chapter 3_syntax analysis.pptx

8/17/2019 Chapter 3_Syntax analysis.pptx

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Contents (Session-1)

ntro!u"tionContext-#ree $rammar%eri&ationParse 'reeAmbi$uityesol&in$ Ambi$uity

mme!iate n!ire"t *e#t e"ursionEliminatin$ mme!iate n!ire"t *e#t e"ursion

*e#t +a"torin$,on-Context +ree *an$ua$e Constru"ts


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Abstra"t representations o# the input pro$ram "oul! be

abstract-syntax tree/parse tree . symbol tableinterme!iate "o!eob/e"t "o!e

Syntax analysis is !one by the parser0Pro!u"es a parse tree #rom whi"h interme!iate "o!e "an be

$enerate!By !ete"tin$ whether the pro$ram is written #ollowin$ the

$rammar rules0eports syntax errors attempts error "orre"tion an!

re"o&ery

Colle"ts in#ormation into symbol tables

ntro!u"tion


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Parsers "an be 'op-!own or Bottom-up

ntro!u"tion2

Sour"e

pro$ram

*exi"al

analyzer

toen

e4uest#or toen

parser

est o##ront en!

Symboltable

nt0

"o!e

Parse

tree

Error


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BNF (Backus Normal Form or Backus–Naur Form) a

notation te"hni4ues #or "ontext-#ree $rammars o#tenuse! to !es"ribe the syntax o# lan$ua$es use! in"omputin$as many extensions an! &ariants

Extended Backus–Naur orm (EB,+) !ugmented Backus–Naur orm (AB,+)0A B,+ spe"i8"ation is a set o# !eri&ation rules written assymbol@ ::= expression

B,+ #or &ali! arithmeti" expression

expr@ ::= expr@ op@ expr@expr@ ::= ( expr@ )

expr@ ::= - expr@

expr@ ::= i!

op@ ::= . 9 - 9 ; 9 <

Context +ree 5rammars(C+5)2


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A se4uen"e o# repla"ements o# non-terminalsymbols to obtain strin$s


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%eri&ate strin$ :(i!.i!) #rom 51

E ⇒ -E ⇒ -(E) ⇒ -(E.E) ⇒ -(i!.E) ⇒ -(i!.i!) (*D%)

E ⇒ -E ⇒ -(E) ⇒ -(E.E) ⇒ -(E.i!) ⇒ -(i!.i!) (D%) At ea"h !eri&ation step we "an "hoose any o# the non-

terminal in the sentential #orm o# 5 #or the repla"ement0

# we always "hoose the le#t-most non-terminal in ea"h!eri&ation step this !eri&ation is "alle! as left-mostderivation(LM!0

# we always "hoose the ri$ht-most non-terminal in ea"h!eri&ation step this !eri&ation is "alle! as ri"#t-mostderivation($M!0

%eri&ation2


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A parse tree "an be seen as a $raphi"alrepresentation o# a !eri&ationnner no!es o# a parse tree are non-terminal

symbols0 'he lea&es o# a parse tree are terminal symbols0

Parse 'ree

E ⇒ -E EE-

E

E

EE

E

.

-

( )

E

E

E-

( )

E

E

i!

E

E

E .

-

( )

i!

E

E

E

EE .

-

( )

i!

⇒ -(E) ⇒ -(E.E)

⇒ -(i!.E) ⇒ -(i!.i!)


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An ambi$uous $rammar is one that pro!u"esmore than one *D% or more than one D% #orthe same senten"e0E ⇒ E.E

⇒ i!.E⇒ i!.E;E

⇒ i!.i!;E⇒ i!.i!;i!

Ambi$uity

E

E .

i! E

E

; E

i! i!

E ⇒ E;E⇒ E.E;E

⇒ i!.E;E⇒ i!.i!;E⇒ i!.i!;i!

E

i!

E .

i!

i!

E

E

; E


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+or the most parsers the $rammar must beunambi$uous0

# a $rammar unambi$uous $rammar then there areuni4ue sele"tion o# the parse tree #or a senten"e=e shoul! eliminate the ambi$uity in the $rammar

!urin$ the !esi$n phase o# the "ompiler0

An unambi$uous $rammar shoul! be written toeliminate the ambi$uity0=e ha&e to pre#er one o# the parse trees o# a

senten"e ($enerate! by an ambi$uous $rammar)to !isambi$uate that $rammar to restri"t to this"hoi"e0

Ambi$uity2


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'ption % a!! a meta-rule e0$0 pre"e!en"e an!

asso"iati&ity rules+or example Helse asso"iates with "losest pre&ious ifIwors eeps ori$inal $rammar inta"ta! ho" an! in#ormal

'ption & rewrite the $rammar to resol&e ambi$uityexpli"itlystmt → matchedstmt $ unmatchedstmt

matchedstmt → if expr then matchedstmt else matchedstmt $

otherstmtsunmatchedstmt → if expr then stmt $

if expr then matchedstmt else unmatchedstmt

#ormal no a!!itional rules beyon! syntaxsometimes obs"ures ori$inal $rammar

esol&in$ Ambi$uity


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'ption ) re!esi$n the lan$ua$e to remo&ethe ambi$uity

Stmt ::= ... |

if Expr then Stmt end |

if Expr then Stmt else Stmt end

#ormal "lear ele$ant

allows se4uen"e o#Stmts

inthen

an!else

bran"hes no > ? nee!e!extra end re4uire! #or e&ery if

esol&in$ Ambi$uity


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A $rammar is left recursive i# it has a non-

terminal A su"h that there is a !eri&ation0

A ⇒ Aα #or some strin$ α

'op-!own parsin$ te"hni4ues cannot han!le le#t-re"ursi&e $rammars0

So we ha&e to "on&ert our le#t-re"ursi&e $rammarinto an e4ui&alent $rammar whi"h is not le#t-re"ursi&e0

