Lexical Analysis: Regular Expressions

1. Lexical Analysis:Regular Expressions CS 671 January 22, 2008

2. Last Time … • A program that translates a program in one language to another language • the essential interface between applications & architectures • Typically lowers the level of abstraction • analyzes and reasons about the program & architecture • We expect the program to be optimized i.e., better than the original • ideally exploiting architectural strengths and hiding weaknesses Compiler High-Level Programming Languages Machine Code Error Messages

3. Phases of a Compiler Source program • Lexical Analyzer • Group sequence of characters into lexemes – smallest meaningful entity in a language (keywords, identifiers, constants) • Characters read from a file are buffered – helps decrease latency due to i/o. Lexical analyzer manages the buffer • Makes use of the theory of regular languages and finite state machines • Lex and Flex are tools that construct lexical analyzers from regular expression specifications Lexical analyzer Syntax analyzer Semantic analyzer Intermediate code generator Code optimizer Code generator Target program

4. Phases of a Compiler • Parser • Convert a linear structure – sequence of tokens – to a hierarchical tree-like structure – an AST • The parser imposes the syntax rules of the language • Work should be linear in the size of the input (else unusable)  type consistency cannot be checked in this phase • Deterministic context free languages and pushdown automata for the basis • Bison and yacc allow a user to construct parsers from CFG specifications Source program Lexical analyzer Syntax analyzer Semantic analyzer Intermediate code generator Code optimizer Code generator Target program

5. Phases of a Compiler • Semantic Analysis • Calculates the program’s “meaning” • Rules of the language are checked (variable declaration, type checking) • Type checking also needed for code generation (code gen for a + b depends on the type of a and b) Source program Lexical analyzer Syntax analyzer Semantic analyzer Intermediate code generator Code optimizer Code generator Target program

6. Phases of a Compiler • Intermediate Code Generation • Makes it easy to port compiler to other architectures (e.g. Pentium to MIPS) • Can also be the basis for interpreters (such as in Java) • Enables optimizations that are not machine specific Source program Lexical analyzer Syntax analyzer Semantic analyzer Intermediate code generator Code optimizer Code generator Target program

7. Phases of a Compiler • Intermediate Code Optimization • Constant propagation, dead code elimination, common sub-expression elimination, strength reduction, etc. • Based on dataflow analysis – properties that are independent of execution paths Source program Lexical analyzer Syntax analyzer Semantic analyzer Intermediate code generator Code optimizer Code generator Target program

8. Phases of a Compiler • Native Code Generation • Intermediate code is translated into native code • Register allocation, instruction selection Source program Lexical analyzer Syntax analyzer Semantic analyzer Intermediate code generator • Native Code Optimization • Peephole optimizations – small window is optimized at a time Code optimizer Code generator Target program

9. Administration • 1. Compiling to assembly • 1. HW1 on website: Fun with Lex/Yacc • 2. Questionnaire Results…

10. Useful Tools! • tar – archiving program • gzip/bzip2 – compression • svn – version control • Make/Scons – build/run utility • Other useful tools: • Man! • Which • Locate • Diff (or sdiff)

11. Makefiles • Target: dependent source file(s) • <tab>command proj1 data.o main.o io.o data.c data.h main.c io.h io.c

12. First Step: Lexical Analysis (Tokenizing) • Breaking the program down into words or “tokens” • Input: stream of characters • Output: stream of names, keywords, punctuation marks • Side effect: Discards white space, comments • Source code: if (b==0) a = “Hi”; • Token Stream: Lexical Analysis Parsing

13. Identifiers: x y11 elsex _i00 • Keywords: if else while break • Integers: 2 1000 -500 5L • Floating point: 2.0 0.00020 .02 1.1e5 0.e-10 • Symbols: + * { } ++ < << [ ] >= • Strings: “x” “He said, \“Are you?\”” • Comments: /** ignore me **/ Lexical Tokens

14. Lexical Tokens • float match0(char *s) /* find a zero */ • { • if (!strncmp(s, “0.0”, 3)) • return 0.; • } • FLOAT ID(match0) _______ CHAR STAR ID(s) RPAREN LBRACE IF LPAREN BANG _______ LPAREN ID(s) COMMA STRING(0.0) ______ NUM(3) RPAREN RPAREN RETURN REAL(0.0) ______ RBRACE EOF

15. Ad-hoc Lexer • Hand-write code to generate tokens • How to read identifier tokens? • Token readIdentifier( ) { • String id = “”; • while (true) { • char c = input.read(); • if (!identifierChar(c)) • return new Token(ID, id, lineNumber); • id = id + String(c); • } • }

