– 1 – CSCE 531 Spring 2006 Lecture 9 SLR Parse Table Construction Topics SLR Parse Table Construction Sets of Items Closure(I) Readings: 4.7 Homework:

– 1 – CSCE 531 Spring 2006

Lecture 9 SLR Parse Table Construction

Lecture 9 SLR Parse Table Construction

Topics Topics SLR Parse Table Construction Sets of Items Closure(I)

Readings: 4.7Readings: 4.7

Homework: Test 1 – Feb 15Homework: Test 1 – Feb 15

February 8, 2006

CSCE 531 Compiler Construction

– 2 – CSCE 531 Spring 2006

Last TimeLast Time Panic mode error recovery in Predictive parsing Overview Bottom-Up Parsing Handles Shift-reduce parsing

Today’s Lecture Today’s Lecture Sets of Items / Closure / GOTO (J, X)

LR(0) sets of items construction SLR parser table construction

Homework: Homework: LL(1) table for core (pdf email handout) grammar

Test 1 Feb 15 !!! Reference: ξ is the greek letter Xi

http://www.mathacademy.com/pr/prime/articles/greek/index.asp

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Slides in LectureSlides in Lecture

ReviewReview

1.1. Model of an LR parserModel of an LR parser

2.2. LR Parse table LR Parse table (Expressions)(Expressions)

3.3. Constructing SLR Parse Constructing SLR Parse TablesTables

4.4. Sets of Items / ClosureSets of Items / Closure

5.5. ExampleExample

6.6. Goto Operation and exampleGoto Operation and example

7.7. Canonical LR(0) sets-of-Canonical LR(0) sets-of-items (fig 4.35)items (fig 4.35)

8.8. Valid Items/Viable prefixesValid Items/Viable prefixes

9.9. SLR table constructionSLR table construction

10.10. ExampleExample

11.11. Example 4.38Example 4.38

12.12. Example 4.39Example 4.39

13.13. Bison/Flex Overview pictureBison/Flex Overview picture

14.14. Bison specification filesBison specification files

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Recall - Model of an LR ParserRecall - Model of an LR Parser

aa11 …… aaii …… aann$$

ssmm

XXmm

ssm-1m-1

XXm-1m-1

……

ss00

Stack

input

outputLR ParsingProgram

Parsing Table

Action goto

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LR Parsing AlgorithmLR Parsing Algorithm

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Expression LR-Parsing Table fig 4.31Expression LR-Parsing Table fig 4.31

StateState ActionAction gotogoto

IdId ++ ** (( )) $$ EE TT FF

00 S5S5 S4S4 11 22 33

11 S6S6 acceptaccept

22 R2R2 S7S7 R2R2

33 R4R4 R4R4 R4R4

44 S5S5 S4S4 88 22 33

55 R6R6 R6R6 R6R6

66 S5S5 S4S4 99 33

77 S5S5 S4S4 1010

88 S6S6 S11S11

99 R1R1 S7S7 R1R1 R1R1

1010 R3R3 R3R3 R3R3 R3R3

1111 R5R5 R5R5 R5R5 R5R5

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Constructing SLR Parse TablesConstructing SLR Parse TablesConstructing SLR Parse TablesConstructing SLR Parse Tables

As with LL(1) or Predictive Parsing table construction As with LL(1) or Predictive Parsing table construction we will use FIRST and FOLLOW. we will use FIRST and FOLLOW.

We will construct an automata for recognizing handles.We will construct an automata for recognizing handles.

This will be similar to subset construction, NFA This will be similar to subset construction, NFA DFADFA

We use “items” to represent partially matched We use “items” to represent partially matched productions.productions.

The sets of items are sort of the collection of The sets of items are sort of the collection of productions we are working on matching.productions we are working on matching.

Grammars Grammars For top-down we avoid left recursion and left factor For LR we avoid right recursion (in some cases we will ignore)

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ItemsItemsItemsItems

An item is a production with a “dot” somewhere on the right hand An item is a production with a “dot” somewhere on the right hand side.side.

Examples:Examples:

A A B C D E B C D E

Yields the following itemsYields the following items

A A . B C D E . B C D E

A A B . C D E B . C D E

A A B C . D E B C . D E

A A B C D . E B C D . E

A A B C D E . B C D E .

Also N Also N εε generates the itemgenerates the item N N . .

