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Symbolic functions without named variables

Is there a way to define a symbolic function that can (e.g.) be differentiated, but doesn't remember the name of its input variable(s)? For instance, consider:

sage: f(x) = x^2
sage: g(x) = x^2
sage: h(t) = t^2

Mathematically, f, g, and h, should all be the same function. However, Sage doesn't think so:

sage: f+g
x |--> 2*x^2
sage: f+h
(t, x) |--> t^2 + x^2

I guess that this is happening because a "function" defined with f(x)=x^2 is actually just a symbolic expression equipped with an ordering on its variables, rather than what a mathematician would call a "function". Is there a way to define an actual mathematical function?