Why doesn't "Defer" work with "TableForm"?

Question

Background:I want to create a "palette" that contains buttons that evaluate the selected part of the expression and replace the selection with the result, just like what the built-in palette "Algebraic Manipulation" does. I found a way to achieve this feature in the documentation of Button:

Button[Defer[Expand[\[SelectionPlaceholder]]], None, BaseStyle -> "Evaluate"]

As you know, this creates a button named Expand that Expand the selected expression and replace it with the result.

(a + b)^5

Select the expression above and click the button, the expression will change to:

a^5 + 5 a^4 b + 10 a^3 b^2 + 10 a^2 b^3 + 5 a b^4 + b^5

I think this feature is very convenient, and I would like to create more stuff with it.e.g: create a button of this style with TableForm,I tried the following code:

Button[Defer[TableForm[\[SelectionPlaceholder]]], None, BaseStyle -> "Evaluate"]

Well, this is a simple imitation of the example shown above. But it gives me a button with a single SelectionPlaceholder.

Finally,I found that Defer won't work with TableForm. When you execute:

Defer[TableForm[{1, 2, 3}]]

It gives me the TableForm of {1,2,3}. But when I use the following code:

Tableform = TableForm; Defer[Tableform[{1, 2, 3}]]

it works fine:

 Tableform[{1, 2, 3}]

And then I can achieve what I want with this:

Tableform=TableForm;
Button[Defer[Tableform[\[SelectionPlaceholder]]], None, BaseStyle -> "Evaluate"]

Q: Could anyone gives me more details of how these things work?

Bonus: How can I create this kind of "inline execute" palette with more complicated user-defined functions? (I would like to add it to the Palettes Menu, but I have no idea of where to get my user-defined function initialized every time I start the palette.) And is there any other way to create a "inline execute" button?

Answer 1

The problem is in the way that various *Form functions are handled. Most of these act as wrappers that change the way their contents are displayed by the FrontEnd (or when converted to Boxes). This is contrary to normal functions which are evaluated by the Kernel and which typically do something with their contents (arguments).

This is somewhat akin to the handling of Dynamic, so please see:
How can I compare a dynamic variable with a literal in Mathematica?

Consider:

x = Hold[TableForm[{1, 2, 3}]]

Yet the definition of x is as we expect:

?x

x = Hold[TableForm[{1, 2, 3}]]

This property of Forms is often very useful, enabling styling without evaluation among other things.

HoldForm @ FullForm[1 + 2 + 3]

Plus[1, 2, 3]

We see that HoldForm works just as it should, preventing the evaluation of its argument but displaying invisibly, yet FullForm is correctly interpreted to display the full bracketed syntax of 1 + 2 + 3.

As Rojo shows in a comment, you just need to keep TableForm[stuff] from appearing in the output to prevent it from being active in formatting. One way to do this is to wrap it in Defer:

Button[Defer[TableForm][\[SelectionPlaceholder]], None, BaseStyle -> "Evaluate"]

You can still wrap the surrounding expression in Defer as well, to prevent other evaluation:

Button[Defer[Defer[TableForm][{1 + 2, 3 + 4}]], None, BaseStyle -> "Evaluate"]