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Sets of Items: Closure fig 4.33Sets of Items: Closure fig 4.33Sets of Items: Closure fig 4.33Sets of Items: Closure fig 4.33

If J is a set of items for a grammar G, then closure(J) is the If J is a set of items for a grammar G, then closure(J) is the set of items constructed from J by the two rules:set of items constructed from J by the two rules:

1.1. Initially, every item in J is added to closure(J)Initially, every item in J is added to closure(J)

2.2. If A If A αα . B . Bββ is in closure(J) and B is in closure(J) and B ηη is a production is a production then add B then add B . . ηη

Apply this rule until no new items can be Apply this rule until no new items can be added to the set.added to the set.

Example:Example:

Assume DAssume D xyF | Bc and B xyF | Bc and BaB | Dd are the productions aB | Dd are the productions then then

Closure(AClosure(ABC.DE) = {ABC.DE) = {ABC.DE, DBC.DE, D.xyF, D.xyF, D . Bc, . Bc,BB.aB, B.aB, B.Dd }.Dd }

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Sets-of-items GOTO(J, X)Sets-of-items GOTO(J, X)Sets-of-items GOTO(J, X)Sets-of-items GOTO(J, X)

If J is a set of items and X is a grammar symbol then If J is a set of items and X is a grammar symbol then

GOTO(J, X) is the closure of the set of all items of the GOTO(J, X) is the closure of the set of all items of the form [Aform [AααX .X .ββ] such that [A] such that [Aαα . X . Xββ] is an item in J.] is an item in J.

GOTO(J, X) = closure ({AGOTO(J, X) = closure ({AααX .X .ββ | A | Aαα . X . Xββ is in J} ) is in J} )

Example given E Example given E E + E | E * E | id E + E | E * E | id

If J = { [E If J = { [E E . + E ], [E E . + E ], [E . id] } then . id] } then

GOTO (J, +) = closure({[E GOTO (J, +) = closure({[E E + . E ] } ) E + . E ] } )

= {[E = {[E E + . E ], … E + . E ], …

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Augmentation and Kernel ItemsAugmentation and Kernel ItemsAugmentation and Kernel ItemsAugmentation and Kernel Items

To facilitate recognition of the sucessful end of a To facilitate recognition of the sucessful end of a parse we will “augment the grammar” adding parse we will “augment the grammar” adding

1.1. a new start symbol S’, anda new start symbol S’, and

2.2. a new production S’ a new production S’ S S

Items with the dot not at the left end and the initial Items with the dot not at the left end and the initial item S’item S’.S are called kernel items..S are called kernel items.

All others will be referred to as non-kernel. All others will be referred to as non-kernel.

Note non-kernel items will have the dot on the left.Note non-kernel items will have the dot on the left.

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LR(0) Sets-of-Items ConstructionLR(0) Sets-of-Items ConstructionLR(0) Sets-of-Items ConstructionLR(0) Sets-of-Items Construction

Figure 4.34Figure 4.34

Procedure items(G’)Procedure items(G’)

BeginBegin

C = { closure({ S’C = { closure({ S’ . S} ) } . S} ) }

repeat repeat

for each set of items J in C and each grammar symbol Xfor each set of items J in C and each grammar symbol X

such that GOT(J, X) is nonempty and not in Csuch that GOT(J, X) is nonempty and not in C

add GOT(J, X) to Cadd GOT(J, X) to C

until no more sets of items can be added to Cuntil no more sets of items can be added to C

endend

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Examples LR(0) sets-of-itemsExamples LR(0) sets-of-itemsExamples LR(0) sets-of-itemsExamples LR(0) sets-of-items

Grammar 4.35 generates LR(0) items in fig 4.35 (p 225).Grammar 4.35 generates LR(0) items in fig 4.35 (p 225).

Example 4.39 (p229)Example 4.39 (p229)

ExampleExample

D D T ; | T R ; D T ; | T R ; D

T T int | float | char int | float | char

R R id | id [ const ] | * id id | id [ const ] | * id

First augment the grammar with S’ First augment the grammar with S’ D D

Then …Then …

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Valid Items/Viable prefixesValid Items/Viable prefixesValid Items/Viable prefixesValid Items/Viable prefixes

The set of prefixes of right sentential forms that can The set of prefixes of right sentential forms that can appear on the stack are called appear on the stack are called viable prefixesviable prefixes..

Alternately it is one that is capable of being extended to Alternately it is one that is capable of being extended to a handle.a handle.

Alternately it is a prefix of a right sentential form that Alternately it is a prefix of a right sentential form that does not extend beyond the right end of the does not extend beyond the right end of the rightmost handle.rightmost handle.

