How to delay this evaluation

Question

I am trying to create two sets, then merge them (they have one common element) and then take the total of the new set.

Let's call them set1 and set2 while their union is called set

set1[t_,gh_,ga_]:=If[gh==0,Reap[For[i=0,i<=10,i++,Sow[fn[0,i,t,gh,ga]]]][[2,1]],{}];
set2[t_,gh_,ga_]:=If[ga==0,Reap[For[i=0,i<=10,i++,Sow[fn[i,0,t,gh,ga]]]][[2,1]],{}];

and

set[t_, gh_, ga_] := 
  Union[set1[t, gh, ga], set2[t, gh, ga]];

I call them by setting t=gh=ga=0 and I get this:

set1[0,0,0]

{fn[0,0,0,0,0],fn[0,1,0,0,0],fn[0,2,0,0,0],fn[0,3,0,0,0],fn[0,4,0,0,0],fn[0,5,0,0,0],fn[0,6,0,0,0],fn[0,7,0,0,0],fn[0,8,0,0,0],fn[0,9,0,0,0],fn[0,10,0,0,0]}

set2[0,0,0]

{fn[0,0,0,0,0],fn[1,0,0,0,0],fn[2,0,0,0,0],fn[3,0,0,0,0],fn[4,0,0,0,0],fn[5,0,0,0,0],fn[6,0,0,0,0],fn[7,0,0,0,0],fn[8,0,0,0,0],fn[9,0,0,0,0],fn[10,0,0,0,0]}

and finally

set[0,0,0]

{fn[0,0,0,0,0],fn[0,1,0,0,0],fn[0,2,0,0,0],fn[0,3,0,0,0],fn[0,4,0,0,0],fn[0,5,0,0,0],fn[0,6,0,0,0],fn[0,7,0,0,0],fn[0,8,0,0,0],fn[0,9,0,0,0],fn[0,10,0,0,0],fn[1,0,0,0,0],fn[2,0,0,0,0],fn[3,0,0,0,0],fn[4,0,0,0,0],fn[5,0,0,0,0],fn[6,0,0,0,0],fn[7,0,0,0,0],fn[8,0,0,0,0],fn[9,0,0,0,0],fn[10,0,0,0,0]}

and then i simply ask for set[0,0,0]//Total.

Here is the thing. When I feed my program with some initial values everything works fine, unless the initial values are such that fn[1,0,0,0,0] is equal to fn[0,1,0,0,0] and so on, for example suppose that they are both equao to 0.2

since two sets (set1,set2) are equal after evaluation for example:

set1 = {0.20, 0.30, 0.40}
set2 = {0.20, 0.30, 0.40}

when I ask for their union I get set = {0.20, 0.30, 0.40} and later on I get half the total I was supposed to get: set[0,0,0]//Total = 0.90 while I was expecting 1.80

So basically I need to form set before fn is evaluated. It is crucial to define fn though before those sets. I tried hold, Unevaluated, Cell [Evaluatable->False] and other functions/properties but none workded. Any idea?

Answer 1

If the problem is that you already defined the function called fn while you are executing your code a simple solution is to execute it inside a Block redefining fn locally:

fn[a_, b_, c_, d_, e_] := a + b + c + d + e;

Block[{fn},
 Union[set1[1, 0, 0], set2[1, 0, 0]] // Total
 ]
(* Out[1] = 131 *)

Union[set1[1, 0, 0], set2[1, 0, 0]] // Total
(* Out[2] = 66 *)

where I arbitrarily defined a fn function to show that this works