cs61a_lec1_function

Names, Assignment, and User-Defined Functions

There are some built-in names in Python:

>>> from math import pi, sin
>>> sin(pi/2)
1.0

We can define our own names using Assignment statements:

>>> radius = 10
>>> radius
10
>>> area, circ = pi * radius * radius, 2 * pi * radius
>>> area
314.1592653589793
>>> radius = 20
>>> area
314.1592653589793 #didn't change!

Assignment statements can also be used to gave name to functions:

>>> max(1, 2, 3)
3
>>> f = max
>>> f
<built-in function max>
>>> max = 7
>>> max
7
>>> f(1, 2, max)
7
>>> max = f
>>> max
<built-in function max>
>>> max(1, 2, 3)
3

There are function names for common infix operators:

>>> from operator import add, mul
>>> add
<built-in function add>
>>> mul
<built-in function mul>

A def statement lets us create our own functions:

>>> from operator import add, mul
>>> def square(x):
...     return mul(x, x)
...
>>> square
<function square at 0x7f65cd0bbd80>
>>> square(11)
121
>>> square(square(3))
81

Back to radius and area, area and radius now are out of sync:

>>> radius
20
>>> area
314.1592653589793 #out of sync
>>> def area():
...     return pi * radius * radius
...
>>> area
<function area at 0x7e6f9330fd80>
>>> area()
1256.6370614359173
>>> radius = 10
>>> area()
314.1592653589793

There are two kinds of expressions:

• Primitive expressions includes:
  • Number or Numeral
  • Name
  • String
• Call expressions are combined with:
  • operator
  • operand

What is the value of the final expression in this sequence?

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

Environment Diagrams

Environment diagrams visualize the interpreter’s process

• Code (left):
  • Concludes statements and expressions:
  • Arrows indicate evaluation order
• Frame (right):
  • Tracks name bounded to a value
  • Within a frame, a name cannot be repeated (the old bond will be lost)
    Here is the link of the online python tutor

Assignment statements change the bindings between names and values in frames

Execution rule for assignment statements:

1. Evaluate all expressions to the right of = from left to right
2. Bind all names to the left of = to the resulting values in the current frame
   Here is an example

Defining Functions

Assignments bind names to values, and function definition is a more powerful means of abstraction: binds names to expressions

def <'name'>(<'formal parameters'>): #names refer to the arguments
                                    #values passed to the function
	return <'return expression'>

Execution procedure for def statements:

1. Create a function with signature <name>(<formal parameters>)
   This signature has all the information needed to create a local frame
2. Set the body of that function to be everything indented after the first line (not executed)
3. Bind <name> to that function in the current frame

Here is the procedure for calling/applying user-defined functions:

1. Add a local frame, forming a new environment
2. Bind the function’s formal parameters to its arguments in that frame
3. Execute the body of the function in that new environment

An environment is a sequence of frames
A name evaluates to the value bound to that name in the earliest frame of the current environment in which that name is found
Here is an example:

>>> from operator import mul
>>> mul(3, 4)
12
>>> def square(square):
...     return mul(square, square)  #Why does this work?
...
>>> square
<function square at 0x76f8f4b47ce0>
>>> square(4)
16

In the frame created by def statement, there is already a formal parameter called ‘square’, the program won’t look it up in global frame, which will not make function square and expression square get mixed.

Print and None

Evaluating something in interpter is not equal to print it out

>>> -2
-2
>>> print(-2)
-2
>>> 'Go Bears!'
'Go Bears!'
>>> print('Go Bears!')
Go Bears!
>>> None
>>> print(None)
None
>>> print(1, 2, 3)
1 2 3
>>> 1, 2, 3
(1, 2, 3)
>>> print(None, None)
None None
>>> print(print(1), print(2))  #What happened here?
1
2
None None

The special value None represents nothing in Python
A function that does not explicitly return a value will return None
None is not displayed by the interpreter as the value of an expression

>>> radius = 10
>>> radius
10
>>> area, circ = pi * radius * radius, 2 * pi * radius
>>> area
314.1592653589793
>>> radius = 20
>>> area
314.1592653589793 #didn't change!

0

There are two kinds of functions:

• Pure Functions:
  • Just return values

>>> radius = 10
>>> radius
10
>>> area, circ = pi * radius * radius, 2 * pi * radius
>>> area
314.1592653589793
>>> radius = 20
>>> area
314.1592653589793 #didn't change!

1

• Non-Pure Functions:
  • Have side effects
    A side effect isn’t a value, but anything that happeds as a consequence of calling a function

>>> radius = 10
>>> radius
10
>>> area, circ = pi * radius * radius, 2 * pi * radius
>>> area
314.1592653589793
>>> radius = 20
>>> area
314.1592653589793 #didn't change!

2