Syntax and Type Analysis Lecture Compilers SS 2009 Dr.-Ing. Ina Schaefer

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Syntax and Type Analysis

Lecture Compilers SS 2009

Dr.-Ing. Ina Schaefer

Software Technology Group TU Kaiserslautern

Ina Schaefer Syntax and Type Analysis 1

Educational Objectives

• Tasks of Different Syntax Analysis Phases

• Interaction of Syntax Analysis Phases

• Specification Techniques for Syntax Analysis

• Generation Techniques

• Usage of Tools

• Lexical Analysis

• Context-free Analysis (Parsing)

• Context-sensitive Analysis

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Introduction to Syntax and Type Analysis

Syntax Analysis

Tasks of Syntax Analysis

• Check if Input is syntactically correct

• Dependant on Result:

! Error Message

! Generation of appropriate Data Structure for subsequent processing

Syntax Analysis Phases

Lexical Analysis:

String → Token Stream (or Symbol String) Context-free Analysis:

Token Stream → Tree

Context-sensitive Analysis:

Tree → Tree with Cross References

Scanner Source Code

as String

Token Stream

Parser

Name and Type Analysis Syntax

Tree

Attributed Syntax Tree

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Reasons for Separation of Phases

• Lexical and Context-free Analysis

! Reduced load for context-free analysis, e.g. whitespaces are not required for context-free analysis

• Context-free and Context-sensitive Analysis

! Context-Sensitive Analysis uses tree structure instead of token stream

! Advantages for construction of target data structure

• For Both Cases

! Increased efficiency

! Natural process (cmp. natural language)

! More appropriate tool support

Lexical Analysis

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Lexical Analysis

Tasks

• Break input character string into symbol stream (or token stream) wrt. language definition

• Classify symbols into classes

• Representation of symbols

! Hashing of identifieres

! Conversion of constants

• Elimination of

! whitespaces (spaces, comments...)

! external constructs (compiler directives...)

Lexical Analysis

Lexical Analysis (2)

Terminology

• Symbol: a word over an alphabet of characters (often with additional information, e.g. token class, encoding, position..)

• Symbol Class: a set of tokens (identifier, constants, ...);

correspond to terminal symbols of a context-free grammar

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Lexical Analysis

Lexical Analysis: Example

Input Line 23:

␣␣if␣(␣A␣<=␣3.14␣)␣␣␣B␣=␣B--

33

© A. Poetzsch-Heffter, TU Kaiserslautern 25.04.2007

Beispiel: (lexikalische Analyse)

Zeile 23 der Eingabedatei:

Ergebnis der lexikalischen Analyse:

if( A <= 3.14) B = B---

Symbolklasse String Codierung Zeile:Spalte IF “if“ 23:3 OPAR “(“ 23:5 ID “A“ 72 23:7 RELOP “<=“ 4 23:9 FLOATCONST “3.14“ 3,14 23:12 CPAR “)“ 23:16 ID “B“ 84 23:20 ...

Hashcode des Identifiers Wert der

Konstanten

Codierung für Operator <=

Symbolinformation

Token

Class String Encoding Col:Row

Value of

Constant Hash Code

of Identifier Encoding of Operator Token

Information

33

Beispiel: (lexikalische Analyse)

Zeile 23 der Eingabedatei:

Ergebnis der lexikalischen Analyse:

if( A <= 3.14) B = B---

Symbolklasse String Codierung Zeile:Spalte IF “if“ 23:3 OPAR “(“ 23:5 ID “A“ 72 23:7 RELOP “<=“ 4 23:9 FLOATCONST “3.14“ 3,14 23:12 CPAR “)“ 23:16 ID “B“ 84 23:20 ...

Hashcode des Identifiers Wert der

Konstanten

Codierung für Operator <=

Symbolinformation

Input Line 23:

Result of Lexical Analysis:

Lexical Analysis Specification of Scanners

Specification

The Specification of the Lexical Analysis is a Part of the Programming Language Specification.

