How Does Operator Precedence and Associativity Get Defined in Programming Languages?

Operator Precedence and Associativity: Who Decides and How It Impacts Evaluation

In programming, operator precedence and associativity play a crucial role in determining the order of operations within an expression. But where does this definition originate, and how does it relate to the order of evaluation?

Definition and Significance of Operator Precedence and Associativity

Operator precedence determines which operations have higher priority. For instance, in C/C , multiplication and division operations have higher precedence than addition and subtraction. Operator associativity specifies the grouping of operators with the same precedence. In the case of addition and subtraction, they are left-to-right associative.

Source of Operator Precedence and Associativity

Contrary to popular belief, the ANSI C11 standard does not explicitly define operator precedence and associativity. Instead, they are inferred from the language's grammar rules. By analyzing the grammar of operators, we can determine their precedence and associativity.

Example: Multiplicative vs. Additive Operators

Consider the grammar rule for additive expressions in C :

additive-expression:
  multiplicative-expression
  additive-expression + multiplicative-expression
  additive-expression - multiplicative-expression

From this rule, we deduce that multiplicative-expression is a subrule of additive-expression, indicating that multiplicative operators have higher precedence. Additionally, the left operand of an additive-expression can itself be another additive-expression, implying left-to-right associativity for addition and subtraction.

Impact on Order of Evaluation vs. Operator Precedence and Associativity

Note that operator precedence and associativity do not directly impact the order of evaluation. For example, although has lower precedence than , f1() f2() f3() is evaluated as f1() (f2() f3()), not (f1() f2()) f3(). In this case, the order of function call evaluations within each subexpression remains undefined.

Exceptions: Operators with Sequencing

While operator precedence and associativity generally do not enforce a specific evaluation order, some operators do impose sequencing. For instance, in the logical OR operator ||, the left operand (x) must be evaluated before the right operand (y) for proper short-circuiting behavior.

Conclusion

Operator precedence and associativity are crucial concepts for understanding the evaluation of expressions. However, their definition lies not in specific standards but is inferred from the grammar of the language itself. By adhering to operator precedence and associativity rules, programmers can correctly anticipate the outcomes of complex expressions, ensuring efficient and accurate code execution.

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