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You are here:Open notes-->VTU-->COMPAILER-DESIGN-10CS63-VTU-NOTES-UNIT-4

**COMPAILER DESIGN 10CS63 VTU NOTES UNIT-4**

## UNIT IV: SYNTAX ANALYSIS 3 SYLLABUS:

* Introduction to LR Parsing:

* Simple LR;

* More powerful LR parsers (excluding Efficient construction and compaction of

parsing tables) ;

* Using ambiguous grammars;

* Parser Generators.

**Constructing Canonical LR(1) Parsing Tables**

In SLR method, the state i makes a reduction by A???? when the current token is

a:

if the A????. in the Ii and a is FOLLOW(A)

In some situations, *A cannot be followed by the terminal a in a rightsentential

form when ???? and the state i are on the top stack. This means

that making reduction in this case is not correct.

S * AaAb S*AaAb*Aab*ab S*BbBa*Bba*ba

S * BbBa

A * * Aab * * ab Bba * * ba

B * * AaAb * Aa * b BbBa * Bb * a

LR(1) Item

To avoid some of invalid reductions, the states need to carry more information.

Extra information is put into a state by including a terminal symbol as a second

component in an item.

A LR(1) item is:

A * ??.??,a where a is the look-head of the LR(1) item

(a is a terminal or end-marker.)

When * ( in the LR(1) item A * ??.??,a ) is not empty, the look-head does not

have any affect.

When * is empty (A * ??.,a ), we do the reduction by A???? only if the next

input symbol is a (not for any terminal in FOLLOW(A)).

A state will contain A * ??.,a1 where {a1,...,an} * FOLLOW(A)

...

A * ??.,an

Canonical Collection of Sets of LR(1) Items

The construction of the canonical collection of the sets of LR(1) items are similar

to the construction of the canonical collection of the sets of LR(0) items, except

that closure and goto operations work a little bit different.

closure(I) is: ( where I is a set of LR(1) items)

every LR(1) item in I is in closure(I)

if A????.B??,a in closure(I) and B???? is a production rule of G; then

B??.??,b will be in the closure(I) for each terminal b in FIRST(??a) .

goto operation

If I is a set of LR(1) items and X is a grammar symbol (terminal or non-terminal),

then goto(I,X) is defined as follows:

If A * ??.X??,a in I then

every item in closure({A * *X.??,a}) will be in goto(I,X).

Construction of The Canonical LR(1) Collection

Algorithm:

C is { closure({S’??.S,$}) }

repeat the followings until no more set of LR(1) items can be added to C.

for each I in C and each grammar symbol X

if goto(I,X) is not empty and not in C

add goto(I,X) to C

goto function is a DFA on the sets in C.

A Short Notation for The Sets of LR(1) Items

A set of LR(1) items containing the following items

A * ??.??,a1

...

A * ??.??,an

can be written as

A * ??.??,a1/a2/.../an

SLR(1) Parsing table

id * = $ S L R

0 s5 s4 1 2 3

1 acc

2 s6/r5 r5

3 r2

4 s5 s4 8 7

5 r4 r4

6 s5 s4 10 9

7 r3 r3

8 r5 r5

9 r1

Canonical LR(1) Collection Example2

S’ * S

1) S *L=R

2) S *R

3) L* *R

4) L * id

5) R * L

I0:S’ ??.S,$

S * .L=R,$

S * .R,$

L * .*R,$/=

L * .id,$/=

R ??.L,$

I1:S’ *S.,$

I2:S * L.=R,$

R *L.,$

I3:S * R.,$

I4:L ??*.R,$/=

R ??.L,$/=

L* .*R,$/=

L * .id,$/=

I5:L *id.,$/=

I6:S * L=.R,$

R ??.L,$

L * .*R,$

L * .id,$

I7:L ??*R.,$/=

I8: R * L.,$/=

I9:S * L=R.,$

I10:R *L.,$

I11:L ??*.R,$

R ??.L,$

L* .*R,$

L * .id,$

I12:L *id.,$

I13:L ??*R.,$

to I6

to I7

to I8

to I4

to I5

to I10

to I11

to I12

to I9

to I10

to I11

to I12

to I13

id

S

L

L

L

R

R

R

id

id

id

R

L

*

*

*

*

I4 and I11

I5 and I12

I7 and I13

I8 and I10

Construction of LR(1) Parsing Tables

1. Construct the canonical collection of sets of LR(1) items for G’. C??{I0,...,In}

2. Create the parsing action table as follows

If a is a terminal, A????.a??,b in Ii and goto(Ii,a)=Ij then action[i,a] is

shift j.

