CS61A: Functions

Elements of Programming

• A programming language provides many means for how to combine simple ideas to perform complex actions. There are three main considerations:
  • Primitive expressions and statements: The most basic building blocks of a language
  • Means of combination: To combine simple components to make more complex ones.
  • Means of Abstraction: To assign a name to a complex/compound element and use it as a simple unit.

Expressions

Primitive Expressions

• A simple example of a primitive expresssion in python is an integer
  • Integers may be combined with math operators such as + or - to form compound expressions.
  • + - * / are examples of infix notation, as they appear between the elements

Call Expressions

• Simply applies a function to given arguments.
  • May be divided into an operator (the function), and the operands (the arguments).
• A function also has a return value

Assignment Statements

• Assigning values/data to a name is the simplest example of abstraction within the Python language.
• In any assignment statement, the expression to the right of the = is always expressed first.
• Most things have a representation in Python. For example, Pi.
  • However, to properly use Pi, we have to first import it with a statement like from math import pi
• Additionally, Python also enables us the feature to assign values to a name through assignment statements
  • Ex: radius = 10
• Consider the Code:

from math import pi
radius = 10
area, circ = pi * radius * radius, 2 * pi * radius
print("Area: " + str(area) + " Circumference: " + str(circ))
radius = 20
print("Area: " + str(area) + " Circumference: " + str(circ))

Area: 314.1592653589793 Circumference: 62.83185307179586
Area: 314.1592653589793 Circumference: 62.83185307179586

• Even though the value of radius was changed to 20, the python interpreter still only recalls the area of the circle when the radius was 10. The value of area is bounded to it at calculation
• Names may also be assigned to functions:

print(type(max))
f = max
print(type(f))
# max = 7 If this line is called, max will no longer refer to the max function. It would be just a number   
print(max(1,2,3))
print(f(1,2,3))

<class 'builtin_function_or_method'>
<class 'builtin_function_or_method'>
3
3

• Operators that are placed in between the operands such as + or - are known as infix operators
  • Some infix operators have function names defined within the operator module
• There are three ways of binding values to a name:
  • Import the name
  • Assign the name
  • Define the name using def

def square(x):
    return x * x

square(11)

121

• Knowing how functions work, we could go back and revise our code to ensure that radius and are are always in sync.

def area():
    return pi * radius * radius

area()
radius = 10
area()

314.1592653589793

• The output of a function gets re-evaluated everytime it is called or appears as a call expression.
• Two main types of expressions: a primative expression, and a call expression

Discussion Question 1

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

The first 4 lines essentially mkae f and h max operations, while g and max itself is finally converted to a min operation. Thus, the final result of this code would be 3.