Transcript Compiler Designs and Constructions

Compiler Designs and
Constructions
Chapter 6: Top-Down Parser
Objectives:
Types
of Parsers
Backtracking Vs. Non-backtracking
PDA
Dr. Mohsen Chitsaz
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Definition:

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Alphabet: Set of Char (token)
Language: Set of Token
Sentence: a group of token
Grammar: a set of (productions) that control
the order of the occurrence of words
Syntax: a set of rules
Parser: software to check the syntax
Parsing: Process of breaking down the
lexemes
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Types of Parser

Universal Parsing Method example:
Cocke-Younger-Kasami Algorithm
•
•
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Top-Down Parsing
•
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Can parse any grammar
too inefficient to use in compiler production
Left most derivation
Bottom-up Parsing
•
Right most derivation
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Top-Down Parsing
Non-backtracking Vs. Backtracking
Large Plant
Green Plant
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Recursive Descent Parsing (Predictive
Parser)
We execute a set of recursive
procedures to process the input
There is one procedure associated with
each non-terminal of a grammar
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Example
<type>  <simple>
 <type>  ^id
 <type>  array [<simple>] of <type>
<simple> integer
 <simple>  char
 <simple>  num .. num

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Procedure Match (T:token);
Begin
If LookaHead==T then
LookaHead==NextToken
Else
Error();
End;
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Procedure Type( );
Begin
If LookaHead in {integer, char, num} then
Simple();
Else
If LookaHead == ‘^’ then
Begin
Match (‘^’);
Match (id);
End
Else
If LookaHead == array then
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Begin
Match (array);
Match (‘[‘);
Simple();
Match (‘]’);
Match (of);
Type();
End
Else
Error();
End;
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Procedure Simple();
Begin
If LookaHead == integer then
Match (integer)
Else
If LookaHead == char then
Match (char)
Else
If LookaHead == num then
Begin
Match (num);
Match (‘..’);
Match (num);
End
Else Error();
End;
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Example
<type>  <simple>
 <type>  ^id
 <type>  array [<simple>] of <type>
<simple> integer
 <simple>  char
 <simple>  num .. num

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Example
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Which production should we use?
integer
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<type>  ^id
<type>  <simple>
<simple>  integer
<simple>  char
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Example

First (simple) = {integer, char, num}
First (^id) = {^}
First (array [<simple>] of type = {array})
First (type) = {^, array, integer, char, num}
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Definition:
A  ab
 First (A) = a

A
A
 First of  &  must be disjoint

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Push Down Automata
(Non-recursive predictive Parsing)
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Push Down Automata
(Non-recursive predictive Parsing)

PDA = {Q, , H,, q0, Z, F}
 Q = finite set of States
  = set of input alphabet
 H = set of stack symbols
  = transition function (q, a, z)
 q0 = starting state
 Z = starting stack
 F = final states
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Operation on 

input
state operation
operation
 change()
 stay()

 advance()
 retain()
stack operation
 push()
 pop()
 replace()
 none()
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Example:
INPUT
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 = { (, ), -| }
H = {A, $}
q0 = {S}
Z = {$}
S
T
A
R
T
(
)
q1 A
Push (A)
State (S)
Advance
Pop
Reject
State (S)
Advance
q0 $
Push (A)
State (S)
Advance
Reject
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-|
Accept
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If input is (())-|
 Stack
Input

$
$A
$AA
$A
$
(())-|
())-|
))-|
)-|
-|
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Derivation Tree

S  (S) | 
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LL(1) Grammar (push down machine)
Scan from Left (L), Leftmost derivation (L), Look a
head 1 Token
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Definition:

