theory of compilation 236360 erez petrank lecture 1: introduction, lexical analysis 1
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Theory of Compilation 236360
Erez Petrank
Lecture 1: Introduction, Lexical Analysis
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2
Compilation Theory
• Lecturer: Assoc. Prof. Erez Petrank– [email protected]– Reception hour: Thursday 14:30—15:30, Taub 528.
• Teaching assistants: – Adi Sosnovich (responsible TA) – Maya Arbel
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3
Administration
• Site: http://webcourse.cs.technion.ac.il/236360 • Grade:
– 25% homework (important!)• 5% dry (MAGEN)• 20% wet: compulsory
– 75% Test
• Failure in test means failure in course, independent of homework grade.
• Prerequisite: Automata and formal languages 236353
• MOED GIMMEL for Miluim only• ... העתקות
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Books
• Main book– A.V. Aho, M. S. Lam, R.
Sethi, and J.D. Ullman – “Compilers – Principles, Techniques, and Tools”, Addison-Wesley, 2007.
• Additional book: – Dick Grune, Kees van
Reeuwijk, Henri E. Bal, Ceriel J.H. Jacobs, and Koen G. Langendoen. “Modern Compiler Design”, Second Edition, Wiley 2010.
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Turing Award
2008: Barbara Liskov, programming languages and system design.2009: Charles P Thacker, architecture.2010: Leslie Valiant, theory of computation.
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Goals
• Understand what a compiler is, • How a compiler works,• Tools and techniques that can be used in other
settings.
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Complexity
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What is a Compiler?
• “A compiler is a computer program that transforms source code written in a programming language (source language) into another language (target language). The most common reason for wanting to transform source code is to create an executable program.”
--Wikipedia
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What is a Compiler?
Executable
code
exe
Source
text
txt
source language target language
Compiler
CC++PascalJava
PostscriptTeX
PerlJavaScriptPythonRuby
Prolog
LispSchemeMLOCaml
IA32IA64SPARC
CC++PascalJava
Java Bytecode…
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What is a Compiler?
Executable
code
exe
Source
text
txt
Compiler
int a, b;a = 2;b = a*2 + 1;
MOV R1,2SAL R1INC R1MOV R2,R1
• The source and target program are semantically equivalent.
• Since the translation is difficult, it is partitioned into standard modular steps.
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Anatomy of a Compiler(Coarse Grained)
Executable
code
exe
Source
text
txt
Intermediate
Representation
Backend
(synthesis)
Compiler
Frontend
(analysis)
int a, b;a = 2;b = a*2 + 1;
MOV R1,2SAL R1INC R1MOV R2,R1
Optimization
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Modularity
SourceLanguage 1
txt
IntermediateRepresentation
Backend
TL2
Frontend
SL2
int a, b;a = 2;b = a*2 + 1;
MOV R1,2SAL R1INC R1MOV R2,R1
Frontend
SL3
Frontend
SL1
Backend
TL1
Backend
TL3
SourceLanguage 2
txt
SourceLanguage n
txt
Executabletarget 1
exe
Executabletarget 2
exe
Executabletarget m
exe
SET R1,2STORE #0,R1SHIFT R1,1STORE #1,R1ADD R1,1STORE #2,R1
Build m+n modules instead of mn compilers…
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Anatomy of a Compiler
Executable
code
exe
Source
text
txt
Intermediate
Representation
Backend
(synthesis)
Compiler
Frontend
(analysis)
int a, b;a = 2;b = a*2 + 1;
MOV R1,2SAL R1INC R1MOV R2,R1
LexicalAnalysi
s
Syntax Analysi
s
Parsing
Semantic
Analysis
IntermediateRepresentati
on
(IR)
Code
Generation
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Interpreter
Interpreter
int a, b;a = 2;b = a*2 + 1;
Source
text
txt
Input
OutputIntermediate
Representation
Frontend
(analysis)
Execution
Engine
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Compiler vs. Interpreter
Executable
code
exe
Source
text
txt
Intermediate
Representation
Backend
(synthesis)
Frontend
(analysis)
Source
text
txt
Input
OutputIntermediate
Representation
Frontend
(analysis)
Execution
Engine
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Compiler vs. Interpreter
Intermediate
Representation
Backend
(synthesis)
Frontend
(analysis)
3
7Intermediate
Representation
Frontend
(analysis)
Execution
Engineb = a*2 + 1;
b = a*2 + 1;
MOV R1,8(ebp)SAL R1INC R1MOV R2,R1
3
7
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Just-in-time Compiler (e.g., Java)
Java
Source
txt
Input
OutputJava source to Java bytecode
compilerJava
Bytecode
txtJava
Virtual Machine
Just-in-time compilation: bytecode interpreter (in the JVM) compiles program fragments during interpretation to avoid expensive re-interpretation.
