Compiler Construction

1
Compiler Construction

• Sohail Aslam
• Lecture 19

2
LL(1) Table Construction

• For each production A ? a
• 1. for each terminal a in FIRST(a), add A ? a to
  MA,a.
• 2. If e is in FIRST(a), add A ? a to MA,b for
  each terminal b in FOLLOW(A).

3
LL(1) Table Construction

• For each production A ? a
• 1. for each terminal a in FIRST(a), add A ? a to
  MA,a.
• 2. If e is in FIRST(a), add A ? a to MA,b for
  each terminal b in FOLLOW(A).

4
LL(1) Table Construction

• For each production A ? a
• 1. for each terminal a in FIRST(a), add A ? a to
  MA,a.
• 2. If e is in FIRST(a), add A ? a to MA,b for
  each terminal b in FOLLOW(A).

5
LL(1) Table Construction

• (2 cont.)If e is in FIRST(a), and is in
  FOLLOW(A), add A ? a to MA,.

6
LL(1) Table Construction

• Make each undefined entry of M be error.

7
LL(1) Table Construction

• Let us apply the algorithm to the expression
  grammar.

8
LL(1) Table Construction

• Since FIRST(TE ') FIRST(T ) (, id
  ,production E ?TE' cause ME,( and ME,id to
  get E ?TE'

9
id ( )
E E ?TE' E ?TE'
E' E' ? TE' E' ?e E' ?e
T T ?FT' T ?FT'
T' T' ?e T ?FT' T' ?e T' ?e
F F ? id F ?(E )
10
LL(1) Table Construction

• Production E' ? TE' causes ME', to get E'
  ?TE'

11
id ( )
E E ?TE' E ?TE'
E' E' ? TE' E' ?e E' ?e
T T ?FT' T ?FT'
T' T' ?e T ?FT' T' ?e T' ?e
F F ? id F ?(E )
12
LL(1) Table Construction

• Production E' ? e causes ME',) and ME', to
  get E' ? e since FOLLOW (E' ) ),

13
id ( )
E E ?TE' E ?TE'
E' E' ? TE' E' ?e E' ?e
T T ?FT' T ?FT'
T' T' ?e T ?FT' T' ?e T' ?e
F F ? id F ?(E )
14
LL(1) Table Construction

• And so on.
• The final parsing table produced is

15
LL(1) Parsing Table
id ( )
E E ?TE' E ?TE'
E' E' ? TE' E' ?e E' ?e
T T ?FT' T ?FT'
T' T' ?e T ?FT' T' ?e T' ?e
F F ? id F ?(E )
16
Left Factoring

• Consider the grammar
• E ? T E TT ? int int? T (E)

17
Left Factoring

• E ? T E TT ? int int? T (E)

Impossible to predict because for T, two
productions start with int
18
Left Factoring

• E ? T E TT ? int int? T (E)

For E, it is not clear how to predict
19
Left Factoring

• A grammar must be left factored before use for
  predictive parsing

20
Left Factoring

• If a ? e, replace all productions A ? ab1 ab2
  .... abn g
• with A ? a Z g Z ? b1 b2 .... bn
• where Z is new nonterminal

21
Left Factoring

• If a ? e, replace all productions A ? ab1 ab2
  .... abn g
• with A ? a Z g Z ? b1 b2 .... bn
• where Z is new nonterminal

22
Left Factoring

• A graphical explanation

23
Left Factoring

• becomes

b1
b2
aZ
b3
24
Left Factoring

• Consider following fragment of expression grammar
• Factor ? id
• id ExprList
• id ( ExprList )

25
Left Factoring

• Factor ? id
• id ExprList
• id ( ExprList )

FIRST(rhs1) id
FIRST(rhs2) id
FIRST(rhs3) id
26
Left Factoring

• after left factoring
• Factor ? id Args
• Args ? ExprList
• ( ExprList )
• e

27
Left Factoring

• Factor ? id Args
• Args ? ExprList
• ( ExprList )
• e

FIRST(rhs1) id
FIRST(rhs2)
FIRST(rhs3) (
FIRST(rhs4) FOLLOW(Factor)
28
Left Factoring
id

Factor
id
ExprList
(
)
id
ExprList
No basis for choice
29
Left Factoring

Factor
ExprList
id
(
)
ExprList
correct choice possible
30
Left Factoring

• QuestionBy eliminating left recursion and left
  factoring, can we transform an arbitrary CFG to a
  form where it meets the LL(1) condition (and can
  be parsed predictively with a single token
  lookahead?)

31
Left Factoring

• AnswerGiven a CFG that does not meet the LL(1)
  condition, it is undecidable whether or not an
  equivalent LL(1) grammar exists