'wo types o# le#t-re"ursionimmediate left-recursion - appear in a sin$le step o# the

!eri&ation ()%ndirect left-recursion - appear in more than one step o# the

!eri&ation0

*e#t e"ursion


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Eliminatin$ mme!iate *e#t e"ursion

A → A α 9 β where β !oes not start with A⇓ eliminate imme!iate le#t

re"ursion

A → β AJ

AJ → α AJ 9 ε

A → A α1 9 000 9 A αm 9 β1 9 000 9 βn where β1 000 βn !o

not start with A

⇓ eliminate imme!iate le#t re"ursionA → β1 AJ 9 000 9 βn AJ

AJ

→ α1 AJ

9 000 9 αm AJ

9 ε an e4ui&alent $rammar

n $eneral

A → β AJ 9 β

AJ → α AJ 9 α


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emo&e le#t re"ursion #rom the $rammarbelowE → E.' 9 '

' → ';+ 9 +

+ → i! 9 (E)Answer

E → ' EJ

EJ → .' EJ 9 ε ' → + 'J

'J → ;+ 'J 9 ε+ → i! 9 (E)

Eliminatin$ *e#t e"ursion2


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A $rammar "annot be imme!iately le#t-re"ursi&ebut it still "an be le#t-re"ursi&e0

By /ust eliminatin$ the imme!iate le#t-re"ursionwe may not $et a $rammar whi"h is not le#t-

re"ursi&e0S → Aa 9 bA → S" 9 !'his $rammar is not imme!iately le#t-

re"ursi&e

but it is still le#t-re"ursi&e0

S ⇒ Aa ⇒ S"a orA ⇒ S" ⇒ Aa" "auses to a le#t-re"ursion

So we ha&e to eliminate all le#t-re"ursions #rom our

$rammar

n!ire"t *e#t-e"ursion


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Arran$e non-terminals in some or!er A1 000 An

we will remo&e in!ire"t le#t re"ursion by"onstru"tin$ an e4ui&alent $rammar 5J su"h that- i# Ai → A /a is any pro!u"tion o# 5J then i /

+or ea"h non-terminal in turn !o+or ea"h terminal *i su"h that %+ +i an! we ha&e a

pro!u"tion rule o# the #orm Ai → A /α where the A /pro!u"tions are A / → β1 9 29Bn !oepla"e the pro!u"tion rule Ai → A / α with the rule Ai

→ β1α 9 29Bnα Eliminate any imme!iate le#t re"ursion amon$ the

pro!u"tions αβ1

Eliminatin$ n!ire"t *e#t-e"ursion


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xample %

S → Aa 9 bA → A" 9 S! 9 #

- r!er o# non-terminals S 6 A1 A 6 AFA1 → AF a 9 bAF → AF " 9 A1 ! 9 #

'he only pro!u"tion with /i is AF → A1 !#or A- epla"e it with AF → AF a! 9 b!

AF → AF " 9 AF a! 9 b! 9 #

- Eliminate the imme!iate le#t-re"ursion in AAF → b!AJ9b!AJAJ → "AJ 9 a!AJ9 ε

So the resultin$ e4ui&alent $rammar whi"h is not le#t-re"ursi&e isS → Aa 9 bA → b!AJ 9 #AJ

AJ → "AJ 9 a!AJ 9 ε

Eliminatin$ n!ire"t *e#t-e"ursion2


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Example F A1 → A2 A3 A2 → A3 A1 | b

A3 → A1 A1 | a

Replace A3 → A1 A1 by A3 → A2 A3 A1

and then replace this by

A3 → A3 A1 A3 A1 and A3 → b A3 A1Eliminating direct left recursion in the above,

gives: A3 → a | b A3 A1

! → A1 A3 A1 | ε

'he resultin$ $rammar is then A1 → A2 A3 A2 → A3 A1 | b

A3 → a | b A3 A1

! → A1 A3 A1 | ε

Eliminatin$ n!ire"t *e#t-e"ursion2


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A pre!i"ti&e parser (a top-!own parser without

ba"tra"in$) insists that the $rammar must beleft-factored0

stmt → if expr then stmt else stmt $

if expr then stmt

when we see if we "annot now whi"hpro!u"tion rule to "hoose to re-write stmt in the!eri&ation0

n $eneral

A → αβ1 9 αβF where α is non-empty an! the 8rstsymbols o# β1 an! βF (i# they ha&e one)are !iLerent

when pro"essin$ α we "annot now whether to expan!

A to αβ1 or A to αβF

*e#t +a"torin$


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But i# we re-write the $rammar as #ollows

A → αAJ AJ → β1 9 βF so we "an imme!iately expan! A to αAJ

*e#t +a"torin$ : Al$orithm

+or ea"h non-terminal A with two or morealternati&es (pro!u"tion rules) with a "ommonnon-empty pre8x let say

A → αβ1 9 000 9 αβn 9 γ 1 9 000 9 γ m "on&ert it intoA → αAJ 9 γ 1 9 000 9 γ m AJ → β1 9 000 9 βn

*e#t +a"torin$2


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'here are some lan$ua$e "onstru"tions in the

pro$rammin$ lan$ua$es whi"h are not "ontext-#ree0 'his means that we "annot write a "ontext-#ree$rammar #or these "onstru"tions0

*1 6 > ω"ω 9 ω is in (a9b);? is not "ontext-#ree!e"larin$ an i!enti8er an! "he"in$ whether it is!e"lare! or not later0 =e "annot !o this with a"ontext-#ree lan$ua$e0 =e nee! semanti" analyzer(whi"h is not "ontext-#ree)0

*F 6 >anbm"n!m 9 n≥1 an! m≥1 ? is not "ontext-#ree!e"larin$ two #un"tions (one with n parameters the

other one with m parameters) an! then "allin$ them

with a"tual parameters0

,on-Context +ree *an$ua$e Constru"ts


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Contents(Session-F)

