Lexical Analysis, Regular Expressions & Finite State Machines
Lexical Analysis: Regular Expressions CS 671 January 22, 2008.
30
Lexical Analysis: Regular Expressions CS 671 January 22, 2008
-
Upload
clement-jennings -
Category
Documents
-
view
214 -
download
0
Transcript of Lexical Analysis: Regular Expressions CS 671 January 22, 2008.
Lexical Analysis:Regular Expressions
CS 671January 22, 2008
2 CS 671 – Spring 2008
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
Last Time …
CompilerHigh-Level
Programming Languages
Machine Code
Error Messages
3 CS 671 – Spring 2008
Phases of a Compiler
Lexical analyzer
Syntax analyzer
Semantic analyzer
Intermediate code generator
Code optimizer
Code generator
Source program
Target 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
4 CS 671 – Spring 2008
Phases of a Compiler
Lexical analyzer
Syntax analyzer
Semantic analyzer
Intermediate code generator
Code optimizer
Code generator
Source program
Target program
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
5 CS 671 – Spring 2008
Phases of a Compiler
Lexical analyzer
Syntax analyzer
Semantic analyzer
Intermediate code generator
Code optimizer
Code generator
Source program
Target program
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)
6 CS 671 – Spring 2008
Phases of a Compiler
Lexical analyzer
Syntax analyzer
Semantic analyzer
Intermediate code generator
Code optimizer
Code generator
Source program
Target program
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
7 CS 671 – Spring 2008
Phases of a Compiler
Lexical analyzer
Syntax analyzer
Semantic analyzer
Intermediate code generator
Code optimizer
Code generator
Source program
Target program
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
8 CS 671 – Spring 2008
Phases of a Compiler
Lexical analyzer
Syntax analyzer
Semantic analyzer
Intermediate code generator
Code optimizer
Code generator
Source program
Target program
Native Code Generation
• Intermediate code is translated into native code
• Register allocation, instruction selection
Native Code Optimization
• Peephole optimizations – small window is optimized at a time
9 CS 671 – Spring 2008
Administration
1. Compiling to assembly
1. HW1 on website: Fun with Lex/Yacc
2. Questionnaire Results…
10 CS 671 – Spring 2008
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 CS 671 – Spring 2008
Makefiles
Target: dependent source file(s)
<tab>command
proj1
main.o io.odata.o
main.c io.h io.cdata.hdata.c
12 CS 671 – Spring 2008
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 CS 671 – Spring 2008
Lexical Tokens
• 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 **/
14 CS 671 – Spring 2008
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 CS 671 – Spring 2008
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 CS 671 – Spring 2008
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 generator that generates efficient tokenizer automatically (e.g., lex, flex)
17 CS 671 – Spring 2008
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 CS 671 – Spring 2008
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 CS 671 – Spring 2008
Regular expressions
Language – set of strings
String – finite sequence of symbols
Symbols – taken from a finite alphabet
Specify languages using regular expressions
Symbol a one instance of a
Epsilon empty string
Alternation R | S string from either L(R) or L(S)
Concatenation
R ∙ Sstring from L(R) followed by L(S)
Repetition R*
20 CS 671 – Spring 2008
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 CS 671 – Spring 2008
Examples
Regular Expression Strings 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 CS 671 – Spring 2008
More Examples
Whitespace:
Integers:
Hex numbers:
Valid UVa User Ids:
Loop keywords in C:
23 CS 671 – Spring 2008
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
else x = 0 ;
elsex = 0 ;
24 CS 671 – Spring 2008
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 CS 671 – Spring 2008
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 CS 671 – Spring 2008
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:1. whether the input is lexically well-formed2. 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 CS 671 – Spring 2008
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 CS 671 – Spring 2008
High Level View
Regular expressions = specification
Finite automata = implementation
Every regex has a FSA that recognizes its language
Scanner
ScannerGenerator
source code
specification
tokens
Design time
Compile time
29 CS 671 – Spring 2008
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
0 1 2
i f
IF
0 1
a-za-z
0-9ID
26 edges
30 CS 671 – Spring 2008
Language
Each string is accepted or rejected
1. Starting in the start state
2. Automaton follows one edge for every character (edge must match character)
3. After n-transitions for an n-character string, if final state then accept
Language: set of strings that the FSA accepts
0 1 2
i f
IFID3
ID
[a-z0-9]
[a-z0-9]
[a-hj-z]
