# What is Handle Pruning?

• Difficulty Level : Easy
• Last Updated : 18 Jan, 2022

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
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 = γn, where γn is the nth right sequential form of an unknown RMD.
• To reconstruct the RMD in reverse, locate handle βn in γn. Replace βn with LHS of some An ⇢ βn to get (n-1)th RSF γn-1. Repeat.

Example 1:

Example 2:

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