Suppose that instead of concatenating the result of the recursive call to to_string with the string from CHAR_FROM_INT, we modified our algorithm to push the strings onto a stack prior to making the recursive call. The code for this modified algorithm might look like:

CHAR_FROM_INT = '0123456789ABCDEF'

def to_string(n,base):
    stack = []
    while n > 0:
        if n < base:
            stack.append(CHAR_FROM_INT[n % base])
        n = n // base
    result = ''
    while stack:
        result = result + stack.pop()
    return result

to_string(1453,16)  # => 5AD

Each time we make a call to to_string, we push a character on the stack. Returning to the previous example we can see that after the fourth call to to_string the stack would look the diagram below. Notice that now we can simply pop the characters off the stack and concatenate them into the final result, '1010'.

Strings placed on the stack during
Strings placed on the stack during conversion

The previous example gives us some insight into how Python implements a recursive function call. When a function is called in Python, a stack frame is allocated to handle the local variables of the function. When the function returns, the return value is left on top of the stack for the calling function to access. The diagram below illustrates the call stack after the return statement.

Call stack generated from
to_string(10, 2)
Call stack generated from to_string(10, 2)

Notice that the call to to_string(2 // 2, 2) leaves a return value of '1' on the stack. This return value is then used in place of the function call (to_string(1,2)) in the expression '1' + CHAR_FROM_INT[2 % 2], which will leave the string '10' on the top of the stack. In this way, the Python call stack takes the place of the stack we used explicitly in our algorithm above. In our list summing example, you can think of the return value on the stack taking the place of an accumulator variable.

The stack frames also provide a scope for the variables used by the function. Even though we are calling the same function over and over, each call creates a new scope for the variables that are local to the function.