Defining new brackets

Question

I would like to wrap double-struck brackets around variables for notation purposes only. For instance [[X]] should display as the first image below. However, these brackets are reserved for the built-in function Part.

At the moment, I use angle brackets and then replace these with the new ones via MaTeX). I apply this to lists of expressions involving elements as ⟨XY⟩ -> ⟨X⟩ ⟨Y⟩, where XY, X and Y are graphs:

(⟨XY⟩ -> ⟨X⟩ ⟨Y⟩) /. ⟨x_⟩ :> 
  GraphicsRow[{MaTeX["\\llbracket"], x, MaTeX["\\rrbracket"]}, 
   Scaled[.01], Method -> {"ShrinkWrap" -> True}, ImageSize -> 40]

However, as shown in the second image, there are alignment and scaling issues. If the double-struck brackets are defined as a new notation, I could use instead

(⟨XY⟩ -> ⟨X⟩ ⟨Y⟩) /. ⟨x_⟩ :> [[x]]

which would keep XY, X and Y consistent with their original alignment and scaling.

Answer 1

One way of doing this is to use $Preprint:

First define the variables you want to print with double brackets. Then define a $PrePrint function:

vars = {a, b, c};
$PrePrint = 
  With[{v = 
     Thread[vars -> ("[LeftDoubleBracket]" <> ToString[#] <> 
           "[RightDoubleBracket]" &) /@ vars]}, # /. v &];

Here is an example:

Sqrt[a] + b^3 - Sin[c]

Answer 2

Via the Notation package, one can define a new command:

Needs["Notation`"];
Notation[ParsedBoxWrapper[
   RowBox[{"\[LeftDoubleBracket]", "x_", 
     "\[RightDoubleBracket]"}]]\[DoubleLongLeftArrow]ParsedBoxWrapper[
   RowBox[{"ll[", "x_", "rr]"}]]]

which is displayed with the notation palette as

and which gives the result