In generative grammar, the technical term operator denotes a type of expression that enters into an a-bar movement dependency. One often says that the operator "binds a variable".
Operators are often determiners, such as interrogatives ('which', 'who', 'when', etc.), or quantifiers ('every', 'some', 'most', 'no'), but adverbs such as sentential negation ('not') have also been treated as operators. It is also common within generative grammar to hypothesise phonetically empty operators whenever a clause type or construction exhibits symptoms of the presence of an a-bar movement dependency, such as sensitivity to extraction islands.
The following examples illustrate the use of the term operator within generative grammatical theory.
The following example is a case of so-called "wh-movement":
1. What did Bill say he wants to buy __ ?
Here, "what" is an operator, binding a phonetically empty "variable" indicated here as "__".
The next example illustrates so-called "Quantifier Raising" ("QR"):
2. I didn't do something.
In this example, "something" occupies the position of a variable which is bound by an operator in the beginning of the sentence.
This example may require some explanation. The sentence is ambiguous between an "I did nothing" reading and another, "there's something I didn't do" reading. On the latter reading, one would represent the sentence as follows within generative grammar (omitting irrelevant details):
3. Somethingx [I didn't do x]
Here, "x" is the variable, and "somethingx" is the operator binding that variable.
Since no movement appears to have taken place in the original sentence, the movement is said to be "covert", and it is usually referred to as "Quantifier Raising" or "QR". Various theories within generative grammar and linguistic semantics have tried to explain this phenomenon, and various semantic approaches argue that no syntactic movement is present in such sentences