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Top-Down and Bottom-Up Parsing

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p p g

TopDownParsing

BottomUpParsing

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Thingstoknow:Topdownparsingisconstructingaparsetreefortheinputstartingfromtherootand

createnodesoftheparsetreeinpreorder(depthfirst).

Ageneralformoftopdownparsingistherecursivedescentparsing.

Arecursivedescentparsingisatopdownparsingtechniquethatexecuteasetof

recursiveprocedurestoprocesstheinput,thatinvolvesbacktracking(meansscanningtheinputrepeatedly).

Backtrackingistimeconsumingandtherefore,inefficient.Thatswhyaspecialcaseoftopdownparsingwasdeveloped,calledpredictiveparsing,wherenobacktrackingisrequired.

Adilemmacanoccurifthereisaleftrecursivegrammar.Evenwithbacktracking,youcanfindtheparsertogointoaninfiniteloop.

Therearetwotypesofrecursion,leftrecursiveandrightrecursive,basedonitsname,aleftrecursivegrammarbuildtreesthatgrowsdowntotheleft,whilerightrecursiveisviceversa.

TopDownParsing

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Top-downParsetreeofGrammarG(Whereinput=id):G=E->TE E->+TE|

T->FT

T->*FT|

F->(E)|id

Anexampleofasimpleproductionwithleftrecursivegrammar

Considerthegrammar:expr -> expr + termThisisanexampleofaleftrecursivegrammar.Wheneverwecallexpr,thesameprocedureiscalledout,andtheparserwillloopforever.

Bycarefullywritingagrammar,onecaneliminateleftrecursionfromit.

expr -> expr + term, canbewrittenasexpr -> expr + term | termAfter obtaining a grammar that needs no backtracking, we can use thePREDICTIVE PARSER

E E

T E

E

T E

F T

E

T E

F T

id

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TopDownParsingTechniques

Recursive-DescentParsing

PredictiveParsing

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Recursive-DescentParsing

Arecursive-descentparsingprogramconsistsofasetofprocedures,oneforeachnonterminal.Executionbeginswiththeprocedureforthestartsymbol,whichhalts

andannouncessuccessifitsprocedurebodyscanstheentireinputstring.Generalrecursive-descentmayrequirebacktracking;thatis,itmayrequirerepeated

scansovertheinput.

Considerthegrammarwithinputstringcad:

S->cAd

A->ab|a

S SS

c ccA AA dd d

a ab

c a d

Back

Recursive-DescentParsing

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PredictiveParsing-aparsingtechniquethatusesalookaheadsymboltodetermineifthecurrentinputargumentsmatchesthelookaheadsymbol.

FirstandFollow

ConstructionofPredictive

ParsingTables

LL(1)

Grammars ErrorRecovery

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FirstandFollowaidstheconstructionofapredictiveparser.

Theyallowustofillintheentriesofapredictiveparsingtable.

aisanystringofterminals,thenFirst(a)isthesetofterminalsthatbeginthestringsderivedfroma.Ifaisanemptystring(),thenisalsoinFirst(a).

Follow(A),foranonterminalA,tobethesetofterminalsathatcanappearimmediatelytotherightofAinasententialform.

Firstand

Follow

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RulesincomputingFIRST(X)whereXcanbeaterminalornonterminal,oreven(emptystring).

1) IfXisaterminal,thenFIRST(X)=X.

2) IfXis,thenFIRST(X)=.3) IfXisanonterminalandYandZarenonterminals,withaproductionof

X->Y

Y->Za

Z->b;thenFIRST(X)=b;whereFIRST(nonterminal1)->FIRST(nonterminal2)oruntilyoureachthefirstterminaloftheproduction.Inthatcase

(FIRST(nonterminaln)=FIRST(nonterminaln+1))

4)IfXisanonterminalandcontainstwoproductions.EX:

X->a|b;thenFIRST(X)={a,b}

Firstand

Follow

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ConsideragaingrammarG:

1)E->TE

E->+TE|

T->FT

T->*FT|

F->(E)|id

2)S->iEtSS|a

S->eS| E->b

ANSWERS(FIRST):

1)FIRST(E)=FIRST(T)=FIRST(F)={(,id}

FIRST(E)={+,}

FIRST(T)={*,}

2)FIRST(S)={i,a}

FIRST(S)={e,} FIRST(E)={b}

FirstandFollow

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RulesincomputingFOLLOW(X)whereXisanonterminal

1) IfXisapartofaproductionandissucceededbyaterminal,forexample:A->Xa;thenFollow(X)={a}

2) IfXisthestartsymbolforagrammar,forex:

X->AB A->a

B->b;thenadd$toFOLLOW(X);FOLLOW(X)={$}

3) IfXisapartofaproductionandfollowedbyanothernonterminal,gettheFIRSTofthatsucceedingnonterminal.

ex:A->XD

D->aB;thenFOLLOW(X)=FIRST(D)={a};andifFIRST(D)contains

(ex:D->aB|),theneverythinginFOLLOW(D)isinFOLLOW(X).

4) IfXisthelastsymbolofaproduction,ex:S->abX,then

FOLLOW(X)=FOLLOW(S)

FirstandFollow

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ConsideragaingrammarG:

1)E->TE

E->+TE|

T->FT T->*FT|

F->(E)|id

2)S->iEtSS|a

S->eS|

E->b

ANSWERS(FIRST):1)FIRST(E)=FIRST(T)=FIRST(F)={(,id}

FIRST(E)={+,}

FIRST(T)={*,}

2) FIRST(S)={i,a};FIRST(S)={e, };FIRST(E)={b}

ANSWERS(FOLLOW):

ANSWERSFORFOLLOW:

1) FOLLOW(E)=FOLLOW(E)={),$}

FOLLOW(T)=FOLLOW(T)={+,),$}

FOLLOW(F)={+,*,),$}

2) FOLLOW(S)=FOLLOW(S)={e,$}

FOLLOW(E)={t}

FirstandFollow

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ThegeneralideaistousetheFIRSTANDFOLLOWtoconstructtheparsingtables.