'op %own Parsin$e"ursi&e-%es"ent Parsin$Pre!i"ti&e Parsere"ursi&e Pre!i"ti&e Parsin$

,on-e"ursi&e Pre!i"ti&e Parsin$**(1) Parser : Parser A"tionsConstru"tin$ **(1) - Parsin$ 'ables

Computin$ +S' an! +**= #un"tions**(1) 5rammarsProperties o# **(1) 5rammars


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'op-!own parsin$ in&ol&es "onstru"tin$ a parse tree #or

the input strin$ startin$ #rom the rootBasi"ally top-!own parsin$ "an be &iewe! as 8n!in$ a

le#tmost !eri&ation #or an input strin$0How it works? Start with the tree o# one no!e labele! with

the start symbol an! repeat the #ollowin$ steps until the #rin$eo# the parse tree mat"hes the input strin$10 At a no!e labele! A sele"t a pro!u"tion with A on its *S

an! #or ea"h symbol on its S "onstru"t the appropriate"hil!

F0 =hen a terminal is a!!e! to the #rin$e that !oesnMt mat"hthe input strin$ ba"tra"

30 +in! the next no!e to be expan!e!

! Minimize the number of backtracks as much as

possible

'op %own Parsin$


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'wo types o# top-!own parsin$

Recursiveescent "arsin#Ba"tra"in$ is nee!e! (# a "hoi"e o# a pro!u"tion rule

!oes not wor we ba"tra" to try other alternati&es0)t is a $eneral parsin$ te"hni4ue but not wi!ely use!

be"ause it is not e"ient"re$ictive "arsin#no ba"tra"in$ an! hen"e e"ientnee!s a spe"ial #orm o# $rammars (**(1) $rammars)0

'wo typesRecursive "re$ictive "arsin# is a spe"ial #orm o#&ecursive 'escent (arsing without ba"tra"in$0

%onRecursive &'able riven( (redictive (arser isalso nown as **(1) parser0

'op %own Parsin$2


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t tries to 8n! the le#t-most !eri&ation0

Ba"tra"in$ is nee!e!Example

S → aB"

B → b" 9 binput ab"

e"ursi&e-%es"ent Parsin$

A left-recursive "rammar "an "ause a

re"ursi&e-!es"ent parser e&en one withba"tra"in$ to $o into an in8nite loop0 'hat is when we try to expan! a non-terminal B

we may e&entually 8n! oursel&es a$ain tryin$

to expan! B without ha&in$ "onsume! any input0


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A $rammar a $rammar suitable #or pre!i"ti&e

eliminate le#t parsin$ (a **(1) $rammar) le#t re"ursion #a"tor no )*++ guarantee0

=hen re-writin$ a non-terminal in a !eri&ation step apre!i"ti&e parser "an uni4uely "hoose a pro!u"tionrule by /ust looin$ the "urrent symbol in the inputstrin$0

stmt → if 000000 9 while 000000 9

begin 000000 9

for 00000

owe&er e&en thou$h we eliminate the le#tre"ursion in the $rammar an! le#t #a"tor it it may not

be suitable #or pre!i"ti&e parsin$ (not **(1) $rammar)0

Pre!i"ti&e Parser

Note =hen we aretryin$ to write the non-terminal stmt we "an

uni4uely "hoose thepro!u"tion rule by /ustlooin$ the "urrenttoen0


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Pre!i"ti&e Parsin$ "an be re"ursi&e or non-re"ursi&e

n re"ursi&e pre!i"ti&e parsin$ ea"h non-terminal"orrespon!s to a pro"e!ure

"ase o# the "urrent toen >

NaJ - mat"h the "urrent toen with a an! mo&e to the next toenO

- "all NBJO

- mat"h the "urrent toen with b an! mo&e to the next toenO

NbJ - mat"h the "urrent toen with b an! mo&e to the next toenO

- "all NAJO

- "all NBJO

?

?

e"ursi&e Pre!i"ti&e Parsin$


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=hen to apply ε-pro!u"tions

A → aA 9 bB 9 l

# all other pro!u"tions #ail we shoul! apply an l-pro!u"tion0 +or example i# the "urrent toen is nota or b we may apply the ε-pro!u"tion0

Most correct choice) =e shoul! apply a l-pro!u"tion #or a non-terminal A when the "urrenttoen is in the follo. set o# A (whi"h terminals "an#ollow A in the sentential #orms)0

e"ursi&e Pre!i"ti&e Parsin$2


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e"ursi&e Pre!i"ti&e Parsin$2


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A non-re"ursi&e pre!i"ti&e parser "an be built

by maintainin$ a sta" expli"itly rather thanimpli"itly &ia re"ursi&e "alls

%onRecursive pre$ictive parsin# is a table-!ri&en top-!own parser0

,on-e"ursi&e Pre!i"ti&e Parsin$

Do!el o# a table-!ri&enpre!i"ti&e parser


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nput buLerour strin$ to be parse!0 =e will assume that its en! is mare!

with a spe"ial symbol Q0

utputa pro!u"tion rule representin$ a step o# the !eri&ation

se4uen"e (le#t-most !eri&ation) o# the strin$ in the input

buLer0

Sta""ontains the $rammar symbolsat the bottom o# the sta" there is a spe"ial en! marer

symbol Q0initially the sta" "ontains only the symbol Q an! the startin$

symbol S0when the sta" is emptie! (i0e0 only Q le#t in the sta") the

parsin$ is "omplete!0

Parsin$ tablea two-!imensional array DRAa

,on-e"ursi&e Pre!i"ti&e Parsin$2


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'he symbol at the top o# the sta" (say T) an! the

"urrent symbol in the input strin$ (say a) !eterminethe parser a"tion0 'here are #our possible parser a"tions0

10 # T an! a are Q parser halts (su""ess#ul"ompletion)

