNIX from version 7 Variants: FLEX (Fast LEXical Analyzer Generator) PCLEX lansat de Abraxax Software Inc. (Windows) YooLex (Yet another Object-Oriented Lex) Flex++: (variantele Bison, Flex care produc cod C++) 14

15 Lex source code C source code Executable file.l lex.yy.c a.out lex file.l gcc lex.yy.c -ll 15

16 Three segments, separated by %% Declarations Rules C code Declarations C declarations, in between the reserved character sequences %{, %} Lex definitions for the rule segment 16

17 General form of Lex definitions <name> <regex> Regex built using characters and operators " \[ ] ^ -?. * + () / {} % <> digit [0-9] letter [a-za-z] 17

18 Symbol Description. Any character but newline \ Escape sequence * zero ore more copies of the preceding expression + one ore more copies of the preceding expression? zero sau no copy of the preceding expression ^ a b negation a or b () character grouping a+b word "a+b [] character class 18

19 Expression Matching words abc abc abc* ab abc abcc abccc... abc+ abc abcc abccc... a(bc)+ abc abcbc abcbcbc... a(bc)? a abc [abc] any of: a, b, c [a-z] any lowercase letter [a\-z] any of the letters: a, -, z [-az] any of the characters: -, a, z [A-Za-z0-9]+ one or more alphanumeric characters [ \t\n]+ white spaces [^ab] any character but: a, b [a^b] any of: a, ^, b [a b] any of: a,, b a b any of: a, b 19

20 Rule section exp_1 exp_2... exp_n {Action_1} {Action_2} {Action_n} Rules are matched in the order they are written in The first rule that matches a word is chosen 20

21 Name int yylex(void) char *yytext yyleng yylval FILE *yyout FILE *yyin Description call to the analyzer pointer to the recognized word length of recognized word value associated to the word output file input file 21

22 %{ int yylineno; %} %% ^(.*)\n printf("%4d\t%s", ++yylineno, yytext); %% int main(int argc, char *argv[]) { yyin = fopen(argv[1], "r"); yylex(); fclose(yyin); } 22

23 letter [A-Za-z] digit [0-9] %{ int count; %} %% {letter}({letter} {digit})* {count++;}.{} %% int main(void) { yylex(); printf("number of identifiers = %d\n", count); return 0; } 23

24 %{ int nchar, nword, nline; %} %% \n { nline++; nchar++; } [^ \t\n]+ { nword++, nchar += yyleng; }. { nchar++; } %% int main(void) { yylex(); printf("%d\t%d\t%d\n", nchar, nword, nline); return 0; } 24

25 %{ # include <stdio.h> %} litera [a-za-z] cifra [0-9] cifre ({cifra})+ semn [+-] operator [+*/<>=-] spatiu [' \t \n ] %% "if" "then" "else {printf("%s cuvant rezervat\n", yytext);} ({litera})({litera} {cifra})* {printf("%s identificator\n", yytext);} {cifre} ({semn})({cifre}) {printf("%s numar intreg\n", yytext);} {operator} {printf("%c operator\n", yytext[0]);} \:\= {printf("%s asignare\n", yytext);} \: {printf("%c doua puncte\n", yytext[0]);} (\() (\)) {printf("%c paranteza\n", yytext[0]);} {spatiu} {}. {printf("%c caracter ilegal\n", yytext[0]);} %% int main( ){ yylex( ); return 0; } 25

26 Grigoraş Gh., Construcţia compilatoarelor. Algoritmi fundamentali, Editura Universităţii Alexandru Ioan Cuza, Iaşi,

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