Predictive Parser LL(1)

Summary

This lecture on LL(1) parsers explains the key steps involved in building a predictive parser in compiler design. It covers the elimination of left recursion, the application of left factoring, and how to compute FIRST and FOLLOW sets. The lecture then guides through constructing the parsing table, followed by parsing an input string using that table. By the end of the session, viewers will understand how to build an LL(1) parser and apply it to process strings, crucial for syntax analysis in compilers.

Takeaways

• 😀 Left recursion in grammar leads to infinite loops, and it must be eliminated for predictive parsing to work.
• 😀 Left recursion is removed by transforming a grammar into two rules, ensuring no recursion happens immediately.
• 😀 Left factoring is applied when multiple productions share a common prefix, improving parser efficiency and predictability.
• 😀 The 'First' set contains the first terminal that can be derived from a non-terminal in a production.
• 😀 The 'Follow' set helps determine what can follow a non-terminal in a production, useful for parsing decisions.
• 😀 A predictive parser uses a parse table, where rows represent non-terminals and columns represent terminals, to guide parsing.
• 😀 The parse table is constructed based on the First and Follow sets, ensuring that each combination of non-terminal and terminal is covered.
• 😀 LL(1) parsing uses a single lookahead symbol, making it fast and efficient but limited to a subset of context-free grammars.
• 😀 In the parsing algorithm, the stack is initialized with the start symbol and a dollar sign, and the input is processed symbol by symbol.
• 😀 When a terminal symbol matches the top of the stack, it is removed from both the stack and the input string.
• 😀 If a non-terminal is at the top of the stack, the corresponding production is applied, guiding the parsing process until the input string is parsed successfully or rejected.

Q & A

What is the first step in building a predictive parser?

The first step is to eliminate left recursion in the given grammar. This is necessary to ensure the grammar is suitable for predictive parsing.

What is left recursion, and how is it eliminated?

Left recursion occurs when a non-terminal in a grammar directly or indirectly refers to itself in its own production. It is eliminated by transforming the grammar using two rules: one for the non-recursive case and one for the recursive case, typically introducing a new non-terminal.

What does left factoring involve in compiler design?

Left factoring is a technique used when there are common prefixes in multiple productions for the same non-terminal. It involves factoring out the common prefix and introducing a new non-terminal to handle the remaining parts of the production.

How are the 'first' and 'follow' sets computed in predictive parsing?

The 'first' set contains the terminals that can appear at the beginning of any string derived from a non-terminal. The 'follow' set contains the terminals that can appear immediately to the right of a non-terminal in a derivation. Both sets are computed using specific rules based on the grammar's productions.

What is the purpose of constructing a predictive parser table?

The predictive parser table helps in deciding which production to apply during parsing. It is constructed by using the 'first' and 'follow' sets to map non-terminals to terminals in the grammar, guiding the parser to make decisions based on the current symbol in the input string.

What role does the 'follow' set play in the construction of the predictive parser table?

The 'follow' set helps in handling epsilon-productions (productions that lead to an empty string) by indicating where these productions can be applied. It also ensures that the parser correctly handles situations when a non-terminal can be followed by other symbols, including the end-of-input symbol ($).

How does the parser process an input string using the predictive parser table?

The parser processes the input string by starting with the start symbol on the stack and comparing the top of the stack with the current input symbol. Based on the predictive parser table, it applies the corresponding production, updates the stack, and continues parsing until the input string is completely processed.

What is the significance of epsilon in the construction of a predictive parser table?

Epsilon represents an empty string and is used in productions that can derive nothing (i.e., epsilon-productions). When constructing the parser table, epsilon-productions are handled by adding the follow set of the left-hand side non-terminal to the table for the corresponding terminal or end-of-input symbol.

What does it mean for a string to be accepted by the predictive parser?

A string is accepted by the predictive parser if, after parsing, the only remaining symbol in the stack is the end-of-input symbol ($), and the input string is completely processed, indicating that the string conforms to the grammar.

How does the parser handle conflicts in the predictive parser table?

Conflicts in the predictive parser table arise when there are multiple productions for the same non-terminal and terminal. To resolve such conflicts, the grammar must be rewritten, often by eliminating left recursion or applying left factoring, ensuring that each table entry corresponds to exactly one production.