LR-parser and detecting syntactic errors

LR-parser: An LR-parser is a type of bottom-up parser that reads input text from left to right and constructs a rightmost derivation of the input. It uses a stack to keep track of previously seen symbols and a parsing table to determine the next action based on the current state and the next input symbol.

Syntactic error: A syntactic error occurs when the input text does not conform to the grammar of the language being parsed. For example, a missing semicolon or a mismatched parenthesis can cause a syntactic error.

Detection of syntactic error: An LR-parser can detect a syntactic error as soon as it is possible to do so with a right-to-left scan of the input. This is because LR-parsers are bottom-up parsers that attempt to construct a rightmost derivation of the input. If the parser encounters an input symbol that cannot be reduced to a valid production in the grammar, it can backtrack and try a different production. If all possible productions fail, the parser reports a syntax error.

Left-to-right scan: While it is possible to detect some syntactic errors with a left-to-right scan of the input, it is not always sufficient. This is because LR-parsers attempt to construct a rightmost derivation of the input, which means they need to look ahead to determine the correct action to take. For example, consider the input "a + b * c". A left-to-right scan would detect the missing semicolon at the end of the input, but it would not detect the fact that the expression is ambiguous without additional parsing information. An LR-parser, on the other hand, can use its parsing table to determine the correct parse tree for the input.

Conclusion: In conclusion, an LR-parser can detect syntactic errors as soon as it is possible to do so with a right-to-left scan of the input. This is because LR-parsers attempt to construct a rightmost derivation of the input and need to look ahead to determine the correct action to take. While it is possible to detect some syntactic errors with a left-to-right scan, it is not always sufficient for LR-parsers.