How can I define a function with a variable with subscript?

Question

I want to define a function in Mathematica:

$$h(\tau_x)=\tau_x$$

$\tau_x$ has no special meaning. To be honest, it's totally OK if I use the function $h(x)=x$ to replace $h(\tau_x)=\tau_x$. It doesn't influence the final value I want. I just want to make this function look better.

Here is what I tried

In[85]:= h[Subscript[\[Tau], x]_]:=Subscript[\[Tau], x]
In[88]:= h[4]
Out[88]= 1
In[89]:= h[x_]:=x
In[90]:= h[4]
Out[90]= 4
In[91]:= <<Notation`
In[92]:= Symbolize[Subscript[\[Tau], x]]
In[93]:= h[Subscript[\[Tau], x]_]:=Subscript[\[Tau], x]
In[94]:= h[4]
Out[94]= Subscript[\[Tau], x]

Here is the image:

Answer 1

Even though this is – as already mentioned by @lericr in the comments and many times across this SE – generally not advised, I still want you to explain why your code does not work.

After symbolizing Subscript[τ, x] and defining h, take a look at the InputForm (!) of downvalues assigned to h:

Clear[h];
h[Subscript[τ, x] _] := Subscript[τ, x]
DownValues[h] // InputForm
(* {HoldPattern[h[τ⎵Subscript⎵x*_]] :> τ⎵Subscript⎵x} *)

Do you see the problem? Subscript[τ, x] _ got parsed as Subscript[τ, x]*_ – multiplication between Subscript[τ, x] and "something". That is why the following code returns a somehow "unexpected" result:

h[2 Subscript[τ, x]]
(* Subscript[τ, x] *)

Therefore, you need to force the parser to understand Subscript[τ, x]_ as Pattern[τ, Blank[]]. The cleanest way to do this is by using a colon:

Clear[h];
h[Subscript[τ, x] : _] := Subscript[τ, x]
h[4]
(* 4 *)