How to assign the real result of *Form function to a variable?

Question

Of course we know,the TreeForm[a + b^2 + c^3 + d] will give a Graphics object.How to assign to a variable an expression which typesets to the same box structure as a TreeForm of a particular input?

Maybe one think we just use the var=TreeForm[a + b^2 + c^3 + d],but you will find the Head of the var is TreeForm.I record a gif for specify this case.

And I found this regular is apply to any *Form function.Such as InputForm

a = InputForm[Graphics[Circle[]]];
Head[a]

InputForm

I have a awkward workaround calling the clipboard can do it almost.

var = NotebookGet[CopyToClipboard[TreeForm[a + b^2 + c^3 + d]]; 
  ClipboardNotebook[]]

But there are some problem in this solution.

1. var include all information,but the Head of var is not Graphics actually.
2. I really don't want to call the clipboard.

So how to assign the Graphics object to a variable?

Answer 1

We have to be careful with wording.

What you really want to do is to "assign to a variable an expression which typesets to the same box structure as a TreeForm of a particular input".

And this can be achieved with:

test = ToExpression @ ToBoxes @ TreeForm[a + b];

So once you know what you want the solution is obvious.

to confirm:

test // InputForm // SequenceForm

   Graphics[Annotation[
  GraphicsComplex[{{0.4472135954999579, 0.8944271909999159}, {0., 
     0.}, {0.8944271909999159, 0.}}, {{RGBColor[0.55, 0.45, 0.45], 
     Line[{{1, 2}, {1, 3}}]}, {Tooltip[
      Inset[Framed[
        Style[Plus, {"StandardForm", "Output", GrayLevel[0]}, 
         FontSize -> Scaled[0.05]], 
        Background -> RGBColor[1., 1., 0.871], 
        FrameStyle -> GrayLevel[0.5], FrameMargins -> Inherited], 1], 
      HoldForm[a + b]], 
     Tooltip[Inset[
       Framed[Style[
         HoldForm[a], {"StandardForm", "Output", GrayLevel[0]}, 
         FontSize -> Scaled[0.05]], 
        Background -> RGBColor[1., 1., 0.871], 
        FrameStyle -> GrayLevel[0.5], FrameMargins -> Inherited], 2], 
      HoldForm[a]], 
     Tooltip[Inset[
       Framed[Style[
         HoldForm[b], {"StandardForm", "Output", GrayLevel[0]}, 
         FontSize -> Scaled[0.05]], 
        Background -> RGBColor[1., 1., 0.871], 
        FrameStyle -> GrayLevel[0.5], FrameMargins -> Inherited], 3], 
      HoldForm[b]]}}, {}], 
  VertexCoordinateRules -> {{0.4472135954999579, 
     0.8944271909999159}, {0., 0.}, {0.8944271909999159, 0.}}], 
 FrameTicks -> Automatic, PlotRange -> All, 
 PlotRangePadding -> Scaled[0.1], AspectRatio -> 1, 
 FormatType :> StandardForm]