Function

expression

>>>max(2, 3)
3
>>>min(2, 3)
2
>>>from operator import add, mul
>>>add(2, 3)
5
>>>mul(2, 3)
6

>>>mul(add(2, 9), mul(3, 4))
132

Types of Expressions

• primitive expressions:
  • number of numeral: 2
  • name: radius
  • string: 'hello'
• call expression:
  • max (2, 3)
  • operator (operand comma operand) parenthesis

name

>>> from math import pi, sin
>>> pi
3.141592653589793
>>> sin (pi / 2)
1

>>> radius = 10
>>> area, circ = pi * radius * radius, 2 * pi * radius
>>> area
314....
>>> radius = 20
>>> area
314....
# things are not sync
# evaluate pi * pi * radius, then the value get bounded to area, but area forget it was defined in terms of radius

# how might we keep them in sync
>>> def area():
...     return pi * radius * radius
...
>>> area()	# have no operands
1256(omission)
>>> pi * radius * radius
1256
>>> radius = 10
>>> area()
314
# keep them in sync by function

>>> max
<built-in function max>
>>> f = max
>>> f
<built-in function max>
# f and max are both names for the function

>>> max = 7
# broke the origin max function, max means sth different
>>> f(1, 2, max)
7
>>> max = f
# fortunately, i have the name for that
>>> max
<built-in function max>

>>>def square(x):
...    return mul(x, x)
...
>>> square
<function square at 0x000001C437536A60>
>>> def sum_squares(x, y):
    return square(x) + square(y)
>>> sum_square(3, 4)
25

• import a name
  • from operator import add, mul
• assign a value to name
  • radius = 10
• def statement by creating our own function
  • def area()

Environment Diagrams

Keep track of what names mean

• Each name is bound to at most one value in a frame
• Within a frame, a name cannot be repeated

pythontutor visualize code, making it clearer

https://pythontutor.com/visualize.html#mode=edit

How to draw an expression tree

• evaluate operator
• evaluate operands
• evaluate subexpression

Function

sorts:

• built-in function
• user-defined function

from operator import mul
def square(x):
    return mul(x, x)
square(-2)

square(x): function signature

x: formal parameter

-2: argument value

• global frames
• local frames

an environment is a sequence of frames

a name evaluates the value bound to the name in the earliest frame of the current environment

to look up some names in the function

1. look for the name in the local frame
2. if not found, look for it in the global frame

use environment more. it's a precise and useful way of keeping track of what happens in the program

environment diagrams only draw user-defined functions

How to write a good function

• func name is short and characteristic
• don't repeat yourself
• functions should be defined generally

documentation

docstring:

• describe the job of function in the first line
• following lines describe the arguments and behavior of the func

use help to see the docstring

help(func)

x = 12

def f():
    '''copy x to a'''
    a = x
    b = a + 1
    print(a, b)

f()

print('hi number ' + str(2))
# str(2) equals to str( 2)

# swap
a, b = b, a

min and max are built-in functions

# when calling a function
# it always evaluate the parameter first, then execute the body.
limit(x, 1/x, a)
# when assignning 0 to x, it causes ZeroDivisionError, because it evaluates 1 / x

HW

>>> c = 'c';print('a');print('b'*2)
# we can use semicolons as delimitors

# use integers to divide, don't use /, use // instead. so that it can generate an integer