Ll(1) Parser in Compilers

MODEL OF COMPILER FRONT END 2
Front End
Also called parsing , where
generates parse tree
Syntax analysis

PARSING 3
When the parser starts constructing the
parse tree from the start symbol and then
tries to transform the start symbol to the
input, it is called top-down parsing.
Where bottom-up parsing starts with
the input symbols and tries to construct
the parse tree up to the start symbol.

TOP DOWN PERSER 4
Predictive parser is a recursive descent
parser, which has the capability to predict
which production is to be used to replace
the input string. The predictive parser
does not suffer from backtracking.

PREDICTIVE PARSER 5
Predictive parsing uses a stack and
a parsing table to parse the input
and generate a parse tree.
Both the stack and the input
contains an end symbol $to denote
that the stack is empty and the input
is consumed.
The parser refers to the parsing
table to take any decision on the
input and stack element
combination.

LL(1) PARSER 6
 An LL parser is called an LL(k) parser if
it uses k tokens of look ahead when
parsing a sentence.
 LL grammars, particularly LL(1)
grammars, as parsers are easy to
construct, and many computer
languages are designed to be LL(1) for
this reason.
 The 1 stands for using one input symbol
of look ahead at each step to make
parsing action decision.

CONTINUE…
LL(k) parsers must predict which production replace a non-terminal with as soon as
they see the non-terminal. The basic LL algorithm starts with a stack containing [S, $]
(top to bottom) and does whichever of the following is applicable until done:
 If the top of the stack is a non-terminal, replace the top of the stack with one of
the productions for that non-terminal, using the next k input symbols to decide
which one (without moving the input cursor), and continue.
 If the top of the stack is a terminal, read the next input token. If it is the same
terminal, pop the stack and continue. Otherwise, the parse has failed and the
algorithm finishes.
 If the stack is empty, the parse has succeeded and the algorithm finishes. (We
assume that there is a unique EOF-marker $ at the end of the input.)
So look ahead meaning is - looking at input tokens without moving the input
cursor.
7

PRIME REQUIREMENT OF LL(1)
 The grammar must be -
 no left factoring
 no left recursion
 FIRST() & FOLLOW()
 Parsing Table
 Stack Implementation
 Parse Tree
8

LEFT FACTORING
 A grammar is said to be left factored when it is of the form –
A -> αβ1 | αβ2 | αβ3 | …… | αβn | γ
 The productions start with the same terminal (or set of terminals).
 When the choice between two alternative A-productions is not clear, we
may be able to rewrite the productions to defer the decision until enough
of the input has been seen to make the right choice.
For the grammar
A -> αβ1 | αβ2 | αβ3 | …… | αβn | γ
The equivalent left factored grammar will be –
A -> αA’ | γ
A’ -> β1 | β2 | β3 | …… | βn
10

CONTINUE…
 For example :
the input string is - aab & grammar is
S ->aAb|aA|ab
A ->bAc|ab
After removing left factoring -
S ->aA’
A’ ->Ab|A|b
A ->ab|bAc
11

RECURSION
RECURSION:
The process in which a function calls itself directly or indirectly is called recursion
and the corresponding function is called as recursive function.
TYPES OF RECURSION
LEFT RECURSION RIGHT RECURSION
13

Left Recursion Right Recursion
For grammar: For grammar:
A -> A | β A ->  A| β
A
A  A
A   A
A   A
β  A
β
This parse tree generate β  * This parse tree generate  * β
14

Right recursion-
 A production of grammar is said to have right recursion if
the right most variable RHS is same as
variable of its LHS. e.g. A ->  A| β
 A grammar containing a production having right recursion is
called as a right recursive grammar.
 Right recursion does not create any problem for the top
down parsers.
 Therefore, there is no need of eliminating right recursion
from the grammar.
15

