Operator associativity

As explained in Building User-Friendly DSLs

A binary operator whose equal-precedence sequences are grouped from left to right.

A left-associative binary operator groups equal-precedence operations from left to right. Thus, 3 - 2 - 1 means (3 - 2) - 1, producing 0 rather than 3 - (2 - 1), which produces 2. section 12.3

The rule applies repeatedly: x1 op1 x2 op2 x3 op3 x4 becomes ((x1 op1 x2) op2 x3) op3 x4 when the operators share precedence and are left-associative. Expression ASTs therefore grow toward the left. section 12.3

Arithmetic chain

For 1 + 2 + 3 + 4, build the tree as (((1 + 2) + 3) + 4). Parentheses can override this grouping, as in 1 + (2 - 3). section 12.3

Figure 12.15 The AST representing the expression 3 – 2 – 1, taking the order of operations for the left-associative – operator into account

Inspect the AST for 3 - 2 - 1 to see how left associativity determines its nested structure. section 12.3

How Building User-Friendly DSLs covers it

How deep it goes

Explains repeated grouping, AST consequences, and parentheses, while contrasting but not developing right-associative implementation.

Examples

Uses 3 - 2 - 1, chained addition, parenthesized subtraction, AST figures, and a requiresParentheses condition.

What it assumes

Assumes binary operations and precedence, then establishes associativity as an additional ordering rule.

What you can do after

Evaluate/understand equal-precedence expression chains and predict their nested AST structure.

How it connects

Connects binary operators with equal precedence, order of operations, abstract syntax trees, parentheses, and right-associative operators.

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Related concepts

• binary expressionkind of · A binary expression applies a binary operator to exactly two operand expressions.
• callused by · A function call is an operation or expression that invokes a function or other callable, optionally supplies arguments, and initiates its execution.
• power functionincludes · Exponentiation is the mathematical operation of raising a base to a specified exponent or power.
• operator precedencepart of · Operator precedence is the set of rules determining how an expression containing multiple operators is grouped and ordered for evaluation.
• associativitycontrasts with · Associativity is the property of a binary operation that regrouping its operands does not change the result.

This explainer was generated by Manning's knowledge graph from the text of Building User-Friendly DSLs. The section links point to the parts of the book it draws on.