Manipulate the list. (Argument does not have the correct form for a variable specification.)

Question

Why doesn't this work:

p = {1,2,3};
Manipulate[{p[[1]], p[[2]], p[[3]]}, {p[[1]], 0, 1}, {p[[2]], 0, 1}, {p[[3]], 0, 
      1}]
"Manipulate argument {p[[1]],0,1} does not have the correct form for \
a variable specification"

Neither this:

Manipulate[{Indexed[p, 1], Indexed[p, 2], 
  Indexed[p, 3]}, {Indexed[p, 1], 0, 1}, {Indexed[p, 2], 0, 
  1}, {Indexed[p, 3], 0, 1}]

and how do I use lists in Manipulate w/o stupid hacks like p[i] and then iterating over it with For?

Answer 1

The correct answer is to use nested With as shown below. Note that the hack i=i is mandatory, and you can't tmp[[i]]=# because you would get Set::setps: {FE` $1462$$530,FE`$1463$$530,FE`$1464$$530} in the part assignment is not a symbol.

ClearAll[p, list, tmp];
list = {1, 2, 3};
MakeTable[] := Table[p[i], {i, 1, Length@list}];
With[{vars = MakeTable[],
  controls = Sequence @@
    Table[{p[i],
      list[[i]],
      With[{i = i, tmp = MakeTable[]},
       (Slider[Dynamic[tmp[[i]],
           (tmp = 
              Normal@SparseArray[
                Join[{i -> #}, 
                 Table[j -> list[[j]], {j, 1, Length@list}]]]; 
             list = tmp) &], {0, 10}]) &]},
     {i, 1, Length@list}]},
 {Manipulate[vars, controls], Dynamic@list}]

Answer 2

As mentioned in comments, it's not clear what you're trying to do.

You're getting an error because p={1,2,3} is a list of numbers. Essentially you have Manipulate[1,{1,0,1}]. 1 is not a variable so you can't range over it, i.e. {1,0,1} makes no sense. It needs to be in the form Manipulate[expr,{u,umin,umax}]. See Manipulate.

If you do Manipulate[{x,y,z},{x,0,1},{y,0,1},{z,0,1}] it will work, but you just get three sliders that vary the output point, so I don't really see the purpose of that. Having {x,y,z} as the expression input expr is pretty boring.