What is Handle Pruning?

The handle is the substring that matches the body of a production whose reduction represents one step along with the reverse of a Rightmost derivation.

The handle of the right sequential form Y is the production of Y where the string S may be found and replaced by A to produce the previous right sequential form in RMD(Right Most Derivation) of Y.

Sentential form: S => a here, ‘a’ is called sentential form, ‘a’ can be a mix of terminals and nonterminals.

Example:

Consider Grammar : S -> aSa | bSb | ε
Derivation:              S => aSa => abSba => abbSbba => abbbba

Left Sentential and Right Sentential Form:

• A left-sentential form is a sentential form that occurs in the leftmost derivation of some sentence.
• A right-sentential form is a sentential form that occurs in the rightmost derivation of some sentence.

Handle contains two things:

• Production
• Position

Example: 

S -> aABe
A -> Abc | b
B -> d

Steps:

abbcde : γ = abbcde , A->b; Handle = b
aAbcde : γ = RHS = aAbcde , A->Abc; Handle = Abc
aAde : γ = aAde , B->d; Handle = d
aABe : γ = aABe, S-> aABe; Handle = aABe

Note- Handles are underlined in the right-sentential forms.

Is the leftmost substring always handled?

No, choosing the leftmost substring as the handle always, may not give correct SR(Shift-Reduce) Parsing.

Handle Pruning:

Removing the children of the left-hand side non-terminal from the parse tree is called Handle Pruning. 

A rightmost derivation in reverse can be obtained by handle pruning.

Steps to Follow:

• Start with a string of terminals ‘w’ that is to be parsed.
• Let w = γ_n, where γ_n is the nth right sequential form of an unknown RMD.
• To reconstruct the RMD in reverse, locate handle βn in γ_n. Replace βn with LHS of some A_n ⇢ βn to get (n-1)^th RSF γ_n-1. Repeat.

Example 1:

Right Sequential Form	Handle	Reducing Production
id + id * id	id	E ⇒ id
E + id * id	id	E ⇒ id
E + E * id	id	E ⇒ id
E + E * E	E + E	E ⇒ E + E
E * E	E * E	E ⇒ E * E
E (Root)

Example 2:

Right Sequential Form	Handle	Production
id + id + id	id	E ⇒ id
E + id + id	id	E ⇒ id
E + E + id	id	E ⇒ id
E + E + E	E + E	E ⇒ E + E
E + E	E + E	E ⇒ E + E
E (Root)