Evaluate arguments in a curried function left to right

Question

I have an inner pattern

f[g, n_] := inner

and I want to define an outer curried pattern

f[h, m_][f[g, n_]] := ...

which has unrelated behaviour to f[g,n] and so should receive expression f[g,n] rather than inner. Alas, f[h,m][f[g,n]] is undesiredly first evaluated as f[h,m][inner]. How can I prevent Mathematica from evaluating the inner f[g,n] whilst still recognising a pattern for f[h,m_][..] without having to explicitly insert Hold into the outermost expression?

Of course SetAttribute[f, HoldAll] doesn't work, and I can't exactly set an attribute for the experssion f[h].

My motivation: I'm creating inner "functions" with subscript "arguments", and I want to define an outer "functional" which also has subscript "arguments" which should start evaluating before the passed inner functions are evaluated.

E.g.

Subscript[g1, n_] := bad[n]
Subscript[g2, n_] := bad[n] 
...

Subscript[h, m_][ Subscript[g_,n_] ] := good[g,m,n]

I want the behaviourwhere $g1_n$ gives bad[n], but $h_m[g1_n]$ gives good[g1,m,n]. The above code instead gives $h_m[bad[n]]$.

I notice that the last line of the above code doesn't affect the DownValues of Subscript:

DownValues[Subscript]

    {HoldPattern[Subscript[g1, n_]] :> bad[n], 
    HoldPattern[Subscript[g2, n_]] :> bad[n]}

Is this at all possible?

Answer 1

When I run into problems like this, I workaround it by using ReplaceAll like so:

rules = {
  f[g, n_] :> inner,
  f[h, m_][f[g, n_]] :> outer
};

f[h, m][f[g, n]] //. rules

(* outer *)

That's because while the standard evaluation procedure looks at elements before moving up, ReplaceAll works by first trying to match the whole expression before going deeper.