A recursive approach requires the function invoking itself with different arguments. How does the computer keep track of the various arguments and different function invocations if it’s the same function definition?

Repeatedly invoking functions may be familiar when it occurs sequentially, but it can be jarring to see this invocation occur within a function definition.

Languages make this possible with call stacks and execution contexts.

Stacks, a data structure, follow a strict protocol for the order data enters and exits the structure: the last thing to enter is the first thing to leave.

Your programming language often manages the call stack, which exists outside of any specific function. This call stack tracks the ordering of the different function invocations, so the last function to enter the call stack is the first function to exit the call stack.

We can think of execution contexts as the specific values we plug into a function call.

A function which adds two numbers:

Invoking the function with 3 and 4 as arguments...
execution context:
X = 3
Y = 4

Invoking the function with 6 and 2 as arguments...
execution context:
X = 6
Y = 2

Consider a pseudo-code function which sums the integers in an array:

 function, sum_list 
   if list has a single element
     return that single element
   otherwise...
     add first element to value of sum_list called with every element minus the first

This function will be invoked as many times as there are elements within the list! Let’s step through:

CALL STACK EMPTY
___________________

Our first function call...
sum_list([5, 6, 7])

CALL STACK CONTAINS
___________________
sum_list([5, 6, 7])
with the execution context of a list being [5, 6, 7]
___________________

Base case, a list of one element not met.
We invoke sum_list with the list of [6, 7]...

CALL STACK CONTAINS
___________________
sum_list([6, 7])
with the execution context of a list being [6, 7]
___________________
sum_list([5, 6, 7])
with the execution context of a list being [5, 6, 7]
___________________

Base case, a list of one element not met.
We invoke sum_list with the list of [7]...

CALL STACK CONTAINS
___________________
sum_list([7])
with the execution context of a list being [7]
___________________
sum_list([6, 7])
with the execution context of a list being [6, 7]
___________________
sum_list([5, 6, 7])
with the execution context of a list being [5, 6, 7]
___________________

We've reached our base case! List is one element. 
We return that one element.
This return value does two things:

1) "pops" sum_list([7]) from CALL STACK.
2) provides a return value for sum_list([6, 7])

----------------
CALL STACK CONTAINS
___________________
sum_list([6, 7])
with the execution context of a list being [6, 7]
RETURN VALUE = 7
___________________
sum_list([5, 6, 7])
with the execution context of a list being [5, 6, 7]
___________________

sum_list([6, 7]) waits for the return value of sum_list([7]), which it just received. 

sum_list([6, 7]) has resolved and "popped" from the call stack...


----------------
CALL STACK contains
___________________
sum_list([5, 6, 7])
with the execution context of a list being [5, 6, 7]
RETURN VALUE = 6 + 7
___________________

sum_list([5, 6, 7]) waits for the return value of sum_list([6, 7]), which it just received. 
sum_list([5, 6, 7]) has resolved and "popped" from the call stack.


----------------
CALL STACK is empty
___________________
RETURN VALUE = (5 + 6 + 7) = 18