Chapter 6 Return Values

Built-in Functions: Functions that are pre-defined in Python.
- Common examples include:
  - abs(): Returns the absolute value of a number.
  - round(): Rounds a number to a specified number of decimal places.
  - Math Module Functions: E.g., math.sqrt(), math.pow().
    - math.sqrt(x): Returns the square root of x.
    - math.pow(x, y): Returns x raised to the power of y.

Functions can return values that can be assigned to variables or used as part of expressions.
- Example: a = circle_area(radius) or circle_area(radius) + 2 * circle_area(radius / 2).
Local Variables: Variables defined within a function (e.g., area in circle_area) cannot be accessed outside that function.
Some functions may not return a value (None), which represents a lack of value:
- None is similar to True and False, but typically represents a non-existent or empty return.
Pure Functions: Functions that only return a value without any other side effects.

Rewrite functions like abs must ensure all code paths hit a return statement.
- Example of unsafe code includes paths where there is no return value leading to None.
Dead Code: Portions of code that cannot execute, often because they follow a return statement.

An approach in coding where development occurs in small increments with testing after each addition.
- Sample arguments should replace print statements with return values to prevent returning None.
- This method helps in ensuring that functions remain pure and effective.

Scaffolding: Temporary code used during development that helps in debugging but is not part of the finished product.
- Effective for troubleshooting code and reducing debugging time.

Functions that return boolean values (True or False).
- They are useful for complex tests especially in conditionals.

Recursion involves a function calling itself and is foundational to many coding problems.
- Turing Complete: A language is this if it can perform any computation that can be described algorithmically.
Writing recursive definitions similar to mathematical equality can help create powerful Python functions.
- A challenge arises when ensuring recursive definitions efficiently calculate results.

To prevent infinite recursion, use isinstance() to check the type of arguments received by functions.

Input Validation: Process of checking parameters to ensure they are of the correct type and hold expected values.

If functions fail, consider these problems:
1. Issues with argument types (PREcondition violated).
2. Issues within the function logic (POSTcondition violated).
3. Mismanagement of returned values by the caller.
Debugging steps include:
- Use print statements to check PREconditions at function entry.
- Insert print statements prior to each return statement.
- Review the function calls to ensure return values are correct and being utilized consistently.

Return value: The result produced by a function.
Pure Function: No side effects; only returns a value.
Dead Code: Code that is unreachable, often due to a prior return statement.
Incremental Development: Strategy of adding code in small, testable increments.
Scaffolding: Temporary support code used during development.
Turing Complete: Indicates a computational system capable of performing any algorithmic computation.
Input Validation: Ensuring function parameters are of correct types and values.