If A????.,a is in Ii , then action[i,a] is reduce A???? where A*S’.

If S’*S.,$ is in Ii , then action[i,$] is accept.

If any conflicting actions generated by these rules, the grammar is not

LR(1).

3. Create the parsing goto table

for all non-terminals A, if goto(Ii,A)=Ij then goto[i,A]=j

4. All entries not defined by (2) and (3) are errors.

Initial state of the parser contains S’??.S,$

LR(1) Parsing Tables (for Example2)

id * = $ S L R

0 s5 s4 1 2 3

1 acc

2 s6 r5

3 r2

4 s5 s4 8 7

5 r4 r4

6 s12 s11 10 9

7 r3 r3

8 r5 r5

9 r1

10 r5

11 s12 s11 10 13

12 r4

13 r3

no shift/reduce or

no reduce/reduce conflict

*

so, it is a LR(1) grammar

LALR Parsing Tables

LALR stands for LookAhead LR.

LALR parsers are often used in practice because LALR parsing tables are smaller

than LR(1) parsing tables.

The number of states in SLR and LALR parsing tables for a grammar G are equal.

But LALR parsers recognize more grammars than SLR parsers.

yacc creates a LALR parser for the given grammar.

A state of LALR parser will be again a set of LR(1) items.

Creating LALR Parsing Tables

Canonical LR(1) Parser LALR Parser

shrink # of states

This shrink process may introduce a reduce/reduce conflict in the resulting

LALR parser (so the grammar is NOT LALR)

But, this shrik process does not produce a shift/reduce conflict.

The Core of A Set of LR(1) Items

The core of a set of LR(1) items is the set of its first component.

Ex: S * L.=R,$ S * L.=R Core

R * L.,$ R * L.

We will find the states (sets of LR(1) items) in a canonical LR(1) parser with

same cores. Then we will merge them as a single state.

I1:L * id.,= A new state: I12: L * id.,=

L * id.,$

I2:L * id.,$ have same core, merge them

We will do this for all states of a canonical LR(1) parser to get the states of the

LALR parser.

In fact, the number of the states of the LALR parser for a grammar will be equal

to the number of states of the SLR parser for that grammar.

Creation of LALR Parsing Tables

Create the canonical LR(1) collection of the sets of LR(1) items for the given

grammar.

Find each core; find all sets having that same core; replace those sets having same

cores with a single set which is their union.

C={I0,...,In} C’={J1,...,Jm} where m * n

Create the parsing tables (action and goto tables) same as the construction of the

parsing tables of LR(1) parser.

Note that: If J=I1 * ... * Ik since I1,...,Ik have same cores

cores of goto(I1,X),...,goto(I2,X) must be same.

So, goto(J,X)=K where K is the union of all sets of items having same

cores as goto(I1,X).

If no conflict is introduced, the grammar is LALR(1) grammar. (We may

only introduce reduce/reduce conflicts; we cannot introduce a shift/reduce

conflict)

Shift/Reduce Conflict

We say that we cannot introduce a shift/reduce conflict during the shrink process

for the creation of the states of a LALR parser.

Assume that we can introduce a shift/reduce conflict. In this case, a state of LALR

parser must have:

A * ??.,a and B * ??.a??,b

This means that a state of the canonical LR(1) parser must have:

A * ??.,a and B * ??.a??,c

But, this state has also a shift/reduce conflict. i.e. The original canonical LR(1)

parser has a conflict.

(Reason for this, the shift operation does not depend on lookaheads)

Reduce/Reduce Conflict

But, we may introduce a reduce/reduce conflict during the shrink process for the

creation of the states of a LALR parser.