Left recursion-
 A production of grammar is said to have left
recursion if the leftmost variable of its RHS is same
as variable of its LHS. e.g. A -> A | β
 A grammar containing a production having left
recursion is called as a left recursive grammar.
 Left recursion is eliminated because top down
parsing method can not handle left recursive
grammar.
16

Left Recursion
A grammar is left recursive if it has a nonterminal A such that there is a
derivation
A -> A | β for some string .
Immediate/direct left recursion:
A production is immediately left recursive if its left hand side and the head of its
right hand side are the same symbol, e.g. A ->A  , where α is  sequence
of non terminals and terminals.
Indirect left recursion:
Indirect left recursion occurs when the definition of left recursion is satisfied via
several substitutions. It entails a set of rules following the pattern
. A → Br
B → Cs
C → At
Here, starting with a, we can derive A -> Atsr
17

Elimination of Left-Recursion
 Suppose the grammar were
A  A | 
How could the parser decide how many times to use the production A 
A before using the production A -->  ?
 Left recursion in a production may be removed by transforming the
grammar in the following way.
Replace
A  A | 
With
A  A'
A'  A' | 
18

Continue…
The case of several immediate left recursive  -productions. Assume
that the set of all  -productions has the form
A → A 1 | A 2 | · · · | A m | β1 | β2| · · · | βn
Represents all the  -productions of the grammar, and no βi begins
with A, then we can replace these  -productions by
A →β1A′ | β2A′| · · · | βnA′
A′ → 1A′ | 2A′ | · · · | mA′ | 
20

Example of elimination indirect left
recursion:
S A A | 0
A S S | 1
Considering the ordering S, A, we get:
S A A | 0
A S | 0S | 1
And removing immediate left recursion, we get
S A A | 0
A 0S A′ | 1A′
A′  ε | AS A′
22

Why using FIRST and FOLLOW:
During parsing FIRST and FOLLOW help us to choose
which production to apply , based on the next input signal.
We know that we need of backtracking in syntax analysis, which is
really a complex process to implement. There can be easier way to
sort out this problem by using FIRST AND FOLLOW.
If the compiler would have come to know in advance, that what is the
“first character of the string produced when a production rule is
applied”, and comparing it to the current character or token in the input
string it sees, it can wisely take decision on which production rule to
apply .
FOLLOW is used only if the current non terminal can derive ε .
24

Rules of FIRST
FIRST always find out the terminal symbol from the grammar.
When we check out FIRST for any symbol then if we find any
terminal symbol in first place then we take it. And not to see the
next symbol.
 If a grammar is
A → a then FIRST ( A )={ a }
 If a grammar is
A → a B then FIRST ( A )={ a }
25

Rules of FIRST
 If a grammar is
A → aB ǀ ε then FIRST ( A )={ a, ε }
 If a grammar is
A → BcD ǀ ε
B → eD ǀ ( A )
Here B is non terminal. So, we check the transition of B and
find the FIRST of A.
then FIRST ( A )={ e,( , ε }
26

Rules of FOLLOW
For doing FOLLOW operation we need FIRST operation mostly. In FOLLOW
we use a $ sign for the start symbol. FOLLOW always check the right
portion of the symbol.
 If a grammar is
A → BAc ; A is start symbol.
Here firstly check if the selected symbol stays in right side of the grammar.
We see that c is right in A.
then FOLLOW (A) = {c , $ }
27

Rules of FOLLOW
 If a grammar is
A → BA’
A' →*Bc
Here we see that there is nothing at the right side of A' . So
FOLLOW ( A' )= FOLLOW ( A )= { $ }
Because A' follows the start symbol.
28

Rules of FOLLOW
 If a grammar is
A → BC
B → Td
C →*D ǀ ε
When we want to find FOLLOW (B),we see that B follows by C . Now
put the FIRST( C) in the there.
FIRST(C)={*, ε }.
But when the value is € it follows the parents symbol. So
FOLLOW(B)={*,$ }
29

