This trace follows the actual state transitions behind the companion How a Parser Turns Tokens Into Structure. It describes a common execution path; implementation details can vary, so keep the contract separate from the mechanism.
Step 1: Scan characters into tokens
A lexer groups characters into tokens such as identifiers, numbers, and punctuation. A parser consumes that token stream according to a grammar and builds a structured representation, often an abstract syntax tree. Separating these jobs makes it easier to handle whitespace, literals, precedence, and syntax errors coherently.
Step 2: Apply grammar and precedence
For the expression 2 + 3 * 4, a precedence-aware parser constructs multiplication beneath addition so evaluation yields 14. Parentheses alter the tree by creating an explicit grouping. The AST usually omits surface details that do not affect meaning, such as redundant whitespace.
Step 3: Build expression structure
For a mixed-precedence expression, the parser groups higher-precedence operators deeper in the tree so later evaluation follows the language’s declared rules.
At this point, record the state that changed and check the invariant before advancing. If the operation repeats, make clear which values persist and which are recomputed.
Step 4: Report or recover from errors
A parser accepting syntactically valid input does not prove the names are declared or types match; those checks belong to later semantic analysis. Error recovery matters in editors, where parsing should continue after a malformed statement to provide useful diagnostics.
Step 5: Pass the syntax tree onward
Draw the AST for a - b - c under left-associative subtraction. Then explain what output would result if the parser accidentally made it right-associative.
The trace is complete when the result satisfies the stated contract. Compare this model with the concrete runtime or system you are studying before making a performance claim.