How to Fill the Entries in Parsing Table?

A parser is the second phase of compilation. The parser takes as its input tokens generated from the previous phase, i.e., the Lexical Analyzer phase, and groups them in such a way that their syntax can be recognized.

For example,

Consider I₀

I₀ − E′ → ∙ E

      E → ∙ E + T

     E → ∙ T

     T → ∙ T ∗ F

     T → ∙ F

     F → ∙ (E)

     F → ∙ id

Filling of Shifting Entries

Applying Rule (2a) of the algorithm of construction of SLR Parsing Table on a set of a production of I₀. Rule (2a) will be applied only when there is a terminal symbol after the dot. Consider F → ∙ (E)

Compare A → α ∙ a β with F → ∙ (E)

∴ A = F, α = ε, a = (, β = E)

Applying Rule, goto (I_i, a) = I_j

∵     goto (I₀, ( ) = I₄

∴    Action [0, ( ] = Shift 4

∴ Write s4 in front of Row 0 and column (

Similarly, compare F → ∙ id

Applying Rule (2a)

Compare A → α ∙ a β with F → ∙ id

∴ A = F, α = ε, a = id, β = ε

∴ goto (I₀, id) = I₅

∴ Action [0, id] = shift 5

Write s5 in front of Row 0 and column id

Similarly, the complete table will be filled with shift actions by processing all states from I₀ to I₁₁ in a similar manner.

Filling of Reduce Entries (r) − For filling reduce (r) entries, we have to apply rule (2b) of the construction of the SLR Parsing Table.

From I₀ to I₁₁ we have to see productions of the form A → α ∙

Consider

I₂ − E → T ∙

T → T ∙ * F

Here, we have the production E → T ∙ of form A → α ∙ in which dot appears at last position. So, compare A → α ∙ with E → T ∙

Applying Rule, we have to find FOLLOW (E)

FOLLOW (E) = { +, ), $}

The production number of E → T in Question is (2)

Write r2 in front of the row of state 2 and column of +,), $.

action [2, +] = r2, action [2, )] = r2, action [2, $] = r2.

Here, r2 refers to reduce using production number 2

Similarly, consider another state I₃

I₃ − T → F ∙

Apply Rule (2b)

Compare T → F ∙ with A → α ∙

∴ A = T, α = F

FOLLOW (T) = { +,*, ), $}

Since T → F is production number (4) in Question

Write r4 in front of the row of state 3 and column of +,*, ), $.

Action [3, +] = r4                 Action [3, $] = r4

Action [3, )] = r4                  Action [3, )] = r4

Similarly, fill up the Action table by reduce (r) entries.

Filling of goto Entries − goto Table can be filled for the non-terminals using Rule (3) of construction of Parsing Table.

Since,             I₁ = goto(I₀, E)

Applying Rule (3)

goto[0, E] = 1

Write 1 in front of Row 0 and Column E.

Similarly,          goto (I₀, T) = I₂

Applying Rule (3)

goto [0, T] = 2

Write 2 in front of Row 0 and Column T.

Similarly, we can fill other entries in goto Table

Filling of "accept" entries

Applying Rule (2C), there is a production.

E′ → E ∙ in I₁.

Therefore, write "accept" in front of Row 1 and Column $.

∴ action [1, $] = "accept. "

By filling all shift, reduce, accept, goto entries, we get the following SLR parsing table.

In table s means shift, r means to reduce.