Expanding/printing function with constrained arguments

Question

Let's say you have a function

$ f(t) = t, \text{ for } t > 0,$

declared in Mathematica as

f[t_?(# > 0 &)] := t;

How do you print that function?

I have tried multiple options like

f[t]
FunctionExpand[f[t], t > 0]
f[t] /; t > 0

These return

f[t]
f[t]
f[t] /; t > 0

and not

t

or

t /; t > 0

Which is what I want.

Answer 1

If possible I would define the function using Simplify or Refine, then use Assuming:

f[t_] /; Refine[t > 0] := t;

Assuming[t > 0, f[t]]

t