HoldFirst being overridden by Activate

Question

So here's the problem a=1;a=2 works because of the HoldFirst attribute of Set, so that it does not become 1=2 But a=1;Activate[Inactivate[a=2]] does not because the attributes of Set is lost during Inactivate. So how do I avoid this problem?

Update So I've read the answers and it was a brilliant solution. The reason for my use of Inactivate is is meta-programming, where the symbols are Inactive during the construction to avoid messing everything up. But I used Set in the code so that's why I encountered this problem.

Answer 1

[Edit: As noted in the comments, you're probably better off using Hold,ReleaseHold etc. to solve your problem, since Inactivate was never designed for this use case. Having said that, below you'll find one possible attempt to replicate the desired behaviour as closely as possible]

The goal

For this answer, I'll try to address the following requirements for a new function myInactivate:

• myInactivate should replicate the behaviour of Inactivate for cases where there are no Hold attributes at play. This includes:
  • Nice typesetting
  • Localized inactivation in the sense that parts are inactivated separately
  • A way to activate only parts again (see possible extensions below)
• Inactivated symbols should still have the same Hold attributes as the original symbol

Examples

You can find the code for myInactivate,myActivate, etc. at the end of the answer.

myInactivate can be used just like Inactivate:

a = 1;
myInactivate[a = 2]
(* myInactive[Set][a, 2] *)
myActivate[%]
(* 2 *)

It also supports the typesetting of Inactive expressions:

myInactivate[Sum[f[a = 2, z], {n, 1, 2}]]

You can filter out all inactive heads using myInactiveQ:

myInactivate[Sum[f[a = 2, z], {n, 1, 2}]] // 
 Cases[#, _?myInactiveQ, All, Heads -> True] &
(* {myInactive[Sum], myInactive[f], myInactive[Set]} *)

You can also manually create inactive symbols using myInactive:

myInactive[Set][a, 2]

Possible extensions

To make something like this really something with more control than Hold and related functions, one would need to implement the two argument forms of Inactivate and Activate (i.e. filtering of what gets inactivated). This would then allow for selective inactivation, something that is difficult to achieve with Hold and friends.

How it works

As noted in the comments, composite heads (e.g. Inactive[Set]) are out, as they can't have any attributes. So the only thing we can to is to replace the heads with a new, inert symbol. This is exactly what myInactive does (let sym be the symbol to inactivate):

• If not already done, it creates a new symbol (e.g. inactivesym), with the same attributes as sym (except Protected and Locked, for obvious reasons).
• It adds the new symbol inactivesym to inactSymbols, the replacement list to revert inactivation.
• It adds a typesetting rule to typeset inactivesym[...] as Inactive[sym][...] (wrapped in an InterpretationBox, to ensure that the output can be copied)
• It adds a typesetting rule to typeset inactivesym as myInactive[sym]
• It marks inactivesym as myInactiveQ

You'll also notice the special casing of List and Rule: Apparently, Inactivate doesn't touch some inert heads such as List and Rule, so I've added them here as well.

Code

inactSymbols = <||>;
Attributes[myInactiveQ] = {HoldFirst};
myInactiveQ[_] := False
Attributes[myInactive] = {HoldFirst};
myInactive[h_] := myInactive[h] = With[
   {s = Unique["inact" <> SymbolName@Unevaluated@h]},
   Attributes[s] = Complement[Attributes[h], {Protected, Locked}];
   MakeBoxes[s[args___], frm_] ^:= With[
     {b = MakeBoxes[Inactive[h][args], frm]},
     InterpretationBox[b, s[args]]
     ];
   AppendTo[inactSymbols, s -> h];
   MakeBoxes[s, frm_] ^:= MakeBoxes[myInactive[h], frm];
   myInactiveQ[s] ^= True;
   s
   ]
myInactive[s_?myInactiveQ] := s
myInactive[s : List | Rule] := s
Attributes[myInactivate] = {HoldFirst};
myInactivate[expr_] := Replace[
  Unevaluated@expr,
  {
   i : HoldPattern[myInactive[h_][args___]] :> i,
   h_Symbol[args___] :> With[
     {in = myInactive[h]},
     in[args] /; True
     ]
   },
  All
  ]
myActivate[expr_] := expr /. inactSymbols