InterpretationBox problem with symbolic expressions

Question

Related to this question,

Why does this InterpretationBox construct work when x, y are numbers but not undefined symbols or more complex expressions?

foo /: MakeBoxes[c : foo[x_, y_], form : (StandardForm | TraditionalForm)] := With[{boxes = SubscriptBox[x, y]}, InterpretationBox[boxes, c]]

EDIT

Originally intended to state the full problem but then simplified it. kglr's answer does not work as intended, so here is the complication:

Would like foo[r,m] to display in subscript form, but when provided with a SubValue, it should evaluate to the rhs:

foo[r_,m_][h_]:= m h + r

END EDIT

Works:

foo[2,3]

Subscript[2, 3]

Plugging in x inserts $CellContext:

foo[2, x]

Subscript[2, $CellContext`x]

or fails with List:

foo[{1, 2}, 3]

An unknown box name (List) was sent as the BoxForm for the expression. Check the format rules for the expression.

Answer 1

Answering the title question, when creating boxes, everything should be a *Box object or a string (or possibly a list). Inside of a box object, excluding options, again, everything should be a *Box object or a string (or list). There is one exception to this rule. It is ok to use integers instead of the corresponding strings. I'm not sure why this exception is made, as it results in the confusion that you face when using x instead of 1 breaks things.

As for the actual format code, another possibility is:

foo /: MakeBoxes[foo[x_, y_], form_] := MakeBoxes[Subscript[x, y], form]

Finally, I think your edited issue is that you included ClearAll[foo] after defining the subvalue definition.

Answer 2

Replace boxes = SubscriptBox[x, y] with SubscriptBox[ToBoxes@x, ToBoxes@y]:

ClearAll[foo]
foo /: MakeBoxes[c : foo[x_, y_], form : (StandardForm | TraditionalForm)] := 
 With[{boxes = SubscriptBox[ToBoxes @ x, ToBoxes @ y]}, InterpretationBox[boxes, c]]

Examples:

foo[2, 3]

Subscript[2, 3]

foo[2, 3]

Subscript[2, x]

foo[{a, b}, {1, 2, 3}]

Subscript[{a,b}, {1,2,3}]

As suggested by @Kuba in comments, use

boxes = SubscriptBox[MakeBoxes @ x, MakeBoxes @ y]

to avoid evaluation leaks in cases like Hold @ foo[f[1 + 2], x + y].