F0 # T an! a are the same terminal symbol (!iLerent#rom Q)

parser pops T #rom the sta" an! mo&es thenext symbol in the input buLer0

30 # T is a non-terminal parser loos at the parsin$ table entry DRTa0# DRTa hol!s a pro!u"tion rule T→ U1 UF000U itpops T #rom the sta" an! pushes UU-1000U1 into

the sta"0 'he parser also outputs the pro!u"tion

**(1) Parser : Parser A"tions


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**(1) Parser : Example1

S → aBa **(1) Parsin$B → bB 9 ε 'able

stack input outputQS abbaQ S → aBaQaBa abbaQ

QaB bbaQ B → bBQaBb bbaQ

QaB baQ B → bBQaBb baQQaB aQ B → εQa aQ

Q Q a""ept su""ess#ul "ompletion

a b $

S S → aBa

B B → ε B → bB*e will see

how to

construct parsin#

table +er,soon


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**(1) Parser : ExampleF

E → 'EJ

EJ → .'EJ 9 ε ' → +'J

'J → ;+'J 9 ε

+ → (E) 9 i!id + * ( ) $E E → TE’ E → TE’

E’ E’ → +TE’ E’ → ε E’ → ε

T T → FT’ T → FT’

T’ T’ → ε T’ → *FT’ T’ → ε T’ → εF F → id F → (E)

E is start symbol


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**(1) Parser : ExampleF

stack inputoutput

QE i!.i!Q E → 'EJ

QEJ ' i!.i!Q ' → +'J

QEJ 'J+ i!.i!Q + → i!

Q EJ 'Ji! i!.i!Q

Q EJ 'J .i!Q 'J → εQ EJ .i!Q EJ → .'EJ

Q EJ '. .i!Q

Q EJ ' i!Q ' → +'J

Q EJ 'J + i!Q + → i!Q EJ 'Ji! i!Q

Q EJ 'J Q 'J → ε

Q EJ Q EJ → ε

Q Q a""ept


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'wo #un"tions are use! in the "onstru"tion o#

**(1) parsin$ tables+S'+**=

F0$3( ! is a set o# the terminal symbols whi"ho""ur as 8rst symbols in strin$s !eri&e! #rom α where α is any strin$ o# $rammar symbols0i# α !eri&es to ε then ε is also in +S'(α) 0

F'LL'4(*! is the set o# the terminals whi"ho""ur imme!iately a#ter the non-terminal ! inthe strin$s !eri&e! #rom the startin$ symbol0

a terminal a is in +**=(A) i# S ⇒ αAaβ

Constru"tin$ **(1) Parsin$ 'ables

C S # S i


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10 # T is a terminal symbol then+S'(T)6>T?

F0 # T is ε then +S'(T)6>ε?

30 # T is a non-terminal symbol an! T → ε isa pro!u"tion rule then a!! ε in +S'(T)0

V0 # T is a non-terminal symbol an! T → U1 UF00Un is a pro!u"tion rule theni# a terminal a in +S'(Ui) an! ε is in all

+S'(U /) #or /61000i-1 then a is in+S'(T)0

Compute +S' #or a Strin$ T

C +S' # S i T


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xample

E → 'EJEJ → .'EJ 9 ε

' → +'J

'J → ;+'J9 ε+ → (E) 9 i!

From $ule %+S'(i!) 6 >i!?

From $ule &+S'(ε) 6 >ε?

From $ule ) and5+irst(+) 6 >( i!?+irst('J) 6 >; ε?

Compute +S' #or a Strin$ T2

+S'(E’) 6 >+ ε?+S'(E) 6 >(id?

't#ers

+S'('EJ) 6 >(i!?+S'(.'EJ ) 6 >.?+S'(+'J) 6 >(i!?+S'(;+'J) 6 >;?

+S'((E)) 6 >(?

C t +**= (# t i l )


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10 Q is in +**=(S) i# S is the start symbol

F0 *oo at the o""urren"e o# a nonWterminal on theS o# a pro!u"tion whi"h is #ollowe! bysomethin$

i# A → αBβ is a pro!u"tion rule then e&erythin$ in+S'(β) ex"ept ε is +**=(B)

30 *oo at B on the S that is not #ollowe! by

anythin$# ( A → αB is a pro!u"tion rule ) or ( A → αBβ is

a pro!u"tion rule an! ε is in +S'(β) ) thene&erythin$ in +**=(A) is in +**=(B)0

Compute +**= (#or non-terminals)


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xample

i0 E → 'EJii0 EJ → .'EJ 9 εiii0 ' → +'J

i&0 'J → ;+'J 9 ε

&0 + → (E) 9 i!+**=(E) 6 > Q ) ? be"ause.+rom 8rst rule +ollow (E) "ontains Q.+rom ule F +ollow(E) is 8rst(!) #rom the pro!u"tion + →

(E)

+**=(EJ) 6 > Q ) ? 20 ule 3+**=(') 6 > . ) Q ?. +rom ule F . is in +**=('). +rom ule 3 E&erythin$ in +ollow(E) is in +ollow(') sin"e

+irst(EJ) "ontains ε

+**=(+) 6 >. ; ) Q ? 2same reasonin$ as

Compute +**= (#or non-terminals)


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+or ea"h pro!u"tion rule A → α o# a $rammar510 #or ea"h terminal a in +S'(α)

a!! A → α to DRAa

F0 # ε in +S'(α)

#or ea"h terminal a in +**=(A) a!! A → α to DRAa

30 # ε in +S'(α) an! Q in +**=(A)

Constru"tin$ **(1) Parsin$ 'able -- Al$orithm


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E → 'EJ +S'('EJ)6>(i!? E → 'EJ into DRE( an! DREi!

