LL(1) Parsing

Summary

This session delves into LL(1) parsing, covering the creation of LL(1) parsing tables and the parsing process using a specific grammar. The video illustrates how to derive first and follow sets for non-terminals, construct the parsing table, and use it to generate a parse tree for a given input string. The importance of non-ambiguous grammars for LL(1) parsing is emphasized, as well as how to identify LL(1) grammars. The session concludes with a demonstration of successful parsing and a preview of upcoming lessons on grammar classification.

Takeaways

• 😀 The session focuses on LL(1) parsing, explaining the procedure using a grammar and an example input string.
• 😀 LL(1) parsing involves constructing a parsing table for a given grammar, which helps in determining the parse tree for an input string.
• 😀 The first step in constructing an LL(1) parsing table is finding the 'First' and 'Follow' sets for all non-terminal symbols in the grammar.
• 😀 The 'First' set of a non-terminal symbol contains the set of terminal symbols that can appear at the beginning of any string derived from that non-terminal.
• 😀 The 'Follow' set of a non-terminal symbol includes the terminal symbols that can appear immediately after that non-terminal in any derivation.
• 😀 The LL(1) parsing table is constructed by mapping non-terminals to the appropriate terminal symbols based on their 'First' and 'Follow' sets.
• 😀 The parsing process begins by pushing the start symbol onto the stack, and then using the LL(1) table to guide the derivation of the input string.
• 😀 As the parser processes the input string, it matches terminal symbols from the input buffer with the symbols in the stack, progressively constructing the parse tree.
• 😀 The parser replaces non-terminals with the corresponding production rules from the LL(1) table, and the stack is updated accordingly.
• 😀 A successful parse is confirmed when the terminal symbols in the stack and input buffer match, and the end-of-input symbol (dollar sign) is matched, signaling completion of parsing.

Q & A

What is LL(1) parsing and what is its main purpose?

LL(1) parsing is a top-down predictive parsing technique used for analyzing context-free grammars. It aims to construct a parse tree for a given input string by using a parsing table to guide the selection of production rules. The '1' in LL(1) indicates that the parser uses one symbol of lookahead to make decisions on which production rule to apply.

Why is it important to construct the first and follow sets in LL(1) parsing?

The first and follow sets are essential in LL(1) parsing because they help determine which production rule to apply based on the lookahead symbol. The 'first' set helps identify which terminals can appear at the start of a non-terminal, and the 'follow' set defines which symbols can follow a non-terminal in any derivation.

How do you construct the 'first' set for a non-terminal?

To construct the 'first' set for a non-terminal, we begin by checking the production rules for that non-terminal. For each production, we add the terminal symbols on the right-hand side to the 'first' set. If a production can generate the epsilon (empty string), we also include epsilon in the 'first' set.

What role do epsilon productions play in the construction of the 'follow' set?

Epsilon productions are crucial when constructing the 'follow' set because if a non-terminal can derive epsilon, the symbols following this non-terminal in the production rules must also be included in its follow set. This ensures the parser handles cases where a non-terminal may be empty.

What happens if a non-terminal symbol appears in the right-hand side of a production rule and is followed by another non-terminal?

If a non-terminal appears on the right-hand side of a production rule and is followed by another non-terminal, we include the 'first' set of the second non-terminal in the 'follow' set of the first non-terminal. This helps in predicting the next step in the parsing process.

How is the LL(1) parsing table constructed?

The LL(1) parsing table is constructed by placing the production rules in the table's cells. Each row corresponds to a non-terminal, and each column corresponds to a terminal (including the dollar symbol '$' as the end-of-input marker). For each non-terminal, the production rule is placed in the cell corresponding to the terminal in its 'first' set. If epsilon is involved, rules based on the 'follow' set are considered.

What does the dollar symbol '$' represent in LL(1) parsing?

In LL(1) parsing, the dollar symbol '$' represents the end-of-input marker. It is used to signify the end of the input string and also helps finalize the parsing when it matches the dollar symbol in the stack.

What is the significance of popping non-terminals from the stack during LL(1) parsing?

Popping non-terminals from the stack signifies that the parser is working to expand the grammar based on the production rules. When a non-terminal is popped, it is replaced by the right-hand side of the corresponding production rule, which then gets processed further by the parser.

How does the lookahead symbol influence the LL(1) parsing process?

The lookahead symbol plays a key role in LL(1) parsing by determining which production rule to apply. The parser uses the current lookahead to match the appropriate production rule from the LL(1) parsing table. If a match is found, the corresponding terminal or non-terminal is popped from the stack and the lookahead moves forward.

What does it mean for a grammar to be an 'LL(1) grammar'?

A grammar is considered an 'LL(1) grammar' if it can be parsed by an LL(1) parser, meaning that for each non-terminal, there is exactly one production rule that can be applied for each terminal in the lookahead. This ensures that the parser can always make a deterministic decision based on the lookahead symbol, without ambiguity or conflicts.