An item [ AAn item [ Aββ11 . . ββ2 2 ] is valid for a viable prefix ] is valid for a viable prefix αβαβ if if there is a derivationthere is a derivation

S’ S’ αα A w A w α βα β11 ββ2 2 ww

An item may be valid for many viable prefixesAn item may be valid for many viable prefixes

– 15 – CSCE 531 Spring 2006

Valid Items Parsing ActionsValid Items Parsing Actions

Valid items indicate possible parsing actionsValid items indicate possible parsing actions

If A If A ββ . Is valid . Is valid the action is reduce by A the action is reduce by A ββ

If [ AIf [ Aββ11 . . ββ2 2 ] is valid ] is valid the action is shift. the action is shift.

Contradictory actions yield conflicts.Contradictory actions yield conflicts.

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SLR table construction Alg 4.8SLR table construction Alg 4.8SLR table construction Alg 4.8SLR table construction Alg 4.8

1.1. Augment G to obtain G’.Augment G to obtain G’.

2.2. Construct C = {IConstruct C = {I00, I, I11, …I, …Inn} the LR(0) items for G’.} the LR(0) items for G’.

3.3. State i corresponds to IState i corresponds to Iii. The parsing actions for state i . The parsing actions for state i are determined as follows:are determined as follows:

a. If [ Aα . a β ] is in Ii and GOTO(Ii, a) = Ij then set action[i, a] = “shift and goto state j” or just “shift j”

b. If [ Aα . ] is in Ii then set action[i, a] = “reduce Aα” for all a in FOLLOW(A). (here A !=S’)

c. If [ S’S . ] is in Ii then set action[i, $] = “accept.”

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Examples of SLR Parse Table ConstructionExamples of SLR Parse Table Construction

Example Grammar 4.42Example Grammar 4.42

S’ S’ S S

S S C C C C

C C c C | d c C | d

GrammarGrammar Sets-of-ItemsSets-of-Items Parse TableParse Table

Example 4.39, pp 229Example 4.39, pp 229 Fig 4.37, pp 229Fig 4.37, pp 229 Conflict bottom pp229Conflict bottom pp229

Example 4.38, pp 228Example 4.38, pp 228 Fig 4.35, pp 225Fig 4.35, pp 225 Fig 4.31, pp 219Fig 4.31, pp 219

– 18 – CSCE 531 Spring 2006

– 19 – CSCE 531 Spring 2006

LR(1) ParsersLR(1) Parsers

A table-driven LR(1) parser looks likeA table-driven LR(1) parser looks like

Tables Tables cancan be built by handbe built by hand

However, this is a perfect task to automateHowever, this is a perfect task to automate

ScannerTable-driven

Parser

ACTION & GOTOTables

ParserGenerator

sourcecode

grammar

IR

– 20 – CSCE 531 Spring 2006

YACCYACC

Yet Another Compiler Compiler Stephen Johnson 1976Yet Another Compiler Compiler Stephen Johnson 1976

Takes grammar specification and generates the Takes grammar specification and generates the Action and GOTO tablesAction and GOTO tables

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YACC Format and UsageYACC Format and Usage

First Bison = new and improved YACCFirst Bison = new and improved YACC

YACC FormatYACC Format

Definitions sectionDefinitions section

%%%%

productions / semantic actions sectionproductions / semantic actions section

%%%%

routinesroutines

– 22 – CSCE 531 Spring 2006

Example (grammar & sets)Example (grammar & sets)Simplified, Simplified, rightright recursive expression grammar recursive expression grammar

Is this what we want?Is this what we want?

Goal ExprExpr Term – ExprExpr TermTerm Factor * Term Term FactorFactor ident

– 23 – CSCE 531 Spring 2006

Simple0.y in web/Examples/SimpleYaccSimple0.y in web/Examples/SimpleYacc

%token DIGIT%token DIGIT

%%%%

line : expr '\n' line : expr '\n'

;;

expr : expr '+' term expr : expr '+' term

| term| term

;;

term : term '*' factor term : term '*' factor

| factor| factor

;;

factor : '(' expr ')' factor : '(' expr ')'

| DIGIT| DIGIT

;;

%%%%

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bison simple0.ybison simple0.y

deneb> deneb>

deneb> ls -lrtdeneb> ls -lrt

……

--rw-r--r-- 1 matthews faculty 28499 Jun 30 12:04 simple0.tab.crw-r--r-- 1 matthews faculty 28499 Jun 30 12:04 simple0.tab.c

deneb> wc simple0.tab.c deneb> wc simple0.tab.c

1084 4111 28499 simple0.tab.c1084 4111 28499 simple0.tab.c

– 25 – CSCE 531 Spring 2006

gcc simple0.tab.c -lygcc simple0.tab.c -ly

Undefined first referencedUndefined first referenced

symbol in filesymbol in file

yylex /var/tmp//ccW88jE5.oyylex /var/tmp//ccW88jE5.o

ld: fatal: Symbol referencing errors. No output written to ld: fatal: Symbol referencing errors. No output written to a.outa.out

collect2: ld returned 1 exit statuscollect2: ld returned 1 exit status

– 26 – CSCE 531 Spring 2006

deneb> more simple1.ydeneb> more simple1.y

%token DIGIT%token DIGIT

%%%%

expr : expr '+' expr expr : expr '+' expr

| expr '*' expr | expr '*' expr

| '(' expr ')' | '(' expr ')'

| DIGIT| DIGIT

;;