Machine dependent and optimized.
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Importance
• Many in this class will build a parser some day– Or wish they knew how to build one…
• Useful techniques and algorithms– Lexical analysis / parsing– Intermediate representation– …– Register allocation
• Understand programming languages better• Understand internals of compilers• Understanding of compilation versus runtime, • Understanding of how the compiler treats the program (how
to improve the efficiency, how to use error messages), • Understand (some) details of target architectures
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Complexity:Various areas, theory and practice.
TargetSource
Compiler
Useful formalisms Regular expressions Context-free grammars Attribute grammars
Data structures Algorithms
Programming LanguagesSoftware Engineering
Operating systemsRuntime environmentGarbage collectionArchitecture
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Course Overview
Executable
code
exe
Source
text
txt
Compiler
LexicalAnalysi
s
Syntax Analysi
s
Parsing
Semantic
Analysis
Inter.Rep.
(IR)
Code
Gen.
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Front End IngredientsCharacter Stream
Lexical Analyzer
Token Stream
Syntax Analyzer
Syntax Tree
Semantic Analyzer
Decorated Syntax Tree
Intermediate Code Generator
Easy, Regular Expressions
More complex, recursive ,context-free grammar
More complex, recursive, requiresWalking up and down in the
Derivation tree .
Get code from the tree. Some optimizations are easier on a tree ,
and some easier on the code.
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Lexical Analysis
LexicalAnalysi
s
Syntax Analysi
s
Sem.Analysi
s
Inter.Rep.
Code Gen.
x = b*b – 4*a*c
txt
<ID,”x”> <EQ> <ID,”b”> <MULT> <ID,”b”> <MINUS> <INT,4> <MULT> <ID,”a”> <MULT> <ID,”c”>
TokenStream
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Syntax Analysis (Parsing)
LexicalAnalysi
s
Syntax Analysi
s
Sem.Analysi
s
Inter.Rep.
Code Gen.
<ID,”b”> <MULT> <ID,”b”> <MINUS> <INT,4> <MULT> <ID,”a”> <MULT> <ID,”c”>
‘b’ ‘4’
‘b’‘a’
‘c’
ID
ID
ID
ID
ID
factor
term factorMULT
term
expression
expression
factor
term factorMULT
term
expression
term
MULT factor
MINUS
SyntaxTree
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Simplified Tree
Sem.Analysi
s
Inter.Rep.
Code Gen.
‘b’
‘4’
‘b’
‘a’
‘c’
MULT
MULT
MULT
MINUS
LexicalAnalysi
s
Syntax Analysi
s
AbstractSyntaxTree
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Semantic Analysis
LexicalAnalysi
s
Syntax Analysi
s
Sem.Analysi
s
Inter.Rep.
Code Gen.
‘b’
‘4’
‘b’
‘a’
‘c’
MULT
MULT
MULT
MINUS
type: intloc: sp+8
type: intloc: const
type: intloc: sp+16
type: intloc: sp+16
type: intloc: sp+24
type: intloc: R2
type: intloc: R2
type: intloc: R1
type: intloc: R1
AnnotatedAbstractSyntaxTree
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Intermediate Representation
LexicalAnalysi
s
Syntax Analysi
s
Sem.Analysi
s
Inter.Rep.
Code Gen.
‘b’
‘4’
‘b’
‘a’
‘c’
MULT
MULT
MULT
MINUS
type: intloc: sp+8
type: intloc: const
type: intloc: sp+16
type: intloc: sp+16
type: intloc: sp+24
type: intloc: R2
type: intloc: R2
type: intloc: R1
type: intloc: R1
R2 = 4*aR1=b*bR2= R2*cR1=R1-R2
IntermediateRepresentation
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Generating Code
Inter.Rep.
Code Gen.
