Bottom Up LR(0) Parsing in C.

8/9/2019 Bottom Up LR(0) Parsing in C.

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BOTTOM UP PARSING

A bottom-up parse corresponds to the construction of a parse tree for an input stringbeginning at the leaves (the bottom) and working up towards the root (the top) . It isconvenient to describe parsing as the process of building parse trees, although a front end

may in fact carry out a translation directly without building an explicit tree.e can think of bottom-up parsing as the process of !reducing! a string w to the start symbolof the grammar. At each reduction step, a specific substring matching the body of a

production is replaced by the non terminal at the head of that production. "he key decisionsduring bottom-up parsing are about when to reduce and about what production to apply, asthe parse proceeds.

LR PARSERS:"he #most prevalent type of bottom-up parser today is based on a concept called $%(k)

parsing& the !$! is for left-to-right scanning of the input, the !%! for constructing a rightmostderivation in reverse, and the k for the number of input symbols of lookahead that are used inmaking parsing decisions.

$% parsing is attractive because of variety of reasons'

$% parsers can be constructed to recognie virtually all programming language

constructs for which context-free grammars can be written. on $% context-freegrammars exist, but these can generally be avoided for typical programming-language constructs.

"he $%-parsing method is the most general non back tracking shift-reduce parsing

method known, yet it can be implemented as efficiently as other, more primitive shift-reduce methods .

An $% parser can detect a syntactic error as soon as it is possible to do so on a left-to-right scan of the input.

$% grammars can describe more languages than $$ grammars.

ITEMS AND THE LR(0) AUTOMATION:An $% parser makes shift-reduce decisions by maintaining states to keep track of where weare in a parse. *tates represent sets of !items.! An $%(+) item (item for short) of a grammar is a production of with a dot at some position of the body. "hus, production A - /0yields the four itemsA - 1/0

A - 1/0A - /1 0A - /01"he production A - generates only one item, A - . . Intuitively, an item indicates how much of a production we have seen at a given point in the

parsing process. 2or example, the item A - 1/ 0 indicates that we hope to see a stringderivable from / 0 next on the input. Item A - 1 / 0 indicates that we have 3ust seen onthe input a string derivable from and that we hope next to see a string derivable from / 0.Item A -/ 01 indicates that we have seen the body / 0 and that it may be time to reduce/0 to A.


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CLOSURE OF ITEM SETS:

If I is a set of items for a grammar , then 4$+*5%6(I) is the set of items constructed from Iby the two rules'

7. Initially, add every item in I to 4$+*5%6(I).8. If A -91:; is in 4$+*5%6(I) and : - is a production, then add the item : - to

4$+*5%6(I), if it is not already there. Apply this rule until no more new items canbe added to 4$+*5%6 (I).

THE FUNCTION GOTO:

"he second useful function is +"+(I, ) where I is a set of items and is a grammarsymbol. +"+ (I, ) is defined to be the closure of the set of all items


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ALGORITHMS USED:

Algorithm to compute closure of an item'

Algorithm to compute set of canonical $%(C) items'

Algorithm to construct $%(C) >arsing "able'


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$% >A%*I A$+%I"?@'

IMPLEMENTATION CODE IN C LANGUAGE:

#include#include

#include#include#defnesize20structstate{ charproductions[size][10],ons!"bol shortintscannedproductions[size],noo$productions,statenu"ber,shi$tin$o[10],nu"bero$shi$t structstate%lin&'t!pede$structstate% ()*+structaction{

intstate

charact't!pede$structactionA-)(A-)(feld[/0][1]()*+frst (33,last (33int nu"bero$states,noo$4ariables,noo$ter"inals,count1,5p0,pgoto[/0][10],tpcharclosureproductions[size][10],input[10][10],pfrst[10][10],p$ollo6[10][10],4ariables[size],ter"inals[size],p[10]4oidclosure7()*+,int%84oidite"s78()*+getnode78{ ()*+te"p

inti te"p 7()*+8 "alloc7sizeo$7structstate88 $or7i 0 i < sizei998


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{ strcp!7te"p:>productions[i],;0;8 te"p:>scannedproductions[i] 0 ' te"p:>noo$productions 0 te"p:>nu"bero$shi$t 0

te"p:>lin& (33 returnte"p'4oidinsert7()*+te"p8{

i$7frst (338 { frst te"p last te"p ' else { last:>lin& te"p

last te"p '

'

4oiddotproductions7charinput[][10],intcount8{ inti 1,5,& 1 charbu=er[10]{0' 6hile7i < count8 { & 0 5 0

6hile7input[i][&] ? 08 { i$7input[i][&] >8 { bu=er[599] > bu=er[599] . ' else bu=er[599] input[i][&] &99 ' bu=er[5] 0 strcp!7closureproductions[i],bu=er8 i99 ''int chec&$orpresenceinproductions7()*+te"p,char%bu=er8{ inti 0 6hile7te"p:>productions[i][0]8 { i$7?strc"p7te"p:>productions[i],bu=er88 return1 i99 ' return0'