The two Parts of Lexical Analysis Specification:

• Scanning Algorithm (often only implicit)

• Specification of Symbols and Symbol Classes

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Examples: Scanning

1. Statement in C B␣=␣B␣---␣A;

Problem: Separation ( - - and - are symbols) Solution: Longest symbol is chosen, i.e B␣=␣B␣--␣-␣A;

2. Java Fragment

class␣public␣{␣public␣m()␣{...}␣}

Problem: Ambiguity (key word, identifier) Solution: Precedence Rules

Standard Scan-Alogrithm (Concept)

Scaning is often implemented as Co-Routine:

• State is remainder of input

• Co-Routine returns next symbol

• In error cases, co-routine returns the UNDEF symbol and updates the input

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Standard Scan-Alogrithm (Pseudo Code)

String left_input : = input;

Symbol nextSymbol() {

Symbol curSymbol := longestSymbolPrefix(left_input);

left_input:= cut(curSymbol, left_input);

return curSymbol;

}

where cut is defined as

• if curToken "= UNDEF, curToken is removed from left_input

• else left_input remains unchanged.

Standard Scan-Alogrithm (2)

longestSymbolPrefix(String egr) {

\\ length(egr) > 0 int curLength := 0;

String curPrefix := prefix(curLength,egr);

Symbol longestSymbol := UNDEF;

while (curLength <= length(egr) && isSymbolPrefix(curPrefix)) if (isSymbol(curPrefix) {

longestSymbol := curPrefix;

}

curLength++;

curPrefix:=prefix(curLength,egr);

}

return longestSymbol;

}

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Standard Scan-Algorithm (3)

Only Predicates have to be defined:

• isSymbolPrefix: String → bool

• isSymbol: String→ bool Remarks:

• Standard Scan-Algorithm is used in many modern languages, but not e.g. in FORTRAN because blanks are not special except in literal symbols, e.g.

! DO 7 I = 1.25 →DO 7 I is an identifier.

! DO 7 I = 1,25 →DO is a keyword.

• Error Cases are not handled

• Complete Realisation of longestSymbolPrefix is discussed later.

Specification of Symbols

• Symbols are specified by regular expressions.

• Symbols Classes are described informally.

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Regular Expressions

Let Σ be an alphabet, i.e. an non-empty set of characters. Σ^∗ is the set of all words overΣ, ! is the empty word.

Definition (Regular Expressions, Regular Languages)

• ! is a regular expression (r.e.) and denotes the language L = {!}.

• Each a ∈ Σ is a r.e. and denotes the language L= {a}.

• Let r and s be two r.e. defining the languages R and S, resp.

Then the following are r.e. and define the corresponding language L:

! (r|s) withL = R∪S Union

! rs withL = {vw |v ∈R,w ∈S} Concatenation

! r^∗ with{v₁. . .v_n|v_i ∈R,0 ≤ i ≤ n} Kleene Star

The languageL ⊆ Σ^∗ is called regular iff there exists r.e.r defining L.

Regular Expressions (2)

Remarks:

• L= ∅ is not regular according to the definition, but is often considered regular.

• Other Operators, e.g. +, ?, ., [] can be defined using the basic operators, e.g.

! r⁺ ≡ (rr^∗) ≡ r^∗ \ {!}

! [aBd] ≡a|B|d

! [a −g]≡ a|b|c|d|e|f|g

Caution: Regular Expressions only define valid symbols and do not specify the program or translation units of a programming language.

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Lexical Analysis Implementation of Scanners

Implementation of Scanners

Scanner Generator

Sequence of Regular Expressions and Actions

(Input Language of Scanner Generator)

Scanner Program

(mostly in Programming Language)

Scanner Generator: JFlex

• Typical Use of JFlex:

java -jar JFlex.jar Example.jflex javac Yylex.java

Actions are written in Java

• Examples :

1. Regular Expression in JFlex [a-zA-Z_0-9] [a-zA-Z_0-9] * 2. JFlex Input with Abbreviations

ZI = [0-9]

BU = [a-zA-Z_]

BUZI = [a-zA-Z_0-9]

%%

{BU}{BUZI}* { anAction(); }

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A complete JFlex Example

enum Token { DO, DOUBLE, IDENT, FLOATCONST, STRING;}

%%

%type Token // declare token type ZI = [0-9]

BU = [a-zA-Z_]

BUZI = [a-zA-Z_0-9]

ZE = [a-zA-Z_0-9!?\]\[\.\t...]

