Use symbol to replace function

Question

I'm trying some transformations and they are getting complicated. It's common in physics to replace functions by symbols so you term get shorter.

Lets say I have transformation

xr[A_,B_] := K A + L B + KK A^2 + LL B^2,

where A = A[x_] and B = B[x_]

I want to input some random values of x. But for the code to be readable I want to substitute the quadratic part as

H =  KK A^2 + LL B^2

How do I go about this? I don't want to define H as a function, since that would make me have to write

xr[A,B] = xr[A,B,H] = xr[A,B,H[A,B]] = xr[A[x],B[x],H[A[x],B[x]]]

which just gets unwieldy.

Essentially I just want to be able to write H such that mathematica would understand that when I define

xr[A,B] := K A + L B + H

Output of sending a x value to it would be

xr[A[x],B[x]] = K A[x] + L B[x] + KK A[x]^2 + LL B[x]^2.

Hopefully you can understand what I'm trying to do. Thank you for your help.

Edit: This is just an example of function. Of course It wouldn't be useful in this case and I also know there are reasons why this specific type substitution wouldn't be a healthy practice but what are the alternatives.

Answer 1

You can display the unevaluated functions in any desired format.

Format[A[x_]] := A;
Format[B[x_]] := B;

xr[a_, b_] := K a + L b + KK a^2 + LL b^2

Then,

xr[A[x], B[x]]

(* K A + KK A^2 + L B + LL B^2 *)