Top-Down Parsing. Identify a leftmost derivation for an input string Why ? By always replacing the leftmost non-terminal symbol via a production rule, we are guaranteed of developing a parse tree in a left-to-right fashion that is consistent with scanning the input. - PowerPoint PPT Presentation
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CH4.1 314ALL Dr. Mohamed Ramadan Saady Top-Down Parsing Top-Down Parsing • Identify a leftmost derivation for an input string • Why ? • By always replacing the leftmost non-terminal symbol via a production rule, we are guaranteed of developing a parse tree in a left-to-right fashion that is consistent with scanning the input. • A aBc adDc adec (scan a, scan d, scan e, scan c - accept!) • Recursive-descent parsing concepts •Predictive parsing • Recursive / Brute force technique • non-recursive / table driven
Transcript
CH4.1
314ALL
Dr. Mohamed Ramadan Saady
Top-Down ParsingTop-Down Parsing
• Identify a leftmost derivation for an input string
• Why ?
• By always replacing the leftmost non-terminal symbol via a production rule, we are guaranteed of developing a parse tree in a left-to-right fashion that is consistent with scanning the input.
• A aBc adDc adec (scan a, scan d, scan e, scan c - accept!)
• Recursive-descent parsing concepts
•Predictive parsing
• Recursive / Brute force technique
• non-recursive / table driven
• Error recovery
• Implementation
CH4.2
314ALL
Dr. Mohamed Ramadan Saady
Top-Down ParsingTop-Down Parsing
From Grammar to Parser, take IFrom Grammar to Parser, take I
• May require backtracking to correct a wrong choice.
• Example: S c A d A ab | a
input: cad
cad S
c dA
cadS
c dA
a b
cadS
c dA
a b Problem: backtrack
cadS
c dA
a
cadS
c dA
a
CH4.4
314ALL
Dr. Mohamed Ramadan Saady
Top-Down ParsingTop-Down Parsing
From Grammar to Parser, take IIFrom Grammar to Parser, take II
CH4.5
314ALL
Dr. Mohamed Ramadan Saady
Predictive ParsingPredictive Parsing
•Backtracking is bad!
•To eliminate backtracking, what must we do/be sure of for grammar?• no left recursion• apply left factoring
• (frequently) when grammar satisfies above conditions:current input symbol in conjunction with current non-terminal uniquely determines the production that needs to be applied.
• Utilize transition diagrams:
For each non-terminal of the grammar do following:
1. Create an initial and final state
2. If A X1X2…Xn is a production, add path with edges X1, X2, … , Xn
• Once transition diagrams have been developed, apply a straightforward technique to algorithmicize transition diagrams with procedure and possible recursion.
CH4.6
314ALL
Dr. Mohamed Ramadan Saady
Transition DiagramsTransition Diagrams
• Unlike lexical equivalents, each edge represents a token•Transition implies: if token, match input else call proc• Recall earlier grammar and its associated transition diagrams
E TE’ E’ + TE’ |
T FT’ T’ * FT’ |
F ( E ) | id
0 21T E’
E:
3 6+
4T
E’: 5E’
7 98F T’
T:
10 13*
11F
T’: 12T’
14 17(
15E
F: 16)
id
How are transition diagrams used ?
Are -moves a problem ?
Can we simplify transition diagrams ?
Why is simplification critical ?
CH4.7
314ALL
Dr. Mohamed Ramadan Saady
How are Transition Diagrams Used ?How are Transition Diagrams Used ?
main(){ TD_E();}
TD_T(){ TD_F(); TD_T’();}
TD_E(){ TD_T(); TD_E’();}
TD_E’(){ token = get_token(); if token = ‘+’ then { TD_T(); TD_E’(); }}
TD_F(){ token = get_token(); if token = ‘(’ then { TD_E(); match(‘)’); } else if token.value <> id then {error + EXIT} else ...}
TD_E’(){ token = get_token(); if token = ‘*’ then { TD_F(); TD_T’(); }}
What happened to -moves?
… “else unget()and terminate”
NOTE: not all error conditions have been represented.
CH4.8
314ALL
Dr. Mohamed Ramadan Saady
How can Transition Diagrams be How can Transition Diagrams be Simplified ?Simplified ?
6E’
E’: 53+
4T
CH4.9
314ALL
Dr. Mohamed Ramadan Saady
How can Transition Diagrams be How can Transition Diagrams be Simplified ? (2)Simplified ? (2)
6E’
E’: 53+
4T
E’: 53+
4T
6
CH4.10
314ALL
Dr. Mohamed Ramadan Saady
How can Transition Diagrams be How can Transition Diagrams be Simplified ? (3)Simplified ? (3)
6E’
E’: 53+
4T
E’: 53+
4T
6
E’: 3+
4
T
6
CH4.11
314ALL
Dr. Mohamed Ramadan Saady
How can Transition Diagrams be How can Transition Diagrams be Simplified ? (4)Simplified ? (4)
6E’
E’: 53+
4T
E’: 53+
4T
6
E’: 3+
4
T
6
21E’T
0E:
CH4.12
314ALL
Dr. Mohamed Ramadan Saady
How can Transition Diagrams be How can Transition Diagrams be Simplified ? (5)Simplified ? (5)
Leftmost Derivation for the ExampleLeftmost Derivation for the Example
The leftmost derivation for the example is as follows:
E TE’ FT’E’ id T’E’ id E’ id + TE’ id + FT’E’
id + id T’E’ id + id * FT’E’ id + id * id T’E’
id + id * id E’ id + id * id
CH4.22
314ALL
Dr. Mohamed Ramadan Saady
What’s the Missing Puzzle Piece ?What’s the Missing Puzzle Piece ?
Constructing the Parsing Table M !
1st : Calculate First & Follow for Grammar
2nd: Apply Construction Algorithm for Parsing Table ( We’ll see this shortly )
Basic Tools:
First: Let be a string of grammar symbols. First() is the set that includes every terminal that appears leftmost in or in any string originating from . NOTE: If , then is First( ).
Follow: Let A be a non-terminal. Follow(A) is the set of terminals a that can appear directly to the right of A in some sentential form. (S Aa, for some and ). NOTE: If S A, then $ is Follow(A).
*
*
*
CH4.23
314ALL
Dr. Mohamed Ramadan Saady
Motivation Behind First & FollowMotivation Behind First & Follow
First:
Follow:
Is used to help find the appropriate reduction to follow given the top-of-the-stack non-terminal and the current input symbol.
Example: If A , and a is in First(), then when a=input, replace A with (in the stack).
( a is one of first symbols of , so when A is on the stack and a is input, POP A and PUSH .
Is used when First has a conflict, to resolve choices, or when First gives no suggestion. When or , then what follows A dictates the next choice to be made.
Example: If A , and b is in Follow(A ), then when and b is an input character, then we expand A with , which will eventually expand to , of which b follows!