Example of FIRST and FOLLOW
Symbol FIRST FOLLOW
E
E’
T
T’
F
GRAMMAR:
E -> TE'
E'-> +TE'|ε
T -> FT'
T' -> *FT'|ε
F -> (E)|id
30

Symbol FIRST FOLLOW
E { ( , id }
E'
T
T'
F
GRAMMAR:
E -> TE'
E'-> +TE'|ε
T -> FT'
T' -> *FT'|ε
F -> (E)|id
31

Symbol FIRST FOLLOW
E { ( , id }
E' { + , ε }
T
T'
F
GRAMMAR:
E -> TE'
E'-> +TE'|ε
T -> FT'
T' -> *FT'|ε
F -> (E)|id
32

Symbol FIRST FOLLOW
E { ( , id }
E' { + , ε }
T { id , ( }
T'
F
GRAMMAR:
E -> TE'
E'-> +TE'|ε
T -> FT'
T' -> *FT'|ε
F -> (E)|id
33

Symbol FIRST FOLLOW
E { ( , id }
E' { + , ε }
T { id , ( }
T' { * , ε }
F
GRAMMAR:
E -> TE'
E'-> +TE'|ε
T -> FT'
T' -> *FT'|ε
F -> (E)|id
34

Symbol FIRST FOLLOW
E { ( , id }
E' { + , ε }
T { id , ( }
T' { * , ε }
F { id , ( }
GRAMMAR:
E -> TE'
E'-> +TE'|ε
T -> FT'
T' -> *FT'|ε
F -> (E)|id
35

Symbol FIRST FOLLOW
E { ( , id } { $ , ) }
E' { + , ε }
T { id , ( }
T' { * , ε }
F { id , ( }
GRAMMAR:
E -> TE'
E'-> +TE'|ε
T -> FT'
T' -> *FT'|ε
F -> (E)|id
36

Symbol FIRST FOLLOW
E { ( , id } { $ , ) }
E' { + , ε } { $ , ) }
T { id , ( }
T' { * , ε }
F { id , ( }
GRAMMAR:
E -> TE'
E'-> +TE'|ε
T -> FT'
T' -> *FT'|ε
F -> (E)|id
37

Symbol FIRST FOLLOW
E { ( , id } { $ , ) }
E' { + , ε } { $ , ) }
T { id , ( } { $ , ) ,+ }
T' { * , ε }
F { id , ( }
GRAMMAR:
E -> TE'
E'-> +TE'|ε
T -> FT'
T' -> *FT'|ε
F -> (E)|id
38

Symbol FIRST FOLLOW
E { ( , id } { $ , ) }
E' { + , ε } { $ , ) }
T { id , ( } { $ , ) ,+ }
T' { * , ε } { $ , ) , + }
F { id , ( }
GRAMMAR:
E -> TE'
E'-> +TE'|ε
T -> FT'
T' -> *FT'|ε
F -> (E)|id
39

Symbol FIRST FOLLOW
E { ( , id } { $ , ) }
E' { + , ε } { $ , ) }
T { id , ( } { $ , ) ,+ }
T' { * , ε } { $ , ) , + }
F { id , ( } { $ , ) , + , * }
GRAMMAR:
E -> TE'
E'-> +TE'|ε
T -> FT'
T' -> *FT'|ε
F -> (E)|id
40

Example of LL(1) grammar
E -> TE’
E’ -> +TE’|ε
T -> FT’
T’ -> *FT’|ε
F -> (E)|id
42

TABLE:
PARSING
TABLE
TABLE:
FIRST & FOLLOW
43
Production Symbol FOLLOW
E -> TE’ { ( , id } { $ , ) }
E’ -> +TE’|ε { + , ε } { $ , ) }
T -> FT’ { ( , id } { + , $ , ) }
T’ -> *FT’|ε { * , ε } { + , $ , ) }
F -> (E)|id { ( , id } { *, + , $ , ) }
Non
Terminal
INPUT SYMBOLS
id + * ( ) $
E
E’
T
T’
F