‘b’
‘4’
‘b’
‘a’
‘c’
MULT
MULT
MULT
MINUS
type: intloc: sp+8
type: intloc: const
type: intloc: sp+16
type: intloc: sp+16
type: intloc: sp+24
type: intloc: R2
type: intloc: R2
type: intloc: R1
type: intloc: R1
R2 = 4*aR1=b*bR2= R2*cR1=R1-R2
MOV R2,(sp+8)SAL R2,2MOV R1,(sp+16)MUL R1,(sp+16)MUL R2,(sp+24)SUB R1,R2
LexicalAnalysi
s
Syntax Analysi
s
Sem.Analysi
s
IntermediateRepresentation
AssemblyCode
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The Symbol Table
• A data structure that holds attributes for each identifier, and provides fast access to them.
• Example: location in memory, type, scope. • The table is built during the compilation process.
– E.g., the lexical analysis cannot tell what the type is, the location in memory is discovered only during code generation, etc.
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Error Checking
• An important part of the process. • Done at each stage.
• Lexical analysis: illegal tokens• Syntax analysis: illegal syntax • Semantic analysis: incompatible types, undefined
variables, …
• Each phase tries to recover and proceed with compilation (why?)– Divergence is a challenge
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Errors in lexical analysis
pi = 3.141.562
txt
Illegal token
pi = 3oranges
txt
Illegal token
pi = oranges3
txt
<ID,”pi”>, <EQ>, <ID,”oranges3”>
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Error detection: type checking
x = 4*a*”oranges”
txt
‘4’ ‘a’
“oranges”MULT
MULT
type: intloc: sp+8
type: intloc: const
type: stringloc: const
type: intloc: R2
type: intloc: R2
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The Real Anatomy of a Compiler
Executable
code
exe
Source
text
txtLexicalAnalys
is
Sem.Analysi
s
Process text input
characters SyntaxAnalys
is
tokens AST
Intermediate code
generation
Annotated AST
Intermediate code
optimization
IR Codegeneratio
n
IR
Target code
optimization
Symbolic Instructions
Machine code
generation
Write executable output
MI
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Optimizations
• “Optimal code” is out of reach – many problems are undecidable or too expensive (NP-
complete)– Use approximation and/or heuristics – Must preserve correctness, should (mostly) improve
code, should run fast.
• Improvements in time, space, energy, etc. • This part takes most of the compilation time. • A major question: how much time should be
invested in optimization to make the code run faster. – Answer changes for the JIT setting.
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Optimization Examples
• Loop optimizations: invariants, unrolling, … • Peephole optimizations• Constant propagation
– Leverage compile-time information to save work at runtime (pre-computation)
• Dead code elimination– space
• …
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Modern Optimization Challenges
• Main challenge is to exploit modern platforms– Multicores– Vector instructions– Memory hierarchy– Is the code sent on the net (Java byte-code)?
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Machine code generation
• A major goal: determine location of variables. • Register allocation
– Optimal register assignment is NP-Complete– In practice, known heuristics perform well
• assign variables to memory locations• Instruction selection
– Convert IR to actual machine instructions
• Modern architectures– Multicores– Challenging memory hierarchies
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Compiler Construction Toolset
• Lexical analysis generators– lex
• Parser generators– yacc
• Syntax-directed translators• Dataflow analysis engines
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Summary
• A compiler is a program that translates code from source language to target language
• Compilers play a critical role– Bridge from programming languages to the machine– Many useful techniques and algorithms– Many useful tools (e.g., lexer/parser generators)
• Compiler are constructed from modular phases– Reusable – Debug-able, understandable. – Different front/back ends
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Theory of Compilation
Lexical Analysis
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You are here
Executable
code
exe
Source
text
txt
Compiler
LexicalAnalysi
s
Syntax Analysi
s
Parsing
Semantic
Analysis
Inter.Rep.
(IR)
Code
Gen.
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From characters to tokens
• What is a token?– Roughly – a “word” in the source language– Identifiers– Values– Language keywords– (Really - anything that should appear in the input to
syntax analysis)
• Technically– A token is a pair of (kind,value)
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Example: kinds of tokens
Type Examples
Identifier x, y, z, foo, bar
NUM 42
FLOATNUM 3.141592654
STRING “so long, and thanks for all the fish”
LPAREN (
RPAREN )
IF if
…
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Strings with special handling
Type Examples
Comments /* Ceci n'est pas un commentaire */
Preprocessor directives #include<foo.h>
Macros #define THE_ANSWER 42
White spaces \t \n
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The Terminology
• Lexeme (aka symbol): a series of letters separated from the rest of the program according to a convention (space, semi-column, comma, etc.)
