The problem is with the closure (the anonymous sub{...}</> that -command is) and the scope of $t.  Put a <c>warn $t in the sub{} to see what it's doing -- you'll see that it's always 3 which is the value of t after the foreach my $f (@foo) ... Here are two different approaches to solving it:

Here, you can use a temp value to hold the current value of $t. Since $i is scoped inside the for loop, it is different for each closure that is made. 
    my $i=$t;
        $bill_table->Button(-text=>'Submit',
                        -command=>sub{if ($checkboxvalue[$i] ==1){prin
+t $f}},
                        )->pack;

[download]
Alternatively, use the form of Tk::callback that lets you provide arguments to a sub. Here our anonymous sub takes two args -- a reference to a scalar which is the checkbox value, and a scalar which is the text of the checkbox. 
        $bill_table->Button(-text=>'Submit',
                        -command=>[
                           sub{
                             my $valref = shift;
                             my $valname=shift;
                             if ($$valref ==1){print $valname}
                           },
                           \$checkboxvalue[$t],
                           $f,
                        ],
                        )->pack;

[download]
Now, there's the issue of your Use of uninitialized value in numeric eq (==) .. That is because the checkbox values are either 1 or undef, so when you check <thecheckboxvalue>==1 it'll do either 1==1 (ok) or undef==1 (warning).
To solve, simply do one of these (probably the first? not sure that being exactly 1 is important, as long as it's true: 
  if( $foo ){ print $f }
  if( defined $foo ){ print $f }

  if( $foo && $foo==1){ print $f }
  if( defined $foo && $foo==1){ print $f }

[download]

In reply to Re^2: Array of TK::Checkbuttons not acting appropriately by davidrw
in thread Array of TK::Checkbuttons not acting appropriately by mikasue

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