Error Resulting from Placing a Dynamic Variable inside of Table

Question

I want to create a list of values, True or False, and to update those values with a Checkbox. But the number of elements needs to be arbitrary.

It should look something like the following code which works perfectly fine:

dyn={False,False,False};
A={{1,dyn[[1]]},{2,dyn[[2]]},{3,dyn[[3]]}}
Row@{Checkbox@Dynamic@dyn[[1]],Checkbox@Dynamic@dyn[[2]],Checkbox@Dynamic@dyn[[3]]}

But, of course, it is not practical to write out every iteration of these things. This is the reason that Table exists. However, when I put everything into tables, it does not work.

n=3;
dyn=Table[False,{i,n}];
A=Dynamic@Table[{i,dyn[[i]]},{i,n}]
Row@Table[Checkbox@Dynamic@dyn[[i]],{i,n}]

The code above results in this error message:

Part::pspec: Part specification i is neither an integer nor a list of integers. >>

I do not understand why Table and Dynamic are in conflict with one another. It is as if Dynamic reaches the i before Table and replace it with an iterative value and then Dynamic has no idea what to do with it. But why is this? Or is the problem something else altogether?

Answer 1

Compare the output of this:

Table[ Dynamic[i], {i,3}]  (* gives {i,i,i} *)

with this:

Table[ With[{i=i},Dynamic[i]], {i,3}]  (* gives {1,2,3} *)

Now you can use that:

a = Range[3];
Table[ With[{i=i}, Dynamic[ a[[i]] ] ], {i,3}]  (* gives {1,2,3} *)

Then:

a+=1;   (* changes output above to {2,3,4} *)

Addendum to address question in the comments below: You can look at the Attributes of a function (in this case Dynamic). If you see that it has a HoldFirst (or HoldRest, or HoldAll) attribute, then that tells you some of its arguments will not be evaluated. For example, consider:

Attributes[foo] = {HoldFirst};
Table[ foo[i], {i,3} ]   (* gives {foo[i], foo[i], foo[i] *)
Table[ With[{i=i},foo[i]], {i,3}]  (* gives {foo[1], foo[2], foo[3] *)

Answer 2

One possibility is to use MapIndexed:

n = 3; dyn = Table[False, {i, n}];
A = Dynamic@Transpose[{Range[n], dyn}]
MapIndexed[Checkbox[Dynamic[dyn[[#2[[1]]]]]] &, Range[n]]