%%[ \t]* /* whitespace */

"do" { return Token.DO; }

"double" { return Token.DOUBLE; } {BU}{BUZI}* { return Token.IDENT; }

{ZI}+\.{ZI}+ { return Token.FLOATCONST; }

\"({ZE}|\\\")*\" { return Token.STRING; }

Scanner Generators

• Scanner Generation uses the Equivalence between

! Regular Expressions

! Non-determininstic finite automata (NFA)

! Deterministic finite automata (DFA)

• Construction Methods is based in two steps:

! Regular Expressions →NFA

! NFA →DFA

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Definition of NFA

Definition (Non-deterministic Finite Automaton)

A non-deterministic finite automaton is defined as a 5-tuple M = (Σ,Q,∆,q0,F)

where

• Σ is the input alphabet

• Q is the set of states

• q₀ ∈ Q is the initial state

• F ⊆ Q is the set of final states

• ∆ ⊆ Q ×Σ ∪{!}× Q is the transition relation.

Regular Expressions → NFA

Principle: For each regular sub-expression, construct NFA with one start and end state that accepts the same language.

1. Schritt: Reguläre Ausdrücke ! NEA Übersetzungsschema:

• !

• a

• (r|s)

• (rs)

• r*

Prinzip: Konstruiere für jeden regulären Teilausdruck NEA mit genau einem Start- und Endzustand, der die gleiche Sprache akzeptiert.

s

₀

f

₀

s

₀

a

• a

• (r|s)

• (rs)

• r*

Prinzip: Konstruiere für jeden regulären Teilausdruck NEA mit genau einem Start- und Endzustand, der die gleiche Sprache akzeptiert.

s₀ f₀

s₀ a

s₀ f₀

! s₁ R f₁

s₂ S f₂

!

! !

s₁ R f₁ ! s₂ S f₂

s₁ R f₁ ! f₀

s₀ !

!

© A. Poetzsch-Heffter, TU Kaiserslautern 43 25.04.2007

1. Schritt: Reguläre Ausdrücke ! NEA Übersetzungsschema:

• !

• a

• (r|s)

• (rs)

• r*

Prinzip: Konstruiere für jeden regulären Teilausdruck NEA mit genau einem Start- und Endzustand, der die gleiche Sprache akzeptiert.

s₀ f₀

s₀

a

s₀ f₀

! s₁ R f₁

s₂ S f₂

!

! !

s₁ R f₁ ! s₂ S f₂

s₁ R f₁ ! f₀

s₀ !

!

43

1. Schritt: Reguläre Ausdrücke ! NEA Übersetzungsschema:

•

!

• a

• (r|s)

• (rs)

• r*

Prinzip: Konstruiere für jeden regulären Teilausdruck NEA mit genau einem Start- und Endzustand, der die gleiche Sprache akzeptiert.

s

Übersetzung am Beispiel von Folie 41: s5s6s7s8s9s10s11

s2s4 s13s12 s17s16s14s15

d elbuods3o

AB BUZI BU ZI ZI. ZI

ZI s19

“

s20ZE s21 s22s23s24\

s26

“

s25

“

!! !

!!

! ! !

! !

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!-closure

Function closure computes the !-closure of a set of states s1, . . . ,sn.

Definition (!-closure)

For an NFA M = (Σ,Q,∆,q₀,F) and a state q ∈ Q, the !-closure of q is defined by

!-closure(q) ={p ∈ Q|p reachable from q via!-transitions} For S ⊆ Q, the !-closure of S is defined by

!-closure(S) = !

s∈S

!-closure(s)

Longest Symbol Prefix with NFA

longestSymbolPrefix(char[] egr) { // length(egr) > 0

StateSet curState : = closure( {s0} );

int curLength := 0;

int symbolLength := undef;

while (curLength <= length(egr) && !isEmptySet(curState) ) if (contains(curState,finalState)) {

symbolLength := curLength;

}

curLength++;

curState:=closure(successor(curState,egr[curLength]));

}

return symbol(prefix(egr,symbolLength));

}

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Longest Symbol Prefix with NFA (2)

Remark:

Problem of Ambiguity is not solved yet:

If there are more than one token matching the longest input prefix, one of these tokens is returned by the function symbol.

