Operator associativity
property that determines how operators of the same precedence are grouped in the absence of parentheses
In programming language theory, the associativity of an operator is a property that determines how operators of the same precedence are grouped in the absence of parentheses. If an operand is both preceded and followed by operators (for example, ^ 3 ^), and those operators have equal precedence, then the operand may be used as input to two different operations (i.e. the two operations indicated by the two operators). The choice of which operations to apply the operand to, is determined by the associativity of the operators. Operators may be associative (meaning the operations can be grouped arbitrarily), left-associative (meaning the operations are grouped from the left), right-associative (meaning the operations are grouped from the right) or non-associative (meaning operations cannot be chained, often because the output type is incompatible with the input types). The associativity and precedence of an operator is a part of the definition of the programming language; different programming languages may have different associativity and precedence for the same type of operator.
Consider the expression a ~ b ~ c. If the operator ~ has left associativity, this expression would be interpreted as (a ~ b) ~ c. If the operator has right associativity, the expression would be interpreted as a ~ (b ~ c). If the operator is non-associative, the expression might be a syntax error, or it might have some special meaning.
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