PrecedenceForm with Format

Question

I'd like to format the output of certain operators with Infix-style formatting to have lower precedence than Times.

Let's say I define foo to format as CenterDot :

Format[x_foo]:=CenterDot@@foo

The following prints with no parentheses (as expected) :

a * foo[x,y]
(* a x \[CenterDot] y *)

This is the sort of output I want :

a*PrecedenceForm[ foo[x,y], 395 ]
(* a (x \[CenterDot] y) *)

However, I'd like to abstract this away a bit more. I'd like to instead do something like

Format[x_foo]:=PrecedenceForm[CenterDot @@ x, 395]

so that this is handled entirely at the output level. However, the PrecedenceForm doesn't seem to do anything:

a*foo[x,y]
(* a x \[CenterDot] y *)

Of course, I'm just as interested in why this doesn't work as I am in solving the problem of inserting parentheses.

Answer 1

\I would suggest to use lower level formatting commands like this

MakeBoxes[foo[arg1_Symbol, arg2_Symbol], StandardForm] := 
 With[{arg1b = MakeBoxes[arg1], arg2b = MakeBoxes[arg2]},
  TemplateBox[{arg1, arg2}, "foo", 
   DisplayFunction :> (RowBox[{"(", 
        RowBox[{arg1b, "\[CenterDot]", arg2b}], ")"}] &)]]

a (x \[CenterDot] y)

Using TemplateBox approach will allow you to convert output into desired input form. If you need only to output, just explicitly form the boxes.

You can add conditions as well, for example, the special formatting will occur only if first argument of bar is 1

MakeBoxes[bar[a__, foo[arg1_Symbol, arg2_Symbol]], StandardForm] :=

 With[{replBox = 
     RowBox[{"(", 
       RowBox[{MakeBoxes[arg1], "\[CenterDot]", MakeBoxes[arg2]}], 
       ")"}]},
   RowBox[{MakeBoxes[bar], "[", MakeBoxes[a], ",",replBox, "]"}]] /; 
  First[{a}] === 1


bar[1, foo[x, y]]

bar[1, (x\[CenterDot]y)]

Answer 2

I think you're looking for SyntaxForm. For example:

foo /: MakeBoxes[foo[x,y], StandardForm] := TemplateBox[
    {MakeBoxes[x], MakeBoxes[y]},
    "foo",
    DisplayFunction->(RowBox[{#1, "\[CenterDot]", #2}]&),
    SyntaxForm->Star
]

I used Star for the SyntaxForm since its precedence is 390, as requested, in between the precedences for Plus and Times:

Precedence /@ {Plus, Star, Times}

{310., 390., 400.}

Then:

a + foo[x, y]
a * foo[x, y]