EJ → .'EJ +S'(.'EJ )6>.? EJ → .'EJ into DREJ. EJ → ε +S'(ε)6>ε? none

but sin"e ε in +S'(ε)an! +**=(EJ)6>Q)? EJ → ε into DREJQ an! DREJ)

' → +'J +S'(+'J)6>(i!? ' → +'J into DR'( an! DR'i!

'J → ;+'J +S'(;+'J )6>;? 'J → ;+'J into DR'J;

'J → ε +S'(ε)6>ε? nonebut sin"e ε in +S'(ε)an! +**=('J)6>Q).? 'J → ε into DR'JQ DR'J)

DR'J.

+ → (E) +S'((E) )6>(? + → (E) into DR+(

Constru"tin$ **(1) Parsin$ 'able -- Example

**(1) 5rammars


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**(1) 5rammarsA $rammar whose parsin$ table has no multiple-!e8ne!

entries is sai! to be **(1) $rammar0+irst * re#ers input s"anne! #rom le#t the se"on! * re#ers le#t-

most !eri&ation an! 1 re#ers one input symbol use! as a loo-hea! symbol !o !etermine parser a"tion input s"anne! #rom le#tto ri$ht

A $rammar 5 is **(1) i# an! only i# the #ollowin$ "on!itions

hol! #or two !istin"ti&e pro!u"tion rules A → α an! A → β10 Both α an! β "annot !eri&e strin$s startin$ with same terminals0F0 At most one o# α an! β "an !eri&e to ε030 # β "an !eri&e to ε then α "annot !eri&e to any strin$ startin$

with a terminal in +**=(A)0

rom * " 0 e can say that irst1 α 2 % irst1 β 2 3 +

rom 40 means that if ε is in irst1 β 20 then irst1 α 2 % ollo1!2 3 +an! the lie

A 5rammar whi"h is not **(1)


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A 5rammar whi"h is not **(1) 'he parsin$ table o# a $rammar may "ontain more than one

pro!u"tion rule0n this "ase we say that it is not a **(1) $rammar0

S → i C t S E 9 aE → e S 9 εC → b

+S'(iCtSE) 6 >i?

+S'(a) 6 >a?

+S'(eS) 6 >e?

+S'(ε) 6 >ε?

+S'(b) 6 >b?+**=(S) 6 > Qe ?

+**=(E) 6 > Qe ?

+**=(C) 6 > t ? two pro!u"tion rules #or DREe

6roblem ambi"uity

a b e i t $

S S → a S → iCtSE

E E → e S

E → ε

E → ε

C C → b

A 5rammar whi"h is not **(1)


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A 5rammar whi"h is not **(1)=hat !o we ha&e to !o i# the resultin$ parsin$ table "ontains

multiply !e8ne! entries

Eliminate le#t re"ursion in the $rammar i# it is not eliminate!A → Aα 9 β any terminal that appears in +S'(β) also appears

+S'(Aα) be"ause Aα ⇒ βα0 # β is ε any terminal that appears in +S'(α) also appears

in +S'(Aα) an! +**=(A)0*e#t #a"tor the $rammar i# it is not le#t #a"tore!0A $rammar is not le#t #a"tore! it "annot be a **(1) $rammar

A → αβ1 9 αβF

any terminal that appears in +S'(αβ1) also appears in+S'(αβ

# its (new $rammarJs) parsin$ table still "ontains multiply!e8ne! entries that $rammar is ambi$uous or it is inherentlynot a **(1) $rammar0

An ambi$uous $rammar "annot be a **(1) $rammar0

Error e"o&ery in Pre!i"ti&e Parsin$


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Error e"o&ery in Pre!i"ti&e Parsin$

An error may o""ur in the pre!i"ti&e parsin$

(**(1) parsin$)i# the terminal symbol on the top o# sta" !oes

not mat"h with the "urrent input symbol0i# the top o# sta" is a non-terminal A the

"urrent input symbol is athe parsin$ table entry DRAa is empty0

=hat shoul! the parser !o in an error "ase 'he parser shoul! be able to $i&e an error

messa$e (as mu"h as possible meanin$#ul errormessa$e)0

t shoul! re"o&er #rom that error "ase an! it

C t t (S i 3)


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Contents (Session-3)

Bottom Xp Parsin$an!le Prunin$mplementation o# A Shi#t-e!u"e

Parser* Parsers* Parsin$ Al$orithm

A"tions o# A *-ParserConstru"tin$ S* Parsin$ 'ablesS*(1) 5rammar

Error e"o&ery in * Parsin$

Bottom Xp Parsin$


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Bottom-Xp Parsin$A bottom-up parser "reates the parse tree o# the

$i&en input startin$ #rom lea&es towar!s the root0A bottom-up parser tries to 8n! the D% o# the $i&en

input in the re&erse or!er0

Bottom-up parsin$ is also nown as s#ift-reduceparsin" be"ause its two main a"tions are shi#t an!re!u"e0At ea"h s#ift action the "urrent symbol in the input

strin$ is pushe! to a sta"0At ea"h reduction step the symbols at the top o# the

sta" will be repla"e! by the non-terminal at the le#tsi!e o# that pro!u"tion0

*ccept Su""ess#ul "ompletion o# parsin$0rror Parser !is"o&ers a syntax error an! "alls an

error re"o&ery routine0

Bottom Xp Parsin$


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Bottom-Xp Parsin$2A shi#t-re!u"e parser tries to re!u"e the $i&en input

strin$ into the startin$ symbol0a strin$ the startin$ symbol

re!u"e! to

At ea"h re!u"tion step a substrin$ o# the input

mat"hin$ to the ri$ht si!e o# a pro!u"tion rule isrepla"e! by the non-terminal at the le#t si!e o# thatpro!u"tion rule0

