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CS1 Python Subgoals

Section 9.1 Variables Call

Subgoals for evaluating a function call:.

  1. Create stack frame for global variables
  2. Ensure function is defined before function call before beginning body of function
  3. Determine parameter values based on positional arguments, keyword arguments, and default values to initialize local variables
  4. Use stack frame for function to trace local variables
  5. At return to call site, pass values back to call site
  6. Delete stack frame with local variables after return to call site

Subsection 9.1.1

Given the following declarations
def foo(alpha, beta):
    delta = alpha * beta - gamma
    return delta * 2
alpha = 9
gamma = 1
Evaluate these statements and determine the final value of the top-level variables.
kappa = foo(7, alpha) - 20

Subsection 9.1.2 1. Create stack frame for global variables

Prior to the execution of the function, there are two global variables (alpha and gamma). The variable kappa will not be defined until after the function foo is executed, so for now our stack frame only has two variables.
Global variables before function call
Figure 9.1.1.

Subsection 9.1.3 2. Ensure function is defined before function call before beginning body of function

The function foo was defined at the very start of the program, and foo is being called at the very end. Therefore, it is safe to say that the function is defined before it was called.

Subsection 9.1.4 3. Determine parameter values based on positional arguments, keyword arguments, and default values to initialize local variables

When we execute foo, we must match each provided argument with the corresponding parameters.
  • The first argument 7 is matched to the parameter alpha
  • The second argument alpha is substituted for 9 (the value associated with that variable in the Global frame), and then 9 is matched to the parameter beta
Stack frames depicting a function call to foo with parameters
Figure 9.1.2.
Notice that the global variable alpha is completely distinct from the parameter alpha inside the function foo frame. The two variables have the same name, but they are in different frames so they each have their own separate values.

Subsection 9.1.5 4. Use stack frame for function to trace local variables

We begin executing the body of the function, one line at a time.
delta = alpha * beta - gamma
In the first line, we evaluate the right-hand side first, substituting the appropriate values:
  • The alpha is substituted for the alpha variable local to the foo frame, which has the value 9 currently.
  • The beta is substituted for the beta variable local to the foo frame, which has the value 9 currently.
  • The gamma is substituted for the gamma variable from the global frame (since there are no local variables with that name), which has the value 1 currently.
The expression becomes 7 * 9 - 1, which is 62. The value 62 is assigned to a new local variable delta.
Stack frame for foo after executing the first line of the body
Figure 9.1.3.
After we execute the first line of the body, we execute the second line, which is a return statement.
return delta * 2
In that line of code, we substitute 62 for delta and then multiply the result by 2. The final result is 124.

Subsection 9.1.6 5. At return to call site, pass values back to call site

The original function call to foo is now complete, with the value 124 to be returned. We substitute the foo(7, alpha) expression for 124.

Subsection 9.1.7 6. Delete stack frame with local variables after return to call site

Because the function call is completed, we must delete the stack frame. The variables that existed inside the stack frame are not considered among the final global variables.
Stack frames for foo after returning to the call site
Figure 9.1.4.
We can now finish executing the original right-hand side of the expression: 124 - 20 is 104, so the final result 104 is assigned to kappa.

Subsection 9.1.8 Answer

  • alpha: 9
  • gamma: 1
  • kappa: 104
These are the only variables in the global frame, since the other stack frame was deleted.
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