16. Problems • Don’t know what kind of token we are going to read from seeing first character • if token begins with “i’’ is it an identifier? • if token begins with “2” is it an integer? constant? • interleaved tokenizer code is hard to write correctly, harder to maintain • More principled approach: lexer generatorthat generates efficient tokenizer automatically (e.g., lex, flex)

17. Issues • How to describe tokens unambiguously • 2.e0 20.e-01 2.0000 • “” “x” “\\” “\”\’” • How to break text down into tokens • if (x == 0) a = x<<1; • if (x == 0) a = x<1; • How to tokenize efficiently • tokens may have similar prefixes • want to look at each character ~1 time

18. How To Describe Tokens • Programming language tokens can be described using regular expressions • A regular expression R describes some set of strings L(R) • L(R) is the language defined by R • L(abc) = { abc } • L(hello|goodbye) = {hello, goodbye} • L([1-9][0-9]*) = _______________ • Idea: define each kind of token using RE

19. Language – set of strings String – finite sequence of symbols Symbols – taken from a finite alphabet Specify languages using regular expressions Regular expressions

20. Convenient Shorthand • [abcd] one of the listed characters (a | b | c | d) • [b-g] [bcdefg] • [b-gM-Qkr] ____________ • [^ab] anything but one of the listed chars • [^a-f] ____________ • M? Zero or one M • M+ One or more M • M* ____________ • “a.+*” literally a.+* • . Any single character (except \n)

21. Examples • Regular ExpressionStrings in L(R) • digit = [0-9] “0” “1” “2” “3” … • posint = digit+ “8” “412” … • int = -? posint “-42” “1024” … • real = int (ε | (. posint)) “-1.56” “12” “1.0” • [a-zA-Z_][a-zA-Z0-9_]* C identifiers • Lexer generators support abbreviations • But they cannot be recursive

22. More Examples • Whitespace: • Integers: • Hex numbers: • Valid UVa User Ids: • Loop keywords in C:

23. else x = 0 ; elsex = 0 ; Breaking up Text • elsex=0; • REs alone not enough: need rules for choosing • Most languages: longest matching token wins • even if a shorter token is only way • Ties in length resolved by prioritizing tokens • RE’s + priorities + longest-matching token rule = lexer definition

24. Lexer Generator Specification • Input to lexer generator: • list of regular expressions in priority order • associated action for each RE (generates appropriate kind of token, other bookkeeping) • Output: • program that reads an input stream and breaks it up into tokens according to the REs. (Or reports lexical error -- “Unexpected character” )

25. Lex: A Lexical Analyzer Generator • Lex produces a C program from a lexical specification • http://www.epaperpress.com/lexandyacc/ • %% • DIGITS [0-9]+ • ALPHA [A-Za-z] • CHARACTER {ALPHA}|_ • IDENTIFIER {ALPHA}({CHARACTER}|{DIGITS})* • %% • if {return IF; } • {IDENTIFIER} {return ID; } • {DIGITS} {return NUM; } • ([0-9]+”.”[0-9]*)|([0-9]*”.”[0-9]+) {return ____; } • . {error(); }

26. Lexer Generator • Reads in list of regular expressions R1,…Rn, one per token, with attached actions • -?[1-9][0-9]* { return new Token(Tokens.IntConst, • Integer.parseInt(yytext()) • } • Generates scanning code that decides: • whether the input is lexically well-formed • corresponding token sequence • Problem 1 is equivalent to deciding whether the input is in the language of the regular expression • How can we efficiently test membership in L(R) for arbitrary R?

27. Regular Expression Matching • Sketch of an efficient implementation: • start in some initial state • look at each input character in sequence, update scanner state accordingly • if state at end of input is an accepting state, the input string matches the RE • For tokenizing, only need a finite amount of state: (deterministic) finite automaton (DFA) or finite state machine

28. High Level View • Regular expressions = specification • Finite automata = implementation • Every regex has a FSA that recognizes its language source code tokens Scanner Compile time Design time Scanner Generator specification

29. i f a-z a-z 0 1 2 0 1 0-9 ID Finite Automata • Takes an input string and determines whether it’s a valid sentence of a language • A finite automaton has a finite set of states • Edges lead from one state to another • Edges are labeled with a symbol • One state is the start state • One or more states are the final state 26 edges IF

30. Language • Each string is accepted or rejected • Starting in the start state • Automaton follows one edge for every character (edge must match character) • After n-transitions for an n-character string, if final state then accept • Language: set of strings that the FSA accepts i f [a-z0-9] [a-z0-9] 0 1 2 3 ID IF ID [a-hj-z]