I1 : A * ??.,a I2: A * ??.,b

B * ??.,b B * ??.,c

*

I12: A * ??.,a/b reduce/reduce conflict

B * ??.,b/c

Canonical LALR(1) Collection Example2

S’ * S

1) S *L=R

2) S *R

3) L* *R

4) L * id

5) R * L

I0:S’ ??.S,$

S * .L=R,$

S * .R,$

L * .*R,$/=

L * .id,$/=

R ??.L,$

I1:S’ *S.,$

I2:S * L.=R,$

R *L.,$

I3:S * R.,$

I411:L ??*.R,$/=

R * .L,$/=

L* .*R,$/=

L * .id,$/=

I512:L *id.,$/=

I6:S * L=.R,$

R ??.L,$

L * .*R,$

L * .id,$

I713:L ??*R.,$/=

I810: R * L.,$/=

I9:S * L=R.,$

to I6

to I713

to I810

to I411

to I512

to I810

to I411

to I512

to I9

S

L

L

L

R

R

id

id

id

R

*

*

*

Same Cores

I4 and I11

I5 and I12

I7 and I13

I8 and I10

Using Ambiguous Grammars

All grammars used in the construction of LR-parsing tables must be un-

ambiguous.

Can we create LR-parsing tables for ambiguous grammars

Yes, but they will have conflicts.

We can resolve these conflicts in favor of one of them to disambiguate the

grammar.

At the end, we will have again an unambiguous grammar.

Why we want to use an ambiguous grammar

Some of the ambiguous grammars are much natural, and a corresponding

unambiguous grammar can be very complex.

Usage of an ambiguous grammar may eliminate unnecessary reductions.

Ex.

E * E+T | T

E * E+E | E*E | (E) | id T * T*F | F

F * (E) | id

Sets of LR(0) Items for Ambiguous Grammar

I0: E’ ??.E

E * .E+E

E * .E*E

E * .(E)

E * .id

I1: E’ *E.

E * E .+E

E * E .*E

I2: E * (.E)

E * .E+E

E * .E*E

E * .(E)

E * .id

I3: E * id.

I4: E * E +.E

E * .E+E

E * .E*E

E * .(E)

E * .id

I5: E * E *.E

E * .E+E

E * .E*E

E * .(E)

E * .id

I6: E * (E.)

E * E.+E

E * E.*E

I7: E * E+E.

E * E.+E

E * E.*E

I8: E * E*E.

E * E.+E

E * E.*E

I9: E * (E).

I5

)

E

E

E

E

*

+

+

+

+

*

*

*

(

(

(

(

id

id

id

id

I4

I2

I2

I3

I3

I4

I4

I5

I5

SLR-Parsing Tables for Ambiguous Grammar

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

State I8 has shift/reduce conflicts for symbols + and *.

I0 I1 I5 I7

E * E

when current token is *

shift ?* is right-associative

reduce ?* is left-associative

when current token is +

shift ?+ has higher precedence than *

reduce ?* has higher precedence than +

SLR-Parsing Tables for Ambiguous Grammar

id + * ( ) $ E

0 s3 s2 1

1 s4 s5 acc

2 s3 s2 6

3 r4 r4 r4 r4

4 s3 s2 7

5 s3 s2 8

6 s4 s5 s9

7 r1 s5 r1 r1

8 r2 r2 r2 r2

9 r3 r3 r3 r3

Action Goto

Error Recovery in LR Parsing

An LR parser will detect an error when it consults the parsing action

table and finds an error entry. All empty entries in the action table are

error entries.

Errors are never detected by consulting the goto table.

An LR parser will announce error as soon as there is no valid

continuation for the scanned portion of the input.

A canonical LR parser (LR(1) parser) will never make even a single

reduction before announcing an error.

The SLR and LALR parsers may make several reductions before

announcing an error.

But, all LR parsers (LR(1), LALR and SLR parsers) will never shift an

erroneous input symbol onto the stack.

Panic Mode Error Recovery in LR Parsing

Scan down the stack until a state s with a goto on a particular

nonterminal A is found. (Get rid of everything from the stack before this

state s).

Discard zero or more input symbols until a symbol a is found that can

legitimately follow A.

The symbol a is simply in FOLLOW(A), but this may not work for all situations.

The parser stacks the nonterminal A and the state goto[s,A], and it

resumes the normal parsing.

This nonterminal A is normally is a basic programming block (there can

be more than one choice for A).

stmt, expr, block, ...

Phrase-Level Error Recovery in LR Parsing

Each empty entry in the action table is marked with a specific error routine.

An error routine reflects the error that the user most likely will make in that case.

An error routine inserts the symbols into the stack or the input (or it deletes the

symbols from the stack and the input, or it can do both insertion and deletion).

missing operand

unbalanced right parenthesis