Reduction & Handle Pruning

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This document discusses bottom-up parsing and handle pruning. It begins with an example grammar and string. Bottom-up parsing works by repeatedly reducing substrings matching production bodies until reaching the start symbol. A handle is a substring matching a production body whose reduction moves backward through a rightmost derivation. Handle pruning is removing nonterminal children from a parse tree, allowing reconstruction of a rightmost derivation by working backward from handles. The document provides steps for using handle pruning to rebuild a rightmost derivation in reverse from a given string. An example demonstrates finding the handles in a string and reducing based on the corresponding productions to reach the start symbol.

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 What is reduction?
 Key decision for reduction
 Example of reduction
 What is Handle?
 What is Handle Pruning?
 Example of Handle Pruning
3

Bottom up parsing is the process of “reducing” a
string ‘w’ to the start symbol of the grammar. At
each reduction step , a specific substring matching
the body of a production is replaced by the
nonterminal at the head of the production.
4

5
The key concern during bottom-up parsing are
about when to reduce and about what production to
apply, as the parse proceeds. It will be discuss in
example section.

GRAMMAR:
E -> E + T | T
T -> T * F | F
F -> ( E ) | id
STRING:
W = id * id
6

id * id
F * id [ F -> id ]
T * id [ T -> F]
T * F [ F -> id ]
T [T -> T*F ]
E [ E -> T ]
The Parse completes with the reduction of string W
to the start symbol E.
7

A “Handle” is a substring that matches
the body of a production and whose
reduction represents one step along the
reverse of a rightmost derivation.
If, A -> α
Then α is the handle
8

9
Removing the children of left hand side non terminal from
the parse tree is called Handle Pruning.
A right most derivation in reverse can be obtained by Handle
Pruning.
If S=>αAw=>αβw ◦ then A->β in the position following α is a
handle of αβw
The handle of right-sentential form γ is a production
A->β and a position of γ where β may be found , such that
replacing β at that position by A produces the previous right
sentential form in a rightmost derivation of γ.

Steps to Follow:
 Start with a string of terminals ‘w’ that is to be
parsed.
 Let w is a string of the grammar.
 w=γn where γn is the n-th right-sentential form of
some unknown rightmost derivation.
 S=γ0=>γ1=>γ2=>… =>γn-1=>γn =w.
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Steps to Follow:
 To rebuild this derivation in reverse order
◦ locate handle βn in γn by production of
An -> βn to get right-sentential form γn-1
◦ handles must be found with specific methods
◦ repeat the process until the start symbol S is
found
◦ reverse of reductions = rightmost derivation
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GRAMMAR:
E -> E + T | T
T -> T * F | F
F -> ( E ) | id
STRING:
W = id * id
12

Right Sentential Form Handle Reducing Production
id1 * id2 id1 F -> id
F * id2 F T -> F
T * id2 id2 F -> id
T * F T * F E -> T * F
E
* Adding subscripts to the tokens ‘id’ for clarity.
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Bottom-up parsing constructs a parse tree for an input string beginning at the leaves and working up to the root. It involves two main actions: shift, which pushes the current input symbol onto a stack, and reduce, which replaces symbols on the top of the stack with a non-terminal symbol according to a production rule. A shift-reduce parser tries to reduce the input string to the start symbol through a sequence of reductions that trace the reverse of the rightmost derivation. It determines which substring to reduce at each step based on the concept of a "handle", which is a substring that matches a production rule.

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Reduction & Handle Pruning

1. Course Code- CSE-3201 1

2. Moderator : Member 1 : Member 2 : Member 3 : Member 4 : Member 5 : 2

3.  What is reduction?  Key decision for reduction  Example of reduction  What is Handle?  What is Handle Pruning?  Example of Handle Pruning 3

4. Bottom up parsing is the process of “reducing” a string ‘w’ to the start symbol of the grammar. At each reduction step , a specific substring matching the body of a production is replaced by the nonterminal at the head of the production. 4

5. 5 The key concern during bottom-up parsing are about when to reduce and about what production to apply, as the parse proceeds. It will be discuss in example section.

6. GRAMMAR: E -> E + T | T T -> T * F | F F -> ( E ) | id STRING: W = id * id 6

7. id * id F * id [ F -> id ] T * id [ T -> F] T * F [ F -> id ] T [T -> T*F ] E [ E -> T ] The Parse completes with the reduction of string W to the start symbol E. 7

8. A “Handle” is a substring that matches the body of a production and whose reduction represents one step along the reverse of a rightmost derivation. If, A -> α Then α is the handle 8

9. 9 Removing the children of left hand side non terminal from the parse tree is called Handle Pruning. A right most derivation in reverse can be obtained by Handle Pruning. If S=>αAw=>αβw ◦ then A->β in the position following α is a handle of αβw The handle of right-sentential form γ is a production A->β and a position of γ where β may be found , such that replacing β at that position by A produces the previous right sentential form in a rightmost derivation of γ.

10. Steps to Follow:  Start with a string of terminals ‘w’ that is to be parsed.  Let w is a string of the grammar.  w=γn where γn is the n-th right-sentential form of some unknown rightmost derivation.  S=γ0=>γ1=>γ2=>… =>γn-1=>γn =w. 10

11. Steps to Follow:  To rebuild this derivation in reverse order ◦ locate handle βn in γn by production of An -> βn to get right-sentential form γn-1 ◦ handles must be found with specific methods ◦ repeat the process until the start symbol S is found ◦ reverse of reductions = rightmost derivation 11

12. GRAMMAR: E -> E + T | T T -> T * F | F F -> ( E ) | id STRING: W = id * id 12

13. Right Sentential Form Handle Reducing Production id1 * id2 id1 F -> id F * id2 F T -> F T * id2 id2 F -> id T * F T * F E -> T * F E * Adding subscripts to the tokens ‘id’ for clarity. 13

14. Thanks All 14

Reduction & Handle Pruning

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Reduction & Handle Pruning