x is a bound variable. It doesn't 'vary' in the sense that the value it refers to can be mutated, as in a imperative language, but it varies between calls to the function f.
It is rebound. It is improper to call it a "variable" because in any given lifetime, it's value cannot vary. That's the point. It is possible to create a new binding with the same name, but any code holding on to the old instance keeps the old value. Subtle but important difference.
"Varying, in the context of mathematical variables, does not mean change in the course of time, but rather dependence on the context in which the variable is used."
"The identifier in computer source code can be bound to a value during run time, and the value of the variable may thus change during the course of program execution. Variables in programming may not directly correspond to the concept of variables in mathematics."
While I agree with your philosophy of vocabulary here, I've read the Harper article too, it's valuable to state directly that everyone knows there's the _(Programming) article too and is simply disagreeing that its a "good" way to use the term. Anyone who isn't familiar with the distinction in terminology ought to consider what things a programming variable represents that a mathematics variable does not..
