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In some applications and programming languages, notably Microsoft Excel, PlanMaker (and other spreadsheet applications) and the programming language bc, unary operations have a higher priority than binary operations, that is, the unary minus has higher precedence than exponentiation, so in those languages −3 2 will be interpreted as (−3) 2 ...
The operator precedence is a number (from high to low or vice versa) that defines which operator takes an operand that is surrounded by two operators of different precedence (or priority). Multiplication normally has higher precedence than addition, [1] for example, so 3+4×5 = 3+(4×5) ≠ (3+4)×5.
"The [C] syntax [i.e., grammar] specifies the precedence of operators in the evaluation of an expression, which is the same as the order of the major subclauses of this subclause, highest precedence first." [8] A precedence table, while mostly adequate, cannot resolve a few details.
A limitation to this strategy is that unary operators must all have higher precedence than infix operators. The "negative" operator in the above code has a higher precedence than exponentiation. Running the program with this input - a ^ 2. produces this output ((((-a)^(2)))) which is probably not what is intended.
Circumfix operators have the highest precedence, with their contents being evaluated and the resulting value used in the surrounding expression. The most familiar circumfix operator are the parentheses mentioned above, used to indicate which parts of an expression are to be evaluated before others.
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.
These phenomena have been taken as motivation for identifying the denotations of natural language conditionals with logical operators including the strict conditional, the variably strict conditional, as well as various dynamic operators. The following table shows the standard classically definable approximations for the English connectives.
One common convention is to associate intersection = {: ()} with logical conjunction (and) and associate union = {: ()} with logical disjunction (or), and then transfer the precedence of these logical operators (where has precedence over ) to these set operators, thereby giving precedence over .