lua not modifying function arguments - function

Question

I've been learning lua and can't seem to make a simple implementation of this binary tree work...
function createTree(tree, max)
if max > 0 then
tree = {data = max, left = {}, right = {}}
createTree(tree.left, max - 1)
createTree(tree.right, max - 1)
end
end
function printTree(tree)
if tree then
print(tree.data)
printTree(tree.left)
printTree(tree.right)
end
end
tree = {}
createTree(tree, 3)
printTree(tree)
the program just returns nil after execution. I've searched around the web to understand how argument passing works in lua (if it is by reference or by value) and found out that some types are passed by reference (like tables and functions) while others by value. Still, I made the global variable "tree" a table before passing it to the "createTree" function, and I even initialized "left" and "right" to be empty tables inside of "createTree" for the same purpose. What am I doing wrong?

Answer 1

It is probably necessary to initialize not by a new table, but only to set its values.
function createTree(tree, max)
if max > 0 then
tree.data = max
tree.left = {}
tree.right = {}
createTree(tree.left, max - 1)
createTree(tree.right, max - 1)
end
end

Answer 2

in Lua, arguments are passed by value. Assigning to an argument does not change the original variable.
Try this:
function createTree(max)
if max == 0 then
return nil
else
return {data = max, left = createTree(max-1), right = createTree(max-1)}
end
end

Answer 3

It is safe to think that for the most of the cases lua passes arguments by value. But for any object other than a number (numbers aren't objects actually), the "value" is actually a pointer to the said object.
When you do something like a={1,2,3} or b="asda" the values on the right are allocated somewhere dynamically, and a and b only get addresses of those. Thus, when you pass a to the function fun(a), the pointer is copied to a new variable inside function, but the a itself is unaffected:
function fun(p)
--p stores address of the same object, but `p` is not `a`
p[1]=3--by using the address you can
p[4]=1--alter the contents of the object
p[2]=nil--this will be seen outside
q={}
p={}--here you assign address of another object to the pointer
p=q--(here too)
end
Functions are also represented by pointers to them, you can use debug library to tinker with function object (change upvalues for example), this may affect how function executes, but, once again, you can not change where external references are pointing.
Strings are immutable objects, you can pass them around, there is a library that does stuff to them, but all the functions in that library return new string. So once, again external variable b from b="asda" would not be affected if you tried to do something with "asda" string inside the function.