typeof operator in C

Since typeof is a compiler extension, there is not really a definition for it, but in the tradition of C it would be an operator, e.g sizeof and _Alignof are also seen as an operators.

And you are mistaken, C has dynamic types that are only determined at run time: variable modified (VM) types.

size_t n = strtoull(argv[1], 0, 0);
double A[n][n];
typeof(A) B;

can only be determined at run time.

Add on in 2021: there are good chances that typeof with similar rules as for sizeof will make it into C23.

It's a GNU extension. In a nutshell it's a convenient way to declare an object having the same type as another. For example:

int x;         /* Plain old int variable. */
typeof(x) y;   /* Same type as x. Plain old int variable. */

It works entirely at compile-time and it's primarily used in macros. One famous example of macro relying on typeof is container_of.