# the substrin$ is "hosen "orre"tly the ri$ht most

!eri&ation o# that strin$ is "reate! in the re&erse or!er0

i$htmost %eri&ation S ⇒ ω

Shi#t-e!u"e Parser 8n!s ω ⇐ 000 ⇐ Srm rm

rm


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an!le


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an!len#ormally a #andle o# a strin$ is a substrin$ that

mat"hes the ri$ht si!e o# a pro!u"tion rule0But not e&ery substrin$ mat"hes the ri$ht si!e o# apro!u"tion rule is han!le

A #andle o# a ri$ht sentential #orm γ (≡ αβω) is a pro!u"tion rule A → β an! a position o# γ where the strin$ β may be #oun! an! repla"e! by A topro!u"e

the pre&ious ri$ht-sentential #orm in a ri$htmost!eri&ation o# γ 0

S ⇒ αAω ⇒ αβω

# the $rammar is unambi$uous then e&ery ri$ht-sentential #orm o# the $rammar has exa"tly one

han!le0

rm rm

an!le Prunin$


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an!le Prunin$A ri$ht-most !eri&ation in re&erse "an be

obtaine! by #andle-prunin"0

S ⇒ γ Y ⇒ γ 1 ⇒ γ F ⇒ 000 ⇒ γ n-1 ⇒ γ n6 ω

input strin$

Start #rom γ n 8n! a han!le An→βn in γ n an!repla"e βn by An to $et γ n-10

'hen 8n! a han!le An-1→βn-1 in γ n-1 an! repla"e βn-1 in by An-1 to $et γ n-F0

epeat this until we rea"h S0

rm rm rm rm rm


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A St l t ti # A Shi#t ! P


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A Sta" mplementation o# A Shi#t-e!u"e Parser

3tack 0nput *ction

Q i!.i!;i!Q shi#t

Qi! .i!;i!Qre!u"e by + → i!

Q+ .i!;i!Qre!u"e by ' → +

Q ' .i!;i!Qre!u"e by E → ' 6arse ree

QE .i!;i!Qshi#t

QE. i!;i!Q shi#t

QE.i!;i!Q re!u"e by + → i!

QE.+ ;i!Q re!u"e by ' → +

QE.' ;i!Q shi#t

QE.'; i!Q shi#t

QE.';i! Q re!u"e by + → i!

QE. ';+ Q re!u"e by ' → ';+

QE.' Q re!u"e by E → E.'

QE Q a""ept

nitial sta" /ust"ontains only the

en!-marer Q the en! o# theinput strin$ ismare! by theen!-marer Q0

Shi#t e!u"e Parsers


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Shi#t-e!u"e Parsers

'he most pre&alent type o# bottom-up parser

to!ay is base! on a "on"ept "alle! *() parsin$O

le#t to ri$ht ri$ht-most loohea! ( is omitte! it is 1)

L$-6arsers o&ers wi!e ran$e o# $rammars0Simple * parser (S* )*oo Ahea! * (*A*)most $eneral * parser (* )

S* * an! *A* wor same only their parsin$tables are !iLerent0

S*

C+5

*

*A*

* Parsers


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* Parsers* parsin$ is attra"ti&e be"ause

* parsers "an be "onstru"te! to re"o$nize &irtually allpro$rammin$-lan$ua$e "onstru"ts #or whi"h "ontext-

#ree $rammars "an be written0* parsin$ is most #eneral nonbacktrackin# shift

re$uce parsin# yet it is still e"ient0

'he "lass o# $rammars that "an be parse! usin$ *metho!s is a proper superset o# the "lass o# $rammars

that "an be parse! with pre!i"ti&e parsers0LL(%!-7rammars ⊂ L$(%!-7rammars

An *-parser "an !ete"t a syntactic error as soon asit is possible to !o so a le#t-to-ri$ht s"an o# the input0

%rawba" o# the * metho! is that it is too mu"hwor to "onstru"t an * parser by han!0Xse tools e0$0 ya""

* Parsin$ Al$orithm


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* Parsin$ Al$orithm

Sm

Xm

Sm-1Xm-1

.

.

S1X1

S0

a1

... ai

... an

$

Action Table

terminal and $t !o"r di!!erenta actionte

#oto Table

non-terminalt eac item ia a tate n"mber te

LR Parsing Algorithm

sta"

input

output

Al$orithm


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Al$orithm

A "on8$uration o# a * parsin$ is

( So S1 000 Sm ai ai.1 000 an Q )

Sta" est o# nput

Sm an! ai !e"i!es the parser a"tion by "onsultin$ the

parsin$ a"tion table0 (%nitially Stack "ontains /ust So )

A "on8$uration o# a * parsin$ represents the ri$htsentential #orm

T1 000 Tm ai ai.1 000 an QTi is the $rammar symbol represente! by state si


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* parsin$ al$orithm


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*-parsin$ al$orithm

5rammar


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5rammar

state id + * ( ) $ E T F0 % & 1 '

1 acc

' r' r' r'

r& r& r& r&

& % & '

% r r r r

% & ,

% & 10

11

, r1 r1 r1

10 r r r r

*ction able 7oto ableExpression

5rammar

1) E → E.'F) E → '

3) ' → ';+V) ' → +Z) + → (E)

[) + → i!

Example


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Example

stack input action output

Y i!;i!.i!Q shi#t Z

Yi!Z ;i!.i!Q re!u"e by +→i! +→i!

Y+3 ;i!.i!Q re!u"e by '→+ '→+

Y'F ;i!.i!Q shi#t \

Y'F;\ i!.i!Q shi#t ZY'F;\i!Z .i!Q re!u"e by +→i! +→i!

Y'F;\+1Y (2).i!Q re!u"e by '→ ';+ '→ ';+

Y'F .i!Q re!u"e by E→ ' E→ '

YE1 .i!Q shi#t [

YE1.[ i!Q shi#t Z

YE1.[i!Z Q re!u"e by +→i! +→i!

YE1.[+3 Q re!u"e by '→+ '→+

YE1.['] (22) Q re!u"e by E→E.' E→E.'

