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

$E \rightarrow E + n \mid E \times n \mid n$

$n + n \times n$

Deriving the above string with rightmost derivation,

$E$

$E \times n$

$E + n \times n $

$n + n \times n$

But right sentential form is the reverse of rightmost derivation,

$n + n \times n$

$E + n \times n$

$E \times n$

$E$

but why reverse?

While pushing terminals to the stack, handles appear at the top of stack which are reduced with appropriate production,

In this question n is pushed then reduced to E, so n is a handle, next + will be pushed oops no match,

next n will be pushed, Stack elements $E + n$ , where $n$ is on the top

This is a handle which will be reduced by $E \rightarrow E +n$

Now stack contents are $E$

pushed $ \times $ and $n$

Elements in stack are, $E \times n$, where n is on the top

$E \times n$ is a handle and will be reduced with $E \rightarrow E \times n$.

So we got 3 handles in this reduction,

- $n$
- $E \times n$
- $E + n$