TABLE:
PARSING
TABLE
TABLE:
FIRST & FOLLOW
44
E -> TE’ { ( , id } { $ , ) }
E’ -> +TE’|ε { + , ε } { $ , ) }
T -> FT’ { ( , id } { + , $ , ) }
T’ -> *FT’|ε { * , ε } { + , $ , ) }
F -> (E)|id { ( , id } { *, + , $ , ) }
Non
Terminal
INPUT SYMBOLS
id + * ( ) $
E E -> TE’
E’
T
T’
F

TABLE:
PARSING
TABLE
TABLE:
FIRST & FOLLOW
45
E -> TE’ { ( , id } { $ , ) }
E’ -> +TE’|ε { + , ε } { $ , ) }
T -> FT’ { ( , id } { + , $ , ) }
T’ -> *FT’|ε { * , ε } { + , $ , ) }
F -> (E)|id { ( , id } { *, + , $ , ) }
Non
Terminal
INPUT SYMBOLS
id + * ( ) $
E E -> TE’ E -> TE’
E’
T
T’
F

TABLE:
PARSING
TABLE
TABLE:
FIRST & FOLLOW
46
E -> TE’ { ( , id } { $ , ) }
E’ -> +TE’|ε { + , ε } { $ , ) }
T -> FT’ { ( , id } { + , $ , ) }
T’ -> *FT’|ε { * , ε } { + , $ , ) }
F -> (E)|id { ( , id } { *, + , $ , ) }
Non
Terminal
INPUT SYMBOLS
id + * ( ) $
E E -> TE’ E -> TE’
E’ E’-> +TE’
T
T’
F

TABLE:
PARSING
TABLE
TABLE:
FIRST & FOLLOW
47
E -> TE’ { ( , id } { $ , ) }
E’ -> +TE’|ε { + , ε } { $ , ) }
T -> FT’ { ( , id } { + , $ , ) }
T’ -> *FT’|ε { * , ε } { + , $ , ) }
F -> (E)|id { ( , id } { *, + , $ , ) }
Non
Terminal
INPUT SYMBOLS
id + * ( ) $
E E -> TE’ E -> TE’
E’ E’-> +TE’ E’ -> ε E’ -> ε
T
T’
F

TABLE:
PARSING
TABLE
TABLE:
FIRST & FOLLOW
48
E -> TE’ { ( , id } { $ , ) }
E’ -> +TE’|ε { + , ε } { $ , ) }
T -> FT’ { ( , id } { + , $ , ) }
T’ -> *FT’|ε { * , ε } { + , $ , ) }
F -> (E)|id { ( , id } { *, + , $ , ) }
Non
Terminal
INPUT SYMBOLS
id + * ( ) $
E E -> TE’ E -> TE’
E’ E’-> +TE’ E’ -> ε E’ -> ε
T T -> FT’
T’
F

TABLE:
PARSING
TABLE
TABLE:
FIRST & FOLLOW
49
E -> TE’ { ( , id } { $ , ) }
E’ -> +TE’|ε { + , ε } { $ , ) }
T -> FT’ { ( , id } { + , $ , ) }
T’ -> *FT’|ε { * , ε } { + , $ , ) }
F -> (E)|id { ( , id } { *, + , $ , ) }
Non
Terminal
INPUT SYMBOLS
id + * ( ) $
E E -> TE’ E -> TE’
E’ E’-> +TE’ E’ -> ε E’ -> ε
T T -> FT’ T -> FT’
T’
F

TABLE:
PARSING
TABLE
TABLE:
FIRST & FOLLOW
50
E -> TE’ { ( , id } { $ , ) }
E’ -> +TE’|ε { + , ε } { $ , ) }
T -> FT’ { ( , id } { + , $ , ) }
T’ -> *FT’|ε { * , ε } { + , $ , ) }
F -> (E)|id { ( , id } { *, + , $ , ) }
Non
Terminal
INPUT SYMBOLS
id + * ( ) $
E E -> TE’ E -> TE’
E’ E’-> +TE’ E’ -> ε E’ -> ε
T T -> FT’ T -> FT’
T’ T’ -> *FT’
F

