Understanding SLR and LALR
* SLR (Simple LR): Uses a single lookahead symbol to determine the correct reduction. This is the simplest LR parser type.
* LALR (Look-Ahead LR): Combines the states of the SLR parser that have the same set of lookahead symbols, resulting in a more powerful parser. It uses a *lookahead set* (multiple symbols) for each state.
Demonstrating LALR but not SLR
1. Construct the SLR Parsing Table: Create the SLR parsing table for your grammar. This involves:
- Building the LR(0) automaton.
- Computing the FOLLOW sets for each nonterminal.
- Filling in the parsing table based on the LR(0) automaton and FOLLOW sets.
2. Identify a Conflict in the SLR Table: Look for any situation where multiple actions (reduce or shift) are required for the same state and lookahead symbol. If you find a conflict, the grammar is not SLR.
3. Construct the LALR Parsing Table: Now, build the LALR parsing table. This involves:
- Combining SLR states with identical lookahead sets.
- Using the combined lookahead sets to resolve any conflicts in the SLR table.
4. Verify the LALR Table is Conflict-Free: If the LALR table does not have any conflicts, the grammar is LALR.
Example
Let's look at a simple example:
```
S -> A a
A -> b | c
```
SLR Conflict:
* The SLR parser will have a conflict in the state where you see "A". You could either shift the "a" or reduce using the rule "A -> b". The SLR parser has only one lookahead symbol, and it can't distinguish between these two actions.
LALR Resolution:
* In the LALR parser, the state where you see "A" will be split into two states based on the lookahead:
* State 1: Lookahead set {a} (reduces to "A -> b")
* State 2: Lookahead set {$} (shifts "a")
This resolution removes the conflict, making the grammar LALR.
Key Points
* If a grammar is SLR, it is also LALR. However, the converse is not true.
* LALR parsers are more powerful than SLR parsers because they can resolve certain conflicts that SLR parsers cannot.
* LALR parsing is often used in practice because it strikes a good balance between parsing power and efficiency.
Let me know if you have a specific grammar in mind and I can help you walk through the process of checking if it's LALR but not SLR.