• Pattern: a rule specifying a set of strings.Example: “an identifier is a string that starts with a letter and continues with letters and digits”.
• Token: a pair of (pattern, attributes)
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From characters to tokens
x = b*b – 4*a*c
txt
<ID,”x”> <EQ> <ID,”b”> <MULT> <ID,”b”> <MINUS>
<INT,4> <MULT> <ID,”a”> <MULT> <ID,”c”>
Token Stream
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Errors in lexical analysis
pi = 3.141.562
txt
Illegal token
pi = 3oranges
txt
Illegal token
pi = oranges3
txt
<ID,”pi”>, <EQ>, <ID,”oranges3”>
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Error Handling
• Many errors cannot be identified at this stage. • For example: “fi (a==f(x))”. Should “fi” be “if”? Or is it a
routine name? – We will discover this later in the analysis. – At this point, we just create an identifier token.
• But sometimes the lexeme does not satisfy any pattern. What can we do?
• Easiest: eliminate letters until the beginning of a legitimate lexeme.
• Other alternatives: eliminate one letter, add one letter, replace one letter, replace order of two adjacent letteres, etc.
• The goal: allow the compilation to continue. • The problem: errors that spread all over.
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How can we define tokens?
• Keywords – easy!– if, then, else, for, while, …
• We need a precise, formal description (that a machine can understand) of things like: – Identifiers– Numerical Values– Strings
• Solution: regular expressions.
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Regular Expressions over ΣBasic Patterns Matching
Φ No string
ε The empty string
a A single letter ‘a’ in Σ
Repetition Operators
R* Zero or more occurrences of R
R+ One or more occurrences of R
Composition Operators
R1|R2 Either an R1 or R2
R1R2 An R1 followed by R2
Grouping
(R) R itself
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Examples
• ab*|cd? = • (a|b)* =• (0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9)* =
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Simplifications
• Precedence: * is of highest priority, then concatenation, and then unification. a | (b (c)*) = a | bc*
• ‘R?’ stands for R or ε.• ‘.’ stands for any character in Σ• [xyz] for letters x,y,z in Σ means (x|y|z)• Use hyphen to denote a range
– letter = a-z | A-Z– digit = 0-9
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More Simplifications
• Assign names for expressions:– letter = a | b | … | z | A | B | … | Z– letter_ = letter | _– digit = 0 | 1 | 2 | … | 9– id = letter_ (letter_ | digit)*
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An Example
• A number is
( 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 )+
( | . ( 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 )+
( | E ( 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 )+
) )
• Using simplifications it is: – digit = 0-9– digits = digit+– number = digits (Є | .digits (Є | e (Є|+|-) digits ) )
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Additional (Practical) Examples
• if = if• then = then• relop = < | > | <= | >= | = | <>
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Escape characters
• What is the expression for one or more ‘+’ symbols coming after the letter ‘C’ ?– C++ won’t work– C(\+)+ will
• backslash \ before an operator turns it to standard character
• \*, \?, \+, …
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Ambiguity
• Consider the two definitions: – if = if– id = letter_ (letter_ | digit)*
• The string “if” is valid for the pattern if and also for the pattern id… so what should it be?
• How about the string “iffy”? – Is it an identifier? Or an “if” followed by the identifier
“fy”?
• Convention:– Always find longest matching token– Break ties using order of definitions… first definition wins
(=> list rules for keywords before identifiers)
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Creating a lexical analyzer
• Input– List of token definitions (pattern name, regular-
expression)– String to be analyzed
• Output– List of tokens
• How do we build an analyzer?
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Character classification
#define is_end_of_input(ch) ((ch) == ‘\0’);#define is_uc_letter(ch) (‘A’<= (ch) && (ch) <= ‘Z’)#define is_lc_letter(ch) (‘a’<= (ch) && (ch) <= ‘z’)#define is_letter(ch) (is_uc_letter(ch) || is_lc_letter(ch))#define is_digit(ch) (‘0’<= (ch) && (ch) <= ‘9’)…
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Main reading routine
void get_next_token() {do { char c = getchar(); switch(c) { case is_letter(c) : return recognize_identifier(c); case is_digit(c) : return recognize_number(c); …} while (c != EOF);
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But we have a much better way!