YE1 Q a""ept

For id2id1id

b


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ConGi"ts %urin$ Shi#t e!u"e Parsin$

'here are "ontext-#ree $rammars #or whi"h shi#t-

re!u"e parsers "annot be use!0Sta" "ontents an! the next input symbol may

not !e"i!e a"tions#ift/reduce con8ict =hether mae a shi#t

operation or a re!u"tion0reduce/reduce con8ict 'he parser "annot

!e"i!e whi"h o# se&eral re!u"tions to mae0

# a shi#t-re!u"e parser "annot be use! #or a$rammar that $rammar is "alle! as non-*()$rammar0

An ambi$uous $rammar "an ne&er be a *

$rammar

:*(Y) tem


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*(Y) temAn * parser maes shi#t-re!u"e !e"isions by maintainin$ states to

eep tra" o# where we are in a parse0

An L$(9! item o# a $rammar 5 is a pro!u"tion o# 5 a !ot at the someposition o# the ri$ht si!e0

Ex A → aBb Possible *(Y) tems A → 0aBb

(#our !iLerent possibility) A → a0Bb

A → aB0b

A → aBb0Sets o# *(Y) items will be the states o# action an! "oto table o# theS* parser0i0e0 States represent sets o# ^items0H

A "olle"tion o# sets o# *(Y) items (t#e canonical L$(9! collection) is

the basis #or "onstru"tin$ S* parsers0

Constru"tin$ S* Parsin$ 'ables


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Constru"tin$ S* Parsin$ 'ables2 'o "onstru"t the canonical L$(9! collection #or a

$rammar we !e8ne an augmented grammar an! two#un"tions0 567S8&E and G797.

!ugmented Grammar 5J is 5 with a new pro!u"tion rule SJ→S where SJ is the new

startin$ symbol0

(urpose to pro&i!e a sin$le pro!u"tion that when re!u"e!si$nals the en! o# parsin$

# / is a set o# *(Y) items #or a $rammar 5 thenclosure&/( is the set o# *(Y) items "onstru"te! #rom

by the two rules10 nitially e&ery *(Y) item in is a!!e! to "losure()0F0 # A → α0Bβ is in "losure() #or all pro!u"tion rules B→γ in 5

a!! B→0γ in the "losure()0*e will appl, this rule until no more new 0R&1( items

can be a$$e$ to closure&/(2

Closure () Example


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Closure () 20 Example

5i&e a $rammarE → E . ' 9 '

' → ' ; + 9 ++ →( E ) 9 i!#en,

Closure(>' → ' 0; +?) 6 >' → ' 0 ; +?Closure (>' → ' 0; + ' → ' ; 0+?) 6 >' → ' 0; + '

→ ' ; 0+ + → 0(E ) + → 0i!?Closure (>+ →( 0E ) ? ) 6 >+ →( 0E ) E → 0 E . ' E

→ 0 ' ' → 0 ' ; + ' → 0 + + → 0( E ) + → 0 i! ?"losure(>EJ → 0E?) 6>EJ → 0E E → 0E.' E → 0' ' → 0';+ ' → 0+ + → 0(E) + → 0i!?

5oto peration


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5oto peration# is a set o# L$(9! items an! T is a $rammar symbol (terminal or non-terminal) then "oto(0,:! is

!e8ne! as #ollows

# A → α0Tβ in then e&ery item in closure(;* → :0 EJ → E0 E → E0.' ?) 6 > EJ → E0 E → E0.' ?)

$oto(') 6 "losure(> E → '0 ' → '0;+ ?) 6 >E → '0 ' → '0;+?

$oto(+) 6 "losure(> ' → +0 ?) 6 > ' → +0

?)

$oto(() 6 "losure(> + → (0E)?) 6 >+ → (0E) E → 0E.' E → 0 ' ' → 0 ';+ ' → 0+ + → 0(E) + → 0i! ?

$oto(i!) 6 "losure( > + → i!0 ?) 6 > + → i!0 ?5oto(>EJ → E 0 E → E . 0'?.) 6 "losure(> ?) 6 > ?

Colle"tion


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Colle"tion

'o "reate the S* parsin$ tables #or a

$rammar 5 we will "reate the "anoni"al *(Y)"olle"tion o# the $rammar 5J0

3l#orithm7oi! items(5J) >

C 6 > C*SXE(>SJ→0S?) ?repeat

for (ea"h set o# items in C)

for(ea"h $rammar symbol T)

if ($oto(T) is not emptyan! not in C(

a!! $oto(T) to C

=ntil no new sets o# items are a!!e!

Example


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Example

C 6 >"losure(>EJ → 0E?) ? 6 >EJ → 0 E E →0 E . ' E

→ 0 ' ' → 0 ' ; + ' →0 + + → 0( E ) + → 0 i!?0 'his $i&es us the items #or the 8rst state (stateY :

Y) o# our %+A

,ow we nee! to "ompute 7oto #un"tions #or all

o# the rele&ant symbols in the set0n this "ase we "are about the symbols F (

an! id sin"e those are the symbols that ha&e a0symbol in #ront o# them in some item o# the set C0

+or symbol E 5oto(Y E) 6 "losure(>EJ → E 0 E → E 0 . '?)

6 >EJ → E 0 E → E 0 . '? 6 call it 0%

+or symbol ' 5oto(Y ') 6 "losure(>E→

' 0 '→

+or symbol + 5oto(Y +) 6"losure(>' → +0?) 6 >' →


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+0? 6 0)

+or symbol ( 5oto(Y () 6 "losure(>+ → ( 0E ) ?) 6 >+

→(0E ) E → 0 E . ' E → 0 ' ' → 0 ' ; + ' → 0 + + → 0(E ) + → 0 !? 6 05

+or symbol i! 5oto(Y i!) 6 "losure(>+ → i!0?) 6 >+→ i!0? 6 0>

epeat this step #or newly "reate! states (1 F 3 V Z)

till 0 o""ures at the en! o# ernal o# ea"h state0+or symbol . 5oto(1 .) 6 "losure(>E → E .0 '?) 6 >E

→ E .0 ' ? ' → 0 ' ; + ' → 0 + + → 0( E ) + → 0 !? 6 0?+or symbol ; 5oto(F ;) 6 "losure(>' → ' ; 0+?)6 >' → ' ; 0+ + → 0( E ) + → 0 !? 6 0@A

+or symbol E 5oto(V E) 6 "losure(>+ → ( E0 ) E → E 0. '?)

