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Verifying whether the string id * id + id is accepted by a given grammar using SLR parsing
Consider the SLR parsing table for the Grammar
E → E + T
E → T
T → T ∗ F
T → F
F → (E)
F → id
Check whether the string id * id + id is accepted or not by using the SLR parsing table constructed in the example.
Solution
Initially, LR Parser in state 0.
Put $ at the end of the string, i.e., id * id + id $.
| Stack | Input String | Reason |
|---|---|---|
| 0 | id ∗ id + id | Action [0, id] = s5 ∴ Shift id and state 5 |
| 0 id 5 | ∗ id + id $ | Action [5,∗] = r6. ∴ Reduce by F → id. goto(0, F) = 3 |
| 0 F 3 | ∗ id + id $ | Action [3,∗] = r4, Reduce by T → F goto(0, T) = 2 |
| 0 T 2 | ∗ id + id $ | Action [2,∗] = s7, shift ∗, 7 |
| 0T2*7 | id + id $ | Action [7, id] = s5, shift id, 5 |
| 0T2*7 id 5 | +id $ | Action [5, +] = r6, Reduce by F → id goto(7, F) = 10 |
| 0T2*7 F 10 | +id $ | Action [10, +] = r3S, Reduce by T → T ∗ F, goto(0, T) = 2 |
| 0 T 2 | +id $ | Action [2, +] = r2, Reduce by E → T goto(0, E) = 1 |
| 0 E 1 | +id $ | Action [1, +] = s6, Shift +, 6 |
| 0 E 1 + 6 | id $ | Action [6, id] = s5, Shift id, 5. |
| 0 E 1 + 6 id 5 | $ | Action [5, $] = s6, Reduce by F → id, goto(6, F) = 3 |
| 0 E 1 + 6 F 3 | $ | Action [3, $] = r4, Reduce by T → F, goto(6, F) = 9 |
| 0 E 1 + 6 T 9 | $ | Action [9, $] = r1, Reduce by E → E + T, goto(0, E) = 1 |
| 0 E 1 | $ | Action [1, $] = accept |
In the first row, we have 0 at the top of the stack, and the id symbol is to be processed. So, check Row (0) and column (id) i.e., Action [0, id] = s5, i.e., Shift id from string and state 5 onto stack.
In Second Row, Action [5, *] = r3 means reduce by production number 6 i.e., F → id. Pop id from the stack and push F. Then see goto (0, F) = 3, so push 3 onto Stack. In Row seven, Action [10, +] = r3 i.e., reduce by production number 3 i.e., T → T ∗ F.
Pop T2 * 7F10 from the stack, push T into the stack. Then see goto [0, T] = 2. So, push 2 onto stack In Last Row Action [1, $] = accept. That means the parser will accept the string.
Algorithm of SLR Parsing Table
There are two parts of the SLR Parsing table
- Action
- goto
Action and goto table can be filled using the following Algorithm −
Algorithm
Input− An Augmented Grammar G′
Output− SLR Parsing Table
Method
- Initially construct a set of items
C = {I0, I1, I2 … … In} where C is a set of LR (0) items for Grammar.
- Parsing actions are based on each item or state I1.
Various Actions are −
- If A → α ∙ a β is in Ii and goto (Ii, a) = Ij then set Action [i, a] = shift j".
- If A → α ∙ is in Ii then set Action [i, a] to "reduce A → α" for all symbol a, where a ∈ FOLLOW (A).
- If S′ → S ∙ is in Ii then the entry in action table Action [i, $] = accept".
- The goto part of the SLR table can be filled as− The goto transition for the state i is considered for non-terminals only. If goto (Ii, A) = Ij then goto [i, A] = j
- All entries not defined by rules 2 and 3 are considered to be "error. "
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