familiar circumfix operator are the parentheses mentioned above, used to indicate which parts of an expression are to be evaluated before others. Another example from physics is the inner product notation of Dirac's bra–ket notation. Circumfix operators are especially useful to denote operations that involve many or varying numbers of operands. The specification of a language will specify the syntax the operators it supports, while languages such as Prolog that support programmer-defined operators require that the syntax be defined by the programmer. Semantics The semantics of operators particularly depends on value, evaluation strategy, and argument passing mode (such as boolean short-circuiting). Simply, an expression involving an operator is evaluated in some way, and the resulting value may be just a value (an r-value), or may be an object allowing assignment (an l-value). In simple cases this is identical to usual function calls; for example, addition x + y is generally equivalent to a function call add(x, y) and less-than comparison x < y to lt(x, y), meaning that the arguments are evaluated in their usual way, then some function is evaluated and the result is returned as a value. However, the semantics can be significantly different. For example, in assignment a = b the target a is not evaluated, but instead its location (address) is used to store the value of b – corresponding to call-by-reference semantics. Further, an assignment may be a statement (no value), or may be an expression (value), with the value itself either an r-value (just a value) or an l-value (able to be assigned to). As another example, the scope resolution operator :: and the element access operator . (as in Foo::Bar or a.b) operate not on values, but on names, essentially call-by-name semantics, and their value is a name. Use of l-values as operator operands is particularly notable in unary increment and decrement operators. In C, for instance, the following statement is legal and well-defined, and depends on the fact that array indexing returns an l-value: x = ++a[i]; An important use is when a left-associative binary operator modifies its left argument (or produces a side effect) and then evaluates to that argument as an l-value. This allows a sequence of operators all affecting the original argument, allowing a fluent interface, similar to method cascading. A common example is the << operator in the C++ iostream library, which allows fluent output, as follows: cout