TABLE:
PARSING
TABLE
TABLE:
FIRST & FOLLOW
51
E -> TE’ { ( , id } { $ , ) }
E’ -> +TE’|ε { + , ε } { $ , ) }
T -> FT’ { ( , id } { + , $ , ) }
T’ -> *FT’|ε { * , ε } { + , $ , ) }
F -> (E)|id { ( , id } { *, + , $ , ) }
Non
Terminal
INPUT SYMBOLS
id + * ( ) $
E E -> TE’ E -> TE’
E’ E’-> +TE’ E’ -> ε E’ -> ε
T T -> FT’ T -> FT’
T’ T’ -> ε T’ -> *FT’ T’ -> ε T’ -> ε
F

TABLE:
PARSING
TABLE
TABLE:
FIRST & FOLLOW
52
E -> TE’ { ( , id } { $ , ) }
E’ -> +TE’|ε { + , ε } { $ , ) }
T -> FT’ { ( , id } { + , $ , ) }
T’ -> *FT’|ε { * , ε } { + , $ , ) }
F -> (E)|id { ( , id } { *, + , $ , ) }
Non
Terminal
INPUT SYMBOLS
id + * ( ) $
E E -> TE’ E -> TE’
E’ E’-> +TE’ E’ -> ε E’ -> ε
T T -> FT’ T -> FT’
T’ T’ -> ε T’ -> *FT’ T’ -> ε T’ -> ε
F F -> id

TABLE:
PARSING
TABLE
TABLE:
FIRST & FOLLOW
53
E -> TE’ { ( , id } { $ , ) }
E’ -> +TE’|ε { + , ε } { $ , ) }
T -> FT’ { ( , id } { + , $ , ) }
T’ -> *FT’|ε { * , ε } { + , $ , ) }
F -> (E)|id { ( , id } { *, + , $ , ) }
Non
Terminal
INPUT SYMBOLS
id + * ( ) $
E E -> TE’ E -> TE’
E’ E’-> +TE’ E’ -> ε E’ -> ε
T T -> FT’ T -> FT’
T’ T’ -> ε T’ -> *FT’ T’ -> ε T’ -> ε
F F -> id F -> (E)

Continue…
54
TABLE: PARSING TABLE
Non
Terminal
INPUT SYMBOLS
id + * ( ) $
E E -> TE’ E -> TE’
E’ E’-> +TE’ E’ -> ε E’ -> ε
T T -> FT’ T -> FT’
T’ T’ -> ε T’ -> *FT’ T’ -> ε T’ -> ε
F F -> id F -> (E)
 This grammar is LL(1).
 So, the parse tree can be derived from the stack
implementation of the given parsing table.

 There are grammars which may requite LL(1) parsing.
 For e.g. Look at next grammar…..
55
Continue…

Continue…
GRAMMAR:
S  iEtSS’ | a
S’  eS |ε
E  b
SYMBOL FIRST FOLLOW
S a , i $ , e
S’ e , ε $ , e
E b t
TABLE: FIRST & FOLLOW
56

TABLE:
PARSING TABLE
TABLE:
FAST & FOLLOW
57
SYMBOL FIRST FOLLOW
S  iEtSS’ | a
a , i $ , e
S’  eS |ε
e, ε $ , e
E  b
b t
Non
Terminal
INPUT SYMBOLS
a b e i t $
S
S’
E

TABLE:
PARSING TABLE
TABLE:
FAST & FOLLOW
58
SYMBOL FIRST FOLLOW
S  iEtSS’ | a
a , i $ , e
S’  eS |ε
e, ε $ , e
E  b
b t
Non
Terminal
INPUT SYMBOLS
a b e i t $
S Sa
S’
E