A production is called NULL if the RHS of
that production is Ø
A
 A production is call NULLABLE if the RHS
can be reduced to Ø
• BA
• A
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Example of LL(1) Grammar:
1- S  AbB-|
2- S  d
3- A  C Ab
4- A  B
5- B  gSd
6- B  
7- C  a
8- C  ed
First(AbB-|) ={a,e,g, }
First(d)
= {d}
First(C Ab) = {a,e}
First(B)
= {g, }
First(gSd) = {g}
First (Ø)
= {}
First (a)
= {a}
First (ed)
= {e}
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First () = {a|  =>*a}
 Set of terminal symbols that occur at the
beginning of string derived from 
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
Follow ()= Set of input symbols that can
immediately follow 
Follow (A) = {b}
Follow (B) = {-|, b, d}
1
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S --->AbB --->BbB
1
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4
5
1
S --->AbB --->AbgSd --->AbgAbBd
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SELECT (PREDICT):
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SELECT (A->) = {First ()
If = Ø; First () U Follow (A)}
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SELECT (1) = {a,e,g} U Follow(A)={a, e, g ,b}
SELECT (2) = {d}
SELECT (3) = {a,e}
SELECT (4) = First(4) U Follow (A) = {g,b}
SELECT (5) = {g}
SELECT (6) = First(6) U Follow (B) = {-|,b,d}
SELECT (7)={a}
SELECT (8) = {e}
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Is this grammar LL(1)?
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S
A
B
C
SELECT (1)  SELECT (2) ={a,e,g,b}  {d}= Ø
SELECT (3)  SELECT (4) ={a,e}  {g,b}= Ø
SELECT (5)  SELECT (6) = {g}  {-|,b,d}= Ø
SELECT (7)  SELECT (8) = {a}  {e}= Ø
Def: Grammar is LL(1), IIF production with the
same LHS have disjoint prediction set.
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Creating the Table:
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Stack symbols=rows
Input symbols=columns
A b 
For row A, column b
=REPLACE(r), ADVANCE
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A 
For row A, column(selection set)
=REPLACE (r), RETAIN
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Ab
For row A, column b
=POP, ADVANCE
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Creating the Table:
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Row b, column b = POP, ADVANCE
Row Δ, column -|=ACCEPT
All other are ERROR
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Parsed Table
S
a
#1
b
#1
g
#1
d
#2
e
#1
-|
Rej
A
#3
#4
#4
Rej
#3
Rej
B
C
Rej
#7
#6
Rej
#5
Rej
#6
Rej
Rej
#8
#6
Rej
b
d
Δ
Rej
Rej
Ad/Pop
Rej
Rej
Rej
Rej
Ad/P
Rej
Rej
Rej
Rej
Rej
Rej
Rej
Rej
Rej
Accept
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1- Replace (Δ B b A), Retain
2- Pop, Advance
3- Replace (bAC), Retain
4- Replace (B), Retain
5- Replace (dS), Advance
6- Pop, Retain
7- Pop, Advance
8- Replace(d), Advance
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Input:
b g d d -|
Stack
Input
Production
Action
S
bgdd-|
#1
Replace (D BbA),
Retain
Δ BbA
bgdd-|
#4
Replace(B), Retain
Δ BbB
bgdd-|
#6
Pop, Retain
Δ Bb
bgdd-|
ΔB
gdd-|
#5
Replace (dS), Advance
Δ dS
dd-|
#2
Pop, Advance
Δd
d-|
Pop, Advance
Δ
-|
Accept
Pop, Advance
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Parse Tree
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Recovery in a Top-Down Parser
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Advantage of TDP is efficient error recovery.
Error: If Top of stack (token) is not the same as
Look a Head (token)
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Recovery:
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Pop stack until Top: Synchronization Token (ST)
ST: is a token that can end blocks of codes
Read input symbol until current LookaHead symbol
matches the symbol at the top of the stack or
reaches the end of input
If not end of input you are recovered
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LL(1) Grammars & Parser:
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facts:
CFG
 Leftmost Parser
 Unambiguous
 O(n)
 Can be used for automatically
generated parser
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Making Grammar: LL(1)
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1-Remove Common Prefixed (Left Factor)
 S --> aBCd
S --> aBD
 S --> aB
D -->
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D --> Cd
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<s> --> if <exp> then <action> endif;
<s> --> if <exp> then <action> else <action> endif;
<s> --> if <exp> then <action> <rest>
<rest> --> endif;
<rest> --> else <action> endif;
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2-Remove Left Recursion:E
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E --> E + T
E --> T
T --> id
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A--> A
A-->B

A-->A1 A2
A1-->B
A2-->A2
A2-->
•E-->E1E2
E1-->T
E2-->+T E2
T-->id
E2-->
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3-Remove Unreachable Products
S-->a
B-->S
S -->a
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4-Corner Substitution
S --> AB
 B -->1
 B -->2
 B -->3

•S --> a
•S --> AS
•A --> ab
•A --> cA
•S --> aB
•B -->
 S --> A1
•B --> bS
 S --> A2
•A --> ab
 S --> A3
•A --> cA
•S
-->
cAS
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5-Singleton Substitution
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S-->B
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S--> S'
S'--> B

<S> --> <LABEL> <UNLABLE>
<LABEL> --> id:
<LABEL> -->
<UNLABLE> --> id:= <EXP>;
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Singleton
Substitution
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-<S> --> id: <UNLABLE>
<S> --> <UNLABLE>
<UNLABLE> --> id:=<EXP>;
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-<S> --> id:<UNLABLE>
<S> --> id:= <EXP>;
<UNLABLE> --> id:= <EXP>;
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-<S> --> id <id-rest>
<id-rest> --> : <UNLABLE>
<id-rest> --> := <EXP>
<UNLABLE> --> id := <EXP>
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Some Grammars Can Not be LL(1)
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*If _ Then _ Else
If <exp> then <action>
If <exp> then <action> else <action>
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*S --> aBcS
S --> aBcSeS
B --> d
S --> b
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Q-Grammar:
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S-Grammar:
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A --> a1
A --> b1
A -->
A --> a1
A --> b2
A and S grammar are a LL(1) and we can make a push
down Machine
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