What is Handle?

A handle is a substring that connects a right-hand side of the production rule in the grammar and whose reduction to the non-terminal on the left-hand side of that grammar rule is a step along with the reverse of a rightmost derivation.

Finding Handling at Each Step

Handles can be found by the following process −

• It can scan the input string from left to right until first .> is encountered.

• It can scan backward until <. is encountered.

• The handle is a string between <. and .>

Example1 − Consider the Grammar

E → E + E|E * E|(E)id.

Find handles at each step for reducing the string id₁ + id₂ * id₃ using operator Precedence Parsing.

Solution

First, Attach $ at starting and ending of string i.e., $id₁ + id₂ * id₃ $.

Put Precedence relation between operators & symbols using Precedence Relation Table.

∴ $ <. id₁. > +<. id₂ >*<. id₃ > $

Apply 3 steps as explained above on the string.

Example2 − Compute FIRST & LAST terminals of non-terminals E, T, and F in the following Grammar.

E → E + T| T

T → T * F | F

F → (E)| id

Solution

On seeing the production, we can judge

+ is the first terminal of E

* is the first terminal of T

(, id is the first terminals of F.

But E → T → F

∴ The First Terminal of F is contained in the First terminal of T and the First Terminal of T is contained in the First Terminal of E.

∴ First(F) = {(, id}

∴ First(T) =*∪ First (F) = {*, (, id}

First(E) = + ∪ First (T) = {+,*, (, id}

Similarly, the Last Terminals can be found.

Example3 − Consider the Grammar

E → E + T|T

T → T ∗ F|F

F → (E)| id

Perform Stack Implementation for string id + id * id using operator precedence parsing.

Solution

Precedence rules <. , .> or =. holds between the top of the stack and the current input symbol. If the top of the stack is Non-terminal, then the terminal below the top of the stack will be compared with the current input symbol.