TABLE:
PARSING TABLE
TABLE:
FAST & FOLLOW
59
SYMBOL FIRST FOLLOW
S  iEtSS’ | a
a , i $ , e
S’  eS |ε
e, ε $ , e
E  b
b t
Non
Terminal
INPUT SYMBOLS
a b e i t $
S Sa
SiEtSS
’
S’
E

TABLE:
PARSING TABLE
TABLE:
FAST & FOLLOW
60
SYMBOL FIRST FOLLOW
S  iEtSS’ | a
a , i $ , e
S’  eS |ε
e, ε $ , e
E  b
b t
Non
Terminal
INPUT SYMBOLS
a b e i t $
S Sa
SiEtSS
’
S’ S’  eS
E

TABLE:
PARSING TABLE
TABLE:
FAST & FOLLOW
61
SYMBOL FIRST FOLLOW
S  iEtSS’ | a
a , i $ , e
S’  eS |ε
e, ε $ , e
E  b
b t
Non
Terminal
INPUT SYMBOLS
a b e i t $
S Sa
SiEtSS
’
S’
S’  eS
S’ε
S’ε
E

TABLE:
PARSING TABLE
TABLE:
FAST & FOLLOW
62
SYMBOL FIRST FOLLOW
S  iEtSS’ | a
a , i $ , e
S’  eS |ε
e, ε $ , e
E  b
b t
Non
Terminal
INPUT SYMBOLS
a b e i t $
S Sa
SiEtSS
’
S’
S’  eS
S’ε
S’ε
E E  b

TABLE:
PARSING TABLE
TABLE:
FAST & FOLLOW
63
AMBIGUITY
SYMBOL FIRST FOLLOW
S  iEtSS’ | a
a , i $ , e
S’  eS |ε
e, ε $ , e
E  b
b t
Non
Terminal
INPUT SYMBOLS
a b e i t $
S Sa
SiEtSS
’
S’
S’  eS
S’ε
S’ε
E E  b

Continue…
 The grammar is ambiguous and it is evident by the fact that
we have two entries corresponding to M[S’,e] containing
S’  ε and S’  eS.
 Note that the ambiguity will be solved if we use LL(2) parser, i.e.
Always see for the two input symbols.
 LL(1) grammars have distinct properties.
- No ambiguous grammar or left recursive grammar
can be LL(1).
 Thus , the given grammar is not LL(1).
64

STACK Implementation
 The predictive parser uses an explicit stack to keep track of pending
non-terminals. It can thus be implemented without recursion.
 Note that productions output are tracing out a lefmost derivation
 The grammar symbols on the stack make up left-sentential forms
66

LL(1) Stack
 The input buffer contains the string to be parsed; $ is the end-
of-input marker
 The stack contains a sequence of grammar symbols
 Initially, the stack contains the start symbol of the grammar on
the top of $.
67

LL(1) Stack
The parser is controlled by a program that behaves as follows:
 The program considers X, the symbol on top of the stack, and a, the
current input symbol.
 These two symbols, X and a determine the action of the parser.
 There are three possibilities.
68

LL(1) Stack
1. X  a  $,
the parser halts and annouces successful completion.
2. X  a  $
the parser pops x off the stack and advances input pointer to next
input symbol
3. If X is a nonterminal, the program consults entry M[x,a] of parsing
table M.
If the entry is a production M[x,a] = {x → uvw } then the
parser replaces x on top of the stack by wvu (with u on top).
As output, the parser just prints the production used:
x → uvw .
69

LL(1) Stack
Example:
Let’s parse the input
string
id+idid
Using the nonrecursive
LL(1) parser
70
Grammar:
E -> TE'
E'-> +TE'|ε
T -> FT'
T' -> *FT'|ε
F -> (E)|id

