Functions

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What we'll discuss today...

Zoom rules
Values
Expressions
Functions

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Expressions & Values

What do programs do?

Programs work by manipulating values
Expressions in programs evaluate to values
- Expression: 'a' + 'hoy'
- Value: 'ahoy'
The Python interpreter evaluates expressions and displays their values

Values

Programs manipulate values.

Each value has a certain data type.

Data type	Example values
Integers	`2` `44` `-3`
Floats	`3.14` `4.5` `-2.0`
Booleans	`True` `False`
Strings	`'¡hola!'` `'its python time!'`

Try in a Python interpreter, like on code.cs61a.org.

Expressions (with operators)

An expression describes a computation and evaluates to a value.

Some expressions use operators:


                    18 + 69


                    6/23


                    2 * 100


                    2 ** 100

Try in a Python interpreter, like on code.cs61a.org.

Call expressions

Many expressions use function calls:


                    pow(2, 100)


                    max(50, 300)


                    min(-1, -300)

Expressions (both ways)

Expressions with operators can also be expressed with function call notation:


                    2 ** 100
                    pow(2, 100)


                    from operator import add

                    18 + 69
                    add(18, 69)

The pow() function is a built-in; it's provided in every Python environment. Other functions (add(), div(), etc) must be imported from the operator module in the Python standard library.

Anatomy of a Call Expression

add	(	18	,	69	)
Operator		Operand		Operand

How Python evaluates a call expression:

Evaluate the operator
Evaluate the operands
Apply the operator (a function) to the evaluated operands (arguments)

Operators and operands are also expressions, so they must be evaluated to discover their values.

Evaluating nested expressions

This is called an expression tree.

Exercise: Expressions

After the lecture, you can try out this exercise. (Not graded, just another way to engage with the material!)

Names

Names

A name can be bound to a value.

One way to bind a name is with an assignment statement:

x	=	7
Name		Value

The value can be any expression:

x	=	1 + 2 * 3 - 4 // 5
Name		Expression

Using names

A name can be referenced multiple times:


                    x = 10
                    y = 3

                    result1 = x * y
                    result2 = x + y

A name that's bound to a data value is also known as a variable.

Name rebinding

A name can only be bound to a single value.


                    my_name = 'Pamela'

                    my_name = my_name + 'ela'

💬 Will that code error? If not, what will my_name store?
It will not error (similar code in other languages might, however). The name my_name is now bound to the value 'Pamelaela'.

Exercise

Try this after the lecture...

What will be the value of the final expression in this sequence?


                    f = min
                    f = max
                    g = min
                    h = max
                    max = g
                    max(f(2, g(h(1, 5), 3)), 4)

Environment diagrams

An environment diagram is a visualization of how Python interprets a program. Use the free website PythonTutor to generate diagrams. View example

Code (left)	Frames (right)

Arrows indicate the order of execution. Green = just executed, red = up next.	Each name is bound to a value. Within a frame, each name cannot be repeated.

Assignments in Environment diagrams

How Python interprets an assignment statement:

Evaluate the expression to the right of =.
Bind the expression's value to the name that's on the left side of the = sign.

View in PythonTutor

Functions

What is a function?

A function is a sequence of code that performs a particular task and can be easily reused. ♻️

We've already used functions:


                    add(18, 69)
                    mul(60, sub(5, 4))

A function takes inputs (the arguments) and returns an output (the return value).

18, 69 → add → 87

Defining functions

The most common way to define functions is Python is the def statement.


                    def <name>(<parameters>):
                        return <return expression>

Example:


                    def add(num1, num2):
                        return num1 + num2

Once defined, we can call it:


                    add(2, 2)
                    add(18, 69)

Anatomy of a function definition

The first line is called the function signature, all lines after are considered the function body.


                    def <name>(<parameters>):        # ← Function signature
                        return <return expression>   # ← Function body


                    def add(num1, num2):             # ← Function signature
                        return num1 + num2           # ← Function body