%%%%

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deneb> bison simple1.ydeneb> bison simple1.y

simple1.y contains 4 shift/reduce conflicts.simple1.y contains 4 shift/reduce conflicts.

bison -v simple1.ybison -v simple1.y

simple1.y contains 4 shift/reduce conflicts.simple1.y contains 4 shift/reduce conflicts.

deneb> ls -lrtdeneb> ls -lrt

……

--rw-r--r-- 1 matthews faculty 2311 Jun 30 12:10 simple1.outputrw-r--r-- 1 matthews faculty 2311 Jun 30 12:10 simple1.output

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.output.output

deneb> more simple1.output deneb> more simple1.output

State 8 contains 2 shift/reduce conflicts.State 8 contains 2 shift/reduce conflicts.

State 9 contains 2 shift/reduce conflicts.State 9 contains 2 shift/reduce conflicts.

GrammarGrammar

Number, Line, RuleNumber, Line, Rule

1 5 expr -> expr '+' expr1 5 expr -> expr '+' expr

2 6 expr -> expr '*' expr2 6 expr -> expr '*' expr

3 7 expr -> '(' expr ')'3 7 expr -> '(' expr ')'

4 8 expr -> DIGIT4 8 expr -> DIGIT

– 29 – CSCE 531 Spring 2006

Terminals, with rules where they appearTerminals, with rules where they appear

$ (-1)$ (-1)

'(' (40) 3'(' (40) 3

')' (41) 3')' (41) 3

'*' (42) 2'*' (42) 2

'+' (43) 1'+' (43) 1

error (256)error (256)

DIGIT (257) 4DIGIT (257) 4

Nonterminals, with rules where they appearNonterminals, with rules where they appear

expr (8)expr (8)

on left: 1 2 3 4, on right: 1 2 3on left: 1 2 3 4, on right: 1 2 3

– 30 – CSCE 531 Spring 2006

state 0state 0

DIGIT shift, and go to state 1DIGIT shift, and go to state 1

'(' shift, and go to state 2'(' shift, and go to state 2

expr go to state 3expr go to state 3

state 1state 1

expr -> DIGIT . (rule 4)expr -> DIGIT . (rule 4)

$default reduce using rule 4 (expr)$default reduce using rule 4 (expr)

44

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state 2state 2

expr -> '(' . expr ')' (rule 3)expr -> '(' . expr ')' (rule 3)

DIGIT shift, and go to state 1DIGIT shift, and go to state 1

'(' shift, and go to state 2'(' shift, and go to state 2

expr go to stateexpr go to state

– 32 – CSCE 531 Spring 2006

state 3state 3

expr -> expr . '+' expr (rule 1)expr -> expr . '+' expr (rule 1)

expr -> expr . '*' expr (rule 2)expr -> expr . '*' expr (rule 2)

$ go to state 10$ go to state 10

'+' shift, and go to state 5'+' shift, and go to state 5

'*' shift, and go to state 6'*' shift, and go to state 6

… … for states 4 through 7for states 4 through 7

– 33 – CSCE 531 Spring 2006

ConflictsConflicts

state 8state 8


expr -> expr '+' expr . (rule 1)expr -> expr '+' expr . (rule 1)




'+' [reduce using rule 1 (expr)]'+' [reduce using rule 1 (expr)]

'*' [reduce using rule 1 (expr)]'*' [reduce using rule 1 (expr)]


– 34 – CSCE 531 Spring 2006

state 9state 9



expr -> expr '*' expr . (rule 2)expr -> expr '*' expr . (rule 2)



'+' [reduce using rule 2 (expr)]'+' [reduce using rule 2 (expr)]

'*' [reduce using rule 2 (expr)]'*' [reduce using rule 2 (expr)]


– 35 – CSCE 531 Spring 2006

state 10state 10

$ go to state 11$ go to state 11

state 11state 11

$default accept$default accept

– 36 – CSCE 531 Spring 2006

Documents

– 1 – CSCE 531 Spring 2006 Lecture 9 SLR Parse Table Construction Topics SLR Parse Table Construction Sets of Items Closure(I) Readings: 4.7 Homework: