Lexical analysis is the process of converting a sequence of characters in a source code file into a sequence of tokens that can be more easily processed by a compiler or interpreter. It is often the first phase of the compilation process and is followed by syntax analysis and semantic analysis.

  1. Non-terminal: This is a placeholder for a part of the language that can be further defined. It's like a variable in a mathematical equation.
  2. Terminal: This is the smallest unit of language, like a single character or word.
  3. Greedy Matching: The * operator in the term and expression rules is greedy. It will consume as many factors as possible.
  4. Backtracking: If a part of the expression doesn't match, the parser backtracks to the previous position and tries a different path. For example
  5. Recursive Definitions: The expression rule refers to itself indirectly through term and factor. This allows for nested expressions. For example, when parsing (1 + 2) * 3, the parser can recursively call the expression rule to parse the inner expression 1 + 2.

How Parsing Expressions Work:

  1. Success and Failure: When a parser processes a string, it tries to match the string to the grammar rules. If it can match, it's a success; if not, it's a failure.
  2. Atomic Expressions:
  3. Sequence: Matches two expressions in order. Both must succeed.
  4. Choice: Tries to match the first expression. If it fails, tries the second.
  5. Repetition: Matches an expression zero or more times (), one or more times (+), or zero or one times (?).
  6. And-predicate: Checks if an expression matches but doesn't consume input.
  7. Not-predicate: Checks if an expression doesn't match and doesn't consume input.

Key Concepts:

parse tree. Each node in the tree represents a rule in the grammar, and the edges represent the application of that rule.