• Generate a lexical analyzer automatically from token definitions
• Main idea– Use finite-state automata to match regular expressions
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Overview
• Produce an finite-state automaton from a regular expression (automatically).
• Simulate a final-state automaton on a computer (automatically).
• Immediately obtain a lexical analyzer.
• Let’s recall material from the Automata course…
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Reminder: Finite-State Automaton
• Deterministic automaton• M = (,Q,,q0,F)
– - alphabet– Q – finite set of state– q0 Q – initial state
– F Q – final states– δ : Q Q - transition function
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Reminder: Finite-State Automaton
• Non-Deterministic automaton• M = (,Q,,q0,F)
– - alphabet– Q – finite set of state– q0 Q – initial state
– F Q – final states
– δ : Q ( {}) → 2Q - transition function
• Possible -transitions• For a word w, M can reach a number of states or
get stuck. If some reached state is final, M accepts w.
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Identifying Patterns = Lexical Analysis
• Step 1: remove shortcuts and obtain pure regular
expressions R1…Rm for the m patterns.
• Step 2: construct an NFA Mi for each regular
expression Ri
• Step 3: combine all Mi into a single NFA• Step 4: convert the NFA into a DFA• DFA is ready to identify the patterns.
• Ambiguity resolution: prefer longest accepting word
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A Comment
• In the Automata course you study of automata as identifiers only: is input in the language or not?
• But when you run an automaton on an input there is no reason to not gather information along the way. – E.g., letters read from input so far, line number in the
code, etc.
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Building NFA: Basic constructs
R =
R =
R = a a
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Building NFA: Composition
R = R1 | R2 M1
M2
R = R1R2
M1 M2
The starting and final states in the original automata become regular states after the composition
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Building NFA: Repetition
R = R1*
M1
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Use of Automata
• Naïve approach: try each automaton separately• Given a word w:
– Try M1(w)– Try M2(w)– …– Try Mn(w)
• Requires resetting after every attempt.• A more efficient method: combine all automata
into one.
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Combine automata: an example.
Combine a, abb, a*b+, abab.
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1 2aa
3 a 4 b 5 b 6abb
7 8b a*b+ba
9 a 10 b 11 a 12 b 13
abab
0
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Ambiguity resolution
• Longest word• Tie-breaker based on order of rules when words
have same length. – Namely, if an accepting state has two labels then we can
select one of them according to the rule priorities.
• Recipe– Turn NFA to DFA– Run until stuck, remember last accepting state, this is
the token to be returned.
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Now let’s return to the previous example…
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Corresponding DFA
0 1 3 7 9
8
7
b
a
a
2 4 7 10
a
bb
6 8
5 8 11b
12 13a b
b
abba*b+a*b+
a*b+
abab
a
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Examples
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0 1 3 7 9
8
7
b
a
a2 4 7
10
a
bb
6 8
5 8 11b 12 13a b
b
abba*b+a*b+
a*b+
abab
a
abaa: gets stuck after aba in state 12, backs up to state (5 8 11) pattern is a*b+, token is ababba: stops after second b in (6 8), token is abb because it comes first in spec
bb
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Summary of Construction
• Developer describes the tokens as regular expressions (and decides which attributes are saved for each token).
• The regular expressions are turned into a deterministic automata (a transition table) that describes the expressions and specifies which attributes to keep.
• The lexical analyzer simulates the run of an automata with the given transition table on any input string.
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Good News• All of this construction is done automatically for
you by common tools. • Lex automatically generates a lexical analyzer
from declaration file.• Advantages: a short declaration, easily verified,
easily modified and maintained.
lexDeclaration file
LexicalAnalysi
s
characters tokens
Intuitively: • Lex builds a DFA table,• The analyzer simulates
the DFA on a given input.
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Summary
• Lexical analyzer– Turns character stream into token stream– Tokens defined using regular expressions– Regular expressions -> NFA -> DFA construction for
identifying tokens– Automated constructions of lexical analyzer using lex
Lex will be presented in the exercise.
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Coming up next time
• Syntax analysis