NFA → DFA

Principle:

For each NFA, a DFA can be constructed that accepts the same language. (In general, this does not hold for NFA with output.) Properties of DFA:

• No !-transitions.

• Transitions are determined by function.

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NFA → DFA (2)

Definition (Deterministic Finite State Automaton)

A deterministic finite automaton is defined as a 5-tuple

M = (Σ,Q,∆,q₀,F) where

• Σ is the input alphabet

• Q is the set of states

• q₀ ∈ Q is the initial state

• F ⊆ Q is the set of final states

• ∆ : Q ×Σ → Q is the transition function.

NFA → DFA (3)

Construction: (according to John Myhill)

• The States of the DFA are subsets of NFA states

(powerset construction). Subsets of finite sets are also finite.

• The start state of the DFA is the!-closure of theNFA start state

• The final states of the DFA are the sets of states that contain an NFA final state.

• The successor state of a state S in the DFA under input ais obtained by

! computing all successors p of q ∈ S undera in the NFA

! and adding the!-closure of p

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NFA → DFA (4)

• If working with character classes (e.g. [a-f]), characters and character classes at outgoing transitions must be disjoint.

• Completion of automaton for error handling:

! Insert additional (final) state (nT)

! For each state, add a transition for each character for which no outgoing transition exists to the nonToken state.

NFA → DFA (5)

Definition (DFA for NFA)

Let M = (Σ,Q,∆,q₀,F) be a NFA. Then, the DFA M^# corresponding to the NFA M is defined as M^# = (Σ,Q^#,∆^#,q₀^#,F^#) where

• the set of states is Q^# ⊆ P(Q), power set of Q

• the initial state q₀^# is the !-closure of q₀

• the final states are F^# = {S ⊆ Q |S ∩F "= ∅}

• ∆^#(S,a) = !-closure({p|(q,a,p) ∈ ∆,q ∈ S}) for all a ∈ Σ.

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Example: DFA

s0,1,2,5,12,14,18

s1 LZ, TAB

LZ, TAB s3,6,13

s4,7,13

s8,13 s 13 BU\{d}d

e l b u o

BUZI\{b} BUZI\{u} BUZI\{o} BUZI

BUZI\{l}

BUZI\{e}

BUZI s17s16s15

ZI ZI.ZI

ZI s19,20,22,25 s19,20,21,22,25 s 26 s19,20,21,22,23,25s19,20,22,24,25,26

“

s9,13

s10,13

s11,13 ZE \

“ “

^\

ZE

“ “

\ZEZE \

ksWg. Übersichtlichkeit Kanten zu ks nur angedeutet.

Transitions to nT sketched.

nT

Longest Symbol Prefix with DFA

longestSymbolPrefix(char[] egr) { // length(egr) > 0

State curState : = start_state;

int curLength := 0;

int symbolLength := undef;

while (curLength <= length(egr) && curState != nT) if ( curState is FinalState) {

tokenLength := curLength;

}

curLength++;

curState := successor(curState,egr[curLength]));

}

return symbol(prefix(egr,tokenLength));

}

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Longest Symbol Prefix with DFA (2)

Remarks:

• Computation of closure at construction time, not at runtime.

(Principle: Do as much statically as you can!)

• Problem of ambiguity still not solved.

Most scanner generators use ordering of rules in case of conflicts.

Longest Token Prefix with DFA (3)

Implementation Aspects:

• Constructed DFA can be minimized.

• Input buffering is important: often use of cyclic arrays (caution with maximal token length, e.g. in case of comments)

• Encode DFA in table

• Choose suitable partitioning of alphabet in order to reduce number of transitions (i.e. size of table)

• Interface with Parser: usually parser asks proactively for next token (co-routines)

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