Define a function for symbols with UpValues

Question

Suppose that we define UpValues for different symbols

isSpecialFunction[N1]^=True
isSpecialFunction[N2]^=True
isSpecialFunction[N3]^=True

I would like to make the following definition

func_?isSpecialFunction[]:= func[t,x]

such that every time I write e.g. func[] Mathematica substitutes it with func[t,x] only if isSpecialFunction[func]==True.

However, func_?isSpecialFunction[]:= func[t,x] is not a good definition because I get the error SetDelayed: "func_?isSpecialFunction[] does not contain a symbol to attach a rule to. What is the proper procedure to give the aforementioned definition for symbols with UpValues defined in this way?

Please, keep in mind that I want to use the fact that these symbols have UpValues. That's because I am using a package (xCoba), which defines ScalarFunctions with these UpValues and I want to substitute all the ScalarFunctions that appear as func[] with func[t,x].

Answer 1

Clear["Global`*"]

isSpecialFunction[N1] ^= True;
isSpecialFunction[N2] ^= True;
isSpecialFunction[N3] ^= True;

Define a replacement RuleDelayed

rule = func_?isSpecialFunction[] :> func[t, x];

Add application of the rule to $Pre

$Pre := # /. rule &;

Testing,

{N1[], N2[], N3[], N4[]}

(* {N1[t, x], N2[t, x], N3[t, x], N4[]} *)

To clear $Pre

$Pre =.