How can I make interdependent Checkboxes?

Question

Consider the following code, where I have a list of variables, each with different specified units. In my real case, these lists are not fixed, hence the surrounding Dynamic and the general definition for selected. I have checkboxes associated with each, but I only want to allow checkboxes to be simultaneously selected if the variables have the same units. So if, for example, I have "a" selected, but then select "b", that is allowed. But if I have "a" and/or "b" selected, and try to select "c", I want "a" and "b" to become deselected in the process. How can I accomplish this?

Module[{vars = {a, b, c, d}, 
        varunits = {"Molar", "Molar", "Seconds", "DimensionlessUnit"}, 
        selected}, 
  selected[index_] = False; 
  Deploy[Dynamic[Column[
    Row[{vars[[#]], " ", 
         Checkbox[Dynamic[selected[#]]], " ", 
         varunits[[#]]}] & /@ Range[Length[vars]]]]]]

Edited to add: It looks like I can do this using the second parameter of “Dynamic.” But that raises a secondary question: suppose this checkbox is already part of a pure function with slots. The second parameter of Dynamic needs to also be a pure function. And I would like to pass it parameters from the outer slots. Can that be done?

Answer 1

 DynamicModule[{vars = {a, b, c, d}, 
   varunits = {"Molar", "Molar", "Seconds", "DimensionlessUnit"}},
  Deploy[Dynamic[Column[Function[u, Row[{vars[[u]], 
   Checkbox[Dynamic[selected[u], (selected[u] = #; (selected[#] = False) & /@ 
     notselected[u]) &]], varunits[[u]]}, Spacer[10]] ] /@ Range[Length[vars]]]]], 
  Initialization :> {selected[_] := False, 
   notselected = Association[Join @@ Values @ 
     Map[Function[x, # -> Complement[Range@Length@vars, x] & /@ x]]@
       PositionIndex[varunits]]}]

Answer 2

Ok, looks like I have found a solution:

DynamicModule[{vars = {a, b, c, d}, 
               varunits = {"Molar", "Molar", "Seconds", "DimensionlessUnit"}, 
               selected}, selected[index_] = False; 
  Deploy[Dynamic[Column[
    Row[{vars[[#]], " ", 
      Checkbox[Dynamic[selected[#], 
                       Function[checked, selected[#] = checked; 
                       If[checked, Do[If[varunits[[i]] != varunits[[#]], 
                                         selected[i] = False], 
                                      {i, Length[vars]}]]]]], 
      " ", varunits[[#]]}] & /@ Range[Length[vars]]]]]]

I'm sure there's a better way than the Do loop to handle the resets, but at least this gives the idea.

Answer 3

Inspired by the implementation of CheckboxBar:

checkboxes[Dynamic[sels_], list : {(_ -> _) ...}] := 
 DynamicModule[{unit},
  DynamicWrapper[Column[
    Labeled[Checkbox[Dynamic[MemberQ[sels, #],
         Function[arg,
          Which[MemberQ[sels, #], sels = DeleteCases[sels, #],
           unit === None || Last@# === unit, AppendTo[sels, #],
           True, sels = {#}]]]],
       List @@ #, {Left, Right}] & /@ list],
   If[! ListQ[sels], sels = {}];
   unit = First[Values@sels, None];
   ]
  ]

and use it like:

DynamicModule[{sels,
  vlist = {a -> "Molar", b -> "Molar", c -> "Seconds", d -> "DimensionlessUnit"}},
 checkboxes[Dynamic[sels], vlist]
]