Why does f[set_]:=AppendTo[set,5] not work when applying f to a set?

Question

The following code works

ccc = {};

AppendTo[ccc, 5];
ccc

and gives the output {5}

However, the following code does not work:

ccc={};
cc[emptySet_] := AppendTo[emptySet, 5]
cc[ccc]

Instead giving the error "AppendTo: {} is not a variable with a value, so its value cannot be changed."

Why does the second way not work?

• From the error I'm guessing the definition of ccc is being substituted for for ccc, which is not a variable.
• I imagine this is probably me just defining the function incorrectly, with some trivial error (maybe I need a hold or a condition something)

Answer 1

To expand upon my comment, in order to pass by reference you can use Hold. So for instance:

In[1]:= foo[Hold[x_], val_] := AppendTo[x, val];

In[5]:= x = {};

In[6]:= foo[Hold@x, 2]

Out[6]= {2}

In[7]:= x

Out[7]= {2}

If you pass a held variable, this has the effect of passing by reference as opposed to by value, so we have access to the variable x rather than the data that x holds.

Answer 2

According to AppendTo documentation:

AppendTo[x,elem] is equivalent to x=Append[x,elem].

When you use AppendTo[{}, 1] Mathematica can't evaluate {}=Append[{},1]. The solution is to give the variable's name to AppendTo and it'll figure it out. That's why Mathematica has something like Hold_sth.

The code below will raise error because when you write f[l1], Mathematica will replace variable's name with it's value and that makes the problem:

l1 = {};
f1[l_] := AppendTo[l, 1]
f1[l1]

(*Out: ERROR *)

Solution

You can do it in different ways, one natural way is to say to your function don't replace names with values:

l2 = {};
f2[l_] := AppendTo[l, 1]
SetAttributes[f2, HoldAll];
f2[l2]

(*Out: {1} *)