What is Operator Precedence Parsing?

Operator Precedence Parsing is also a type of Bottom-Up Parsing that can be used to a class of Grammars known as Operator Grammar.

A Grammar G is Operator Grammar if it has the following properties −

• Production should not contain ϵ on its right side.

• There should not be two adjacent non-terminals at the right side of production.

Example1 − Verify whether the following Grammar is operator Grammar or not.

E → E A E |(E)|id

A → +| − | ∗

Solution

No, it is not an operator Grammar as it does not satisfy property 2 of operator Grammar.

As it contains two adjacent Non-terminals on R.H.S of production E → E A E.

We can convert it into the operator Grammar by substituting the value of A in E → E A E.

E → E + E |E − E |E * E |(E) | id.

Operator Precedence Relations

Three precedence relations exist between the pair of terminals.

Depending upon these precedence Relations, we can decide which operations will be executed or parsed first.

Association and Precedence Rules

• If operators have different precedence

Since * has higher precedence than +

Example−

In a statement a + b * c

∴ + <. *

In statement a * b + c

∴ ∗ . > +

• If operators have Equal precedence, then use Association rules.

(a) Example minus; In statement a + b + c here + operators are having equal precedence.

As '+' is left Associative in a + b + c

∴ (a + b) will be computed first, and then it will be added to c.

i.e., (a + b) + c

+ .> +

Similarly, '*' is left Associative in a * b * c

(b) Example − In a statement a ↑ b ↑ c here, ↑ is the Right Associative operator

∴ It will become a ↑ (b ↑ c)

∴ (b ↑ c) will be computed first.

∴ ↑<. ↑

• Identifier has more precedence then all operators and symbols.

∴ θ <. id           $ <. id
id . > θ            id . > $
id . >)
(<. id.

• $ has less precedence than all other operators and symbols.

$ <.           ( id . > $
$ <. +         ). > $
$ <.*

Example2 − Construct the Precedence Relation table for the Grammar.

E → E + E | E ∗ E/id

Solution

Operator-Precedence Relations

Advantages of Operator Precedence Parsing

• It is accessible to execute.

Disadvantages of Operator Precedence Parsing

• Operator Like minus can be unary or binary. So, this operator can have different precedence’s in different statements.

• Operator Precedence Parsing applies to only a small class of Grammars.