EachFIRSTofeveryproductionislabeledinthetablewhenevertheinputmatcheswithit.

WhenaFIRSTofaproductioncontains,thenwegettheFollowoftheproduction

ConstructionofPredictive

ParsingTables

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ConsideragaingrammarG:E->TEE->+TE|T->FT

T-->*FT|F->(E)|idandtheirFirstandFollow

FIRST(E)=FIRST(T)=FIRST(F)={(,id} FOLLOW(E)=FOLLOW(E)={),$}

FIRST(E)={+,} FOLLOW(T)=FOLLOW(T)={+,),$}

FIRST(T)={*,} FOLLOW(F)={+,*,),$}

ConstructionofPredictive

ParsingTables

Nonterminals Id + * ( ) $EE

TTF

E->TE

T->FT

F->id

E->+TE

T->

T->*FT

E->TE

T-FT

F->(E)

E->

T->

E->

T->

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Back

STACK INPUT ACTION$E$ET$ETF

$ETid$ET$E$ET+$ET$ETF

$ETid$ET$ETF*$ETF$ETid$ET$E

$

id+id*id$id+id*id$id+id*id$

id+id*id$+id*id$+id*id$+id*id$id*id$id*id$

id*id$*id$*id$id$id$$$

$

E->TET->FT

F->id

T->E->+TE

T->FT

F->idT->*FT

F->id

T->

E->

Nonterminals Id + * ( ) $EET

TF

E->TE

T->FT

F->id

E->+TE

T->

T->*FT

E->TE

T->FT

F->(E)

E->

T->

E->

T->

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WhatdoesLL(1)mean?

ThefirstLinLL(1)standsforscanningtheinputfromlefttoright,thesecondL

isforproducingaleftmostderivation,andthe1forusingoneinputsymboloflookaheadateachsteptomakeparsingactiondecisions.

NoambiguousorleftrecursivegrammarisLL(1).

LL(1)

Grammars

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Thereremainsaquestionofwhatshouldbedonewhenaparsingtablehasmultiple-definedentries.

Onesolutionistotransformthegrammarbyeliminatingallleftrecursionandthenleftfactoringwhenpossible,butnotallgrammarscanyieldanLL(1)grammaratall.

Themaindifficultyinusingapredictiveparsingisinwritingagrammarforthesourcelanguagesuchthatapredictiveparsercanbeconstructedfromthegrammar.

Toalleviatesomeofthedifficulty,onecanuseaoperatorprecedence,orevenbettertheLRparser,thatprovidesboththebenefitsofpredictiveparsingandoperatorprecedenceautomatically.

BACK

LL(1)

Grammars

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Whendoesanerrorpossiblyoccur?

-AnerrorisdetectedwhentheterminalonthetopofthestackdoesnotmatchthenextinputsymbolorwhenthenonterminalAisonthetopofthestack,aisthenextinputsymbol,andtheparsingtableentryM[A,a]isempty.

Howcanwedealwitherrors?

Panic-modeerrorrecoveryisbasedontheideaofskippingsymbolsontheinputuntilatokeninaselectedsetofsynchtokensappears.

ErrorRecovery

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Howdoesitwork?

Usingfollowandfirstsymbolsassynchronizingtokensworkswell.TheparsingtablewillbefilledwithsynchtokensobtainedfromtheFOLLOWsetofthenonterminal.

WhenaparserlooksupentryM[A,a]andfindsitblank,thenaisskipped.Iftheentryissynch,thenthenonterminalispoppedinanattempttoresumeparsing.

ErrorRecovery

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Back

Nonterminals Id + * ( ) $EET

TF

E->TE

T->FT

F->id

E->+TEsynch

T->synch

T->*FTsynch

E->TE

T->FT

F->(E)

synch

E->synch

T->synch

synch

E->synch

T->synchTACK INPUT ACTION

$E$E$ET$ETF

$ETid$ET$ETF*$ETF$ET$E$ET+$ET$ETF$ETid$ET$E$

)id*+id$id*+id$

id*+id$id*+id$

id*+id$*+id$*+id$+id$+id$+id$+id$id$id$id$$$$

Error,skip)IdisinFIRST(E)

Error,M[F,+1=synchFhasbeenpopped

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AnothererrorrecoveryprocedureisthePhrase-levelRecovery.Thisisimplementedbyfillingintheblankentries

intheparsingtablewithpointerstoerrorroutines.Theseroutinescanalsopopsymbolsfromthestack,change,insertordeletesymbolsontheinput,andissueappropriateerrormessages.Thealterationofstack

symbolsisveryquestionableandrisky.

BACK

ErrorRecovery

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Ageneralstyleofbottomupparsingwillbeintroduced,itistheshift-reduceparsing.

Shiftreduceparsingworksbasedonitsname,ShiftandReduce,sowheneverthestackholdssymbolsthat

cannotbereducedanymore,weshiftanotherinput,andwhenitmatches,wereduce.

BottomUpParsing

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STACK INPUT ACTION1) $2) $id13) $E

4) $E+5) $E+id26) $E+E7) $E+E*8) $E+E*id39) $E+E*E10)$E+E11)$E

id1+id2*id3$+id2*id3$+id2*id3$

id2*id3$*id3$*id3$id3$

$$$$

ShiftReducebyE->id

ShiftShiftReducebyE->idShiftShiftReducebyE->idReducebyE->E*EReducebyE->E+E

ACCEPT

BottomUpParsing