The function body can have multiple lines:


                    def add(num1, num2):             # ← Function signature
                        sum = num1 + num2            # ← Function body
                        return sum                   # ← Function body

Function arguments

We can pass in any expressions as arguments.


                    def add(num1, num2):
                        return num1 + num2


                    x = 1
                    y = 2
                    add(x, y)


                    x = 3
                    add(x * x, x + x)

Example with strings

Return values

The return keyword returns a value to whoever calls the function (and exits the function).


                    def add(num1, num2):
                        return num1 + num2

                    sum = add(2, 4)

Reminder: You can use function calls in expressions:


                    big_sum = add(200, 412) + add(312, 256)

...and nest function calls inside function calls:


                    huge_sum = add(add(200, 412), add(312, 256))

Spot the bug #1

What's wrong with this code?


                    def add(num1, num2):
                        return sum
                        sum = num1 + num2

                    sum = add(2, 4)

The code after the return statement will not be executed, that line belongs before the return.

Spot the bug #2

What's wrong with this code?


                    def add():
                        return num1 + num2

                    sum = add(2, 4)

The function body is referring to variables that don't seem to exist. Most likely, they should be parameters in the function signature.

Spot the bug #3

What's wrong with this code?


                    def add(num1, num2):
                        sum = num1 + num2

                    sum = add(2, 4)

The function body does not return any value. However, the code that calls it tries to use the result of the expression. It should have a return statement that returns the sum.

Functions in environment diagrams

How Python interprets a def statement:

It creates a function with the name and parameters
It sets the function body to everything indented after the first line
It binds the function name to that function body (similar to an assignment statement)

screenshot of PythonTutor executing a def statement

View in PythonTutor

Function calls in environment diagrams

How Python interprets a function call:

It creates a new frame in the environment
It binds the function call's arguments to the parameters in that frame
It executes the body of the function in the new frame

View in PythonTutor

More on names

Names and environments

All Python code is evaluated in the context of an environment, which is a sequence of frames.

We've seen two possible environments:

Global frame
Function's local frame, child of Global frame

Name lookup rules

How Python looks up names in a user-defined function:

Look it up in the local frame
If name isn't in local frame, look it up in the global frame
If name isn't in either frame, throw a NameError

*This is simplified since we haven't learned all the Python features that complicate the rules.

Name lookup example #1


                    def exclamify(text):
                        start_exclaim = "¡"
                        end_exclaim = "!"
                        return start_exclaim + text + end_exclaim

                    exclamify("the snails are eating my lupines")

On line 4, which frame is start_exclaim found in?
The local frame for exclamify
On line 4, Which frame is text found in?
The local frame for exclamify
On line 6, which frame is exclamify found in?
The global frame

View in PythonTutor

Name lookup example #2


                    start_exclaim = "¡"
                    end_exclaim = "❣️"

                    def exclamify(text):
                        return start_exclaim + text + end_exclaim

                    exclamify("the voles are digging such holes")

On line 5, which frame is start_exclaim found in?
The global frame
On line 5, Which frame is text found in?
The local frame for exclamify
On line 6, which frame is exclamify found in?
The global frame

View in PythonTutor

Name lookup example #3


                    def exclamify(text):
                        end_exclaim = "⁉️️️"
                        return start_exclaim + text + end_exclaim

                    exclamify("the voles are digging such holes")

Which name will cause a NameError?
The start_exclaim name, since it was never assigned.
When will that error happen?
It will happen when exclamify is called and Python tries to execute the return statement.

View in PythonTutor

Summary

Programs consist of statements, or instructions for the computer, containing expressions, which describe computation and evaluate to values.
Values can be assigned to names to avoid repeating computations.
An assignment statement assigns the value of an expression to a name in the current environment.
Functions encapsulate a series of statements that maps arguments to a return value.
A def statement creates a function object with certain parameters and a body and binds it to a name in the current environment.
A call expression applies the value of its operator, a function, to the value(s) or its operand(s), some arguments.

Exercises

You can try these exercises after the lecture for some additional practice:

To run the doctests, press the red test tube in the upper right corner.