71
id
E
+ id  id
$
$
stack Parsing
Table

Parsing Table
72
id + * ( ) $
E E →TE' E →TE'
E' E' →
+TE'
E' → E' →
T T →FT' T →FT'
T' T' →  T →*FT' T' → T' →
F F → id F →(E )

73
id
E
+ id  id
$
$
stack Parsing
Table
E →T E'

74
id + id  id
$
$
stack Parsing
Table M
T →
T
E'
F T'
Non
Terminal
INPUT SYMBOLS
id + * ( ) $
E E -> TE’ E -> TE’
E’ E' -> +TE’ E’ -> ε E’ -> ε
T T -> FT’ T -> FT’
T’ T’ -> ε T’ -> *FT’ T’ -> ε T’ -> ε
F F -> id F -> (E)

75
T'
id + id  id
$
$
stack Parsing
Table M
→
E'
F
F id
Non
Terminal
INPUT SYMBOLS
id + * ( ) $
E E -> TE’ E -> TE’
E’ E' -> +TE’ E’ -> ε E’ -> ε
T T -> FT’ T -> FT’
T’ T’ -> ε T’ -> *FT’ T’ -> ε T’ -> ε
F F -> id F -> (E)

76
T'
id + id  id
$
$
stack Parsing
Table M
E'
id
Non
Terminal
INPUT SYMBOLS
id + * ( ) $
E E -> TE’ E -> TE’
E’ E' -> +TE’ E’ -> ε E’ -> ε
T T -> FT’ T -> FT’
T’ T’ -> ε T’ -> *FT’ T’ -> ε T’ -> ε
F F -> id F -> (E)

77
T'
+ id  id
$
$
stack Parsing
Table M
→
E'
T' 
id
Non
Terminal
INPUT SYMBOLS
id + * ( ) $
E E -> TE’ E -> TE’
E’ E' -> +TE’ E’ -> ε E’ -> ε
T T -> FT’ T -> FT’
T’ T’ -> ε T’ -> *FT’ T’ -> ε T’ -> ε
F F -> id F -> (E)

78
+ id  id
$
$
stack Parsing
Table M
→
E'
E' +
id
E'T
Non
Terminal
INPUT SYMBOLS
id + * ( ) $
E E -> TE’ E -> TE’
E’ E' -> +TE’ E’ -> ε E’ -> ε
T T -> FT’ T -> FT’
T’ T’ -> ε T’ -> *FT’ T’ -> ε T’ -> ε
F F -> id F -> (E)

79
+ id  id
$
$
stack Parsing
Table M
E'
+
id
T
Non
Terminal
INPUT SYMBOLS
id + * ( ) $
E E -> TE’ E -> TE’
E’ E' -> +TE’ E’ -> ε E’ -> ε
T T -> FT’ T -> FT’
T’ T’ -> ε T’ -> *FT’ T’ -> ε T’ -> ε
F F -> id F -> (E)

80
MATCHED STACK INPUT ACTION
E$ id+id * id$
TE’$ id+id * id$ E->TE’
FT’E’$ id+id * id$ T->FT’
id T’E’$ id+id * id$ F->id
id T’E’$ +id * id$ Match id
id E’$ +id * id$ T’->Є
id +TE’$ +id * id$ E’-> +TE’
id+ TE’$ id * id$ Match +
id+ FT’E’$ id * id$ T-> FT’
id+ idT’E’$ id * id$ F-> id
id+id T’E’$ * id$ Match id
id+id * FT’E’$ * id$ T’-> *FT’
id+id * FT’E’$ id$ Match *
id+id * idT’E’$ id$ F-> id
id+id * id T’E’$ $ Match id
id+id * id E’$ $ T’-> Є
id+id * id $ $ E’-> Є

LL(1) Parse Tree
 Top-down parsing expands a parse tree from the start
symbol to the leaves
 Always expand the leftmost non-terminal
82

id+idid
83E
T
E'
F
id
T'

E'
T+
F T'
id

* F T'
id 
DONE…

Ll(1) Parser in Compilers

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Editor's Notes