6 6

Summary o# states obtaine! an! to whi"h state ea"h! i i


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pro!u"tion in a state $oes

+un"tion


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+un"tion

*(Y) automaton #or the Example


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EJ → E "losure(>EJ → 0E?) 6

E → E.' > EJ → 0E ule 1

E → ' E → 0E.' ule F

' → ';+ E → 0 ' ule F

' → + ' → 0 ';+ ule F

Example


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ExampleBe#ore we start "onstru"tion o# S* a"tionQ).?3 ' → ' ; + +ollow(') 6 >Q).?V ' → + +ollow(+) 6 >Q).;?

Z + →( E )[ + → i!Ea"h terminal is "olumn #or a"tion table ea"h non-

terminal is "olumn #or 5' table an! ea"h state is

row #or both tables

Constru"tin$ S* Parsin$ 'able 2


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$ $

10 Constru"t the "anoni"al "olle"tion o# sets o# *(Y)items #or 5J0 C←>Y000n?

F0 Create the parsin$ a"tion table as #ollows

F010 # a is a terminal A→α0aβ in i an! $oto(ia)6 / then a"tionRi a is shift 4 A

F0F0 # A→α0 is in i then a"tionRia is re$uce 3 #orall a in +**=(A) where A≠SJ0

F030 # SJ→S0 is in i then a"tionRiQ is accept 0

F0V0 # any "onGi"tin$ a"tions $enerate! by these rulesthe $rammar is not S*(1)0

30 Create the parsin$ $oto table. #or all non-terminals A i# $oto(iA)6 / then $otoRiA6/

V0 All entries not !e8ne! by (F) an! (3) are errors0

Z0 nitial state o# the parser "ontains SJ→0S

Example


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Example

From Rule 5262

'ae + → 0( E ) #rom Y 5oto(Y ( ) 6 V then a"tionRY ( 6 shi#tV 'ae E → E 0 . ' #rom 1 5oto(1 .) 6 [ then a"tionR1 . 6

shi#t [ 'ae ' → ' 0 ; + #rom F 5oto(F ;) 6 \ then a"tionRF ; 6 shi#t

\

2other shifts can be populate$ in the same wa,7

From Rule 5252 'ae E → '0 #rom F +ollow(') 6 >Q).? a"tionRFQ 6 re!u"e F (F E → ' ) A"tionRF ) 6 re!u"e F A"tionRF .) 6 re!u"e F

7other re$uces can be $one in the same wa,7

From Rule 52-2 EJ → E 0 is 1 a"tionR1Q 6 accept

Example


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Example

+rom 3 - Creatin$ the parsin$ $oto table

o 'ae E in Y $oto(YE)61 then $otoRYE61. 'ae ' in Y $oto(Y')6 F then $otoRY ' 6 F

. 'ae ' in Y $oto(Y+)6 3 then $otoRY + 6 3

. 'ae E in V $oto(VE)6_ then $otoRVE6_

. 'ae ' in V $oto(V')6 F then $otoRV ' 6 F

. 'ae + in V $oto(V+)6 3 then $otoRV + 6 3

. 'ae ' in [ $oto([')6 ] then $otoR[ ' 6 ]

. 'ae + in [ $oto([+)6 3 then $otoR[ + 6 3

. 'ae + in \ $oto(\+)6 1Y then $otoR\ + 6 1Y

x5rammar


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5rammar

state

id + * ( ) $ E T F

0 % & 1 '

1 acc

' r' r' r'

r& r& r& r&& % & '

% r r r r

% & ,

% & 10

11

, r1 r1 r1

10 r r r r

"tion 'able 5oto 'able

Exer"ise


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Exer"ise

Constru"t S* Parse table #or the au$mente!$rammar an! show how the parser a""epts thestrin$ or input () ()

1 SJ →S

FS →(S)S3S →lAnswer

S*(1) 5rammar


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S*(1) 5rammar

An * parser usin$ S*(1) parsin$ tables #or a$rammar 5 is "alle! as the S*(1) parser #or 50

# a $rammar 5 has an S*(1) parsin$ table it is"alle! S*(1) $rammar (or S* $rammar in short)0

E&ery S* $rammar is unambi$uous but e&eryunambi$uous $rammar is not a S* $rammar0

# the S* parsin$ table o# a $rammar 5 has a"onGi"t we say that that $rammar is not S*$rammar0shi#t


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An * parser will !ete"t an error when it

"onsults the parsin$ a"tion table an! 8n!san error entry0 All empty entries in the a"tiontable are error entries0missin$ operan!

unbalan"e! ri$ht parenthesisErrors are ne&er !ete"te! by "onsultin$ the

$oto table0

Some error re"o&ery are%is"ar! zero or more input symbols until a symbol

a is #oun!By marin$ ea"h empty entry in the a"tion table

with a spe"i8" error routine0

Assi$nment 3


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5i&en the #ollowin$ $rammar where a b "

are terminals an! S T U are non-terminalsS ` TaUb 9 U 9l

T ` aU 9 "

U ` bT 9 aBuil! **(1) Parsin$ table #or the $rammar (Show

all the ne"essary steps)0=hat "an you say about ambi$uity o# the $rammarshow how the parser a""epts

chapter 3_syntax analysis.pptx

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