Define Custom Notation in Mathematica

Question

I often need to extract to restrict value lists to sublists, ie if vals gives values of vars={x1,x2,x3,x4}, and I need values of svars={x2,x4

Answer 1

Good notations can be very useful - but I'm not sure that this particular one is needed...

That said, the Notation package makes this pretty easy. As there are many hidden boxes when you use the Notation palette, I'll use a screenshot:

You can see the underlying NotationMake* downvalues construct by using the Action -> PrintNotationRules option. In[4] in the screenshot generates

NotationMakeExpression[
  SubscriptBox[vals_, RowBox[{vars_, "|", svars_}]], StandardForm] := 
 MakeExpression[
  RowBox[{"restrict", "[", RowBox[{vars, ",", svars, ",", vals}], 
    "]"}], StandardForm]

NotationMakeBoxes[Subscript[vals_, vars_ | svars_], StandardForm] := 
 SubscriptBox[MakeBoxes[vals, StandardForm], 
  RowBox[{Parenthesize[vars, StandardForm, Alternatives], "|", 
    Parenthesize[svars, StandardForm, Alternatives]}]]