4oidaug"entgra""ar7charinput[][10]8{ input[0][0] input[1][0]


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{i$7c4ariables[i]8{

returni

'

'return:1'intfndt7charc8{

inti0$or7i0i


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''

''

''

intdetectepslon7charc8{int4ar,i4ar fnd47c8i$74ar :18

return0$or7i0i


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"99 else

brea& '

'

'''intfndp7char%str8{ inti

charbu=[20]strcp!7bu=,str8bu=[strlen7str8:1]0$or7i1ions!"bolch8 {

$or7515statenu"berfeld[te"p:>shi$tin$o[5]][i].acts

' ' te"pte"p:>lin&

''te"pfrst

6hile7te"p?(338{

i$7te"p:>statenu"ber?18$or7i0iproductions[i]8&::


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i$7te"p:>productions[i][&].8{

lfndp7te"p:>productions[i]8"fnd47input[l][0]8$or7505statenu"ber][poster"7p$ollo6["][5]8].act(338

{feld[te"p:>statenu"ber][poster"7p$ollo6["]

[5]8].statelfeld[te"p:>statenu"ber][poster"7p$ollo6["]

[5]8].actr'else{

print$7;Ecr conflctn;,feld[te"p:>statenu"ber][poster"7p$ollo6["][5]8].act8

getch78

eCit708'

'

'

'else{

feld[1][poster"7F8].state1feld[1][poster"7F8].acta

'

te"pte"p:>lin&'

'4oidco"putegoto78{ inti,5

charch()*+te"p

$or7i0istatenu"ber'

' te"pte"p:>lin&

''

'4oidparse7char%str8

{inti0,stac&[1],5,top 0,&,",pos:1,l0


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charch,action[G]{0',s!"bol[20]{0',%p,te"pstac&[0] 06hile7str[i] ?08{

5 poster"7str[i]8

pstr[i]i$7feld[stac&[top]][5].act a8{

strcp!7action,;Accept;8print$7;n;8print$7;E1s ;,action8

$or7l0l


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'

'int4alidi7char%str8{ inti0

$or7i0iEsn;,4ariables[i],pfrst[i]8 ' $or7505productions[i][0] ? 08


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print$7;nEs;,frst:>productions[i99]8print$7; Edn;,frst:>noo$productions8%Jite"s78te"p frst6hile7te"p ? (338

{ i 0 print$7;nEd ;,te"p:>statenu"ber8 6hile7i < te"p:>noo$productions8 print$7;nEs;,te"p:>productions[i99]8 $or7i 1i ons!"bol,te"p:>statenu"ber8 te"p te"p:>lin&'getch78co"puteaction78co"putegoto78print$7;n::::::::::::::::::::::::::3I708 LAIH(M -AN3+:::::::::::::::::::::::::::::::::;8

print$7;n ;8$or7i0i


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{ " 0 6hile7te"p:>productions[i]["] ? .8 "99 "99

i$7te"p:>productions[i]["] > P te"p:>productions[i]["] productions[7%place899],closureproductions[5]8

te"p:>noo$productions 9 1 '

'599

''

i99 ''4oidite"s78{ ()*+te"p,te"p1 (33 inti0,50,&0,place0 charch,bu=er[10]

te"p frst

6hile7te"p ? (338 { 6hile7i < te"p:>noo$productions8 { i$7te"p:>scannedproductions[i] 08 {

5 0

te"p:>scannedproductions[i] 1 6hile7te"p:>productions[i][599] ? .8

ch te"p:>productions[i][5]

i$7 ch ? 0ch?B8 { place 0 te"p1 getnode78 te"p1:>ons!"bol ch

te"p1:>shi$tin$o[99te"p1:>nu"bero$shi$t] te"p:>statenu"ber strcp!7bu=er,te"p:>productions[i]8 bu=er[5:1] ch bu=er[5] . strcp!7te"p1:>productions[0],bu=er8 te"p1:>noo$productions 1 place 1

closure7te"p1,place8 & 0 6hile7te"p:>productions[&][0] ? 08


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{ 5 0 i$7te"p:>scannedproductions[&] 08 { 6hile7te"p:>productions[&][599] ? .8

i$7ch te"p:>productions[&][5] 8 { te"p:>scannedproductions[&] 1 strcp!7bu=er,te"p:>productions[&]8 bu=er[5:1] ch bu=er[5] . strcp!7te"p1:>productions[place99],bu=er8 te"p1:>noo$productions 9 1 closure7te"p1,place8 '

' &99 ' J%$or7i 0i < te"p1:>noo$productionsi998 print$7;nEs;,te"p1:>productions[i]8%J i$7?statenotadded7te"p1,te"p:>statenu"ber88

{ insert7te"p18

te"p1:>statenu"ber 99nu"bero$states ' else

$ree7te"p18

'

i0 '

else i99 ' te"p te"p:>lin& i 0 ''

SAMPLE OUTPUT:


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Bottom Up LR(0) Parsing in C.

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