1. Fundamentals of Programming I Higher-Order Functions
Computer Science 111
Fundamentals of Programming I
Higher-Order Functions

2. Functions and Data
In Python, functions are also first-class data objects
Functions can be stored in data structures (lists, dictionaries, etc.)
Functions can be passed as arguments to other functions and returned as the values of other functions

3. Example: Obtain a List of Integers
grades = inputIntegers("Enter a grade")
scores = inputIntegers("Enter a score")
weights = inputIntegers("Enter a weight")
def inputIntegers(prompt):
"""Returns a list of input integers, using the
string prompt."""
result = []
while True:
data = input(prompt + " or return to quit: ")
if data == "":
break
result.append(int(data))
return result

4. Example: Obtain a List of Inputs
names = inputList("Enter a name")
ints = inputList("Enter an integer", int)
floats = inputList("Enter a float", float)
Inputs zero or more strings, using the prompt for each one
Converts these strings using the type conversion function
Returns a list of the results
The default type conversion function is str

5. Example: Obtain a List of Inputs
names = inputList("Enter a name")
ints = inputList("Enter an integer", int)
floats = inputList("Enter a float", float)
def inputList(prompt, convert = str):
"""Returns a list of input values, using the
string prompt and the convert function."""
result = []
while True:
data = input(prompt + " or return to quit: ")
if data == "":
break
result.append(convert(data))
return result

6. Example: Analyzing Integers
file = open("numbers.txt", "r")
words = file.read().split()
integers = []
for word in words:
integers.append(int(word))
maximum = max(integers)
minimum = min(integers)
average = sum(integers) / len(integers)
Must transform a list of strings into a list of ints

7. Example: Analyzing Integers
file = open("numbers.txt", "r")
words = file.read().split()
integers = list(map(int, words))
maximum = max(integers)
minimum = min(integers)
average = sum(integers) / len(integers)
map applies a function to a list of arguments and returns an iterator on the results
map is a higher-order function, because it expects another function as an argument

8. Example: A List of Square Roots
oldlist = [2, 3, 4]
newlist = []
for n in oldlist:
newlist.append(math.sqrt(n))
# Do something with newlist

9. Example: A List of Square Roots
oldlist = [2, 3, 4]
newlist = []
for n in oldlist:
newlist.append(math.sqrt(n))
oldlist = [2, 3, 4]
newlist = list(map(math.sqrt, oldlist))
Note that map does not return a list, but we can run list to get one from it

10. Syntax of map oldlist = [2, 3, 4]
newlist = list(map(math.sqrt, oldlist))
map(<a function>, <an iterable object>)
A function
An iterable
object
A list
map
list

11. Using map
def cube(n):
return n ** 3
oldlist = [2, 3, 4]
newlist = list(map(cube, oldlist))
print(newlist) # Displays [8, 27, 64]
Define the function to use in the mapping, and then map it onto a list

12. Using map How could we round to 1 place of precision?
oldlist = [2.17, 3.46, 4.54]
newlist = list(map(round, oldlist))
print(newlist) # Displays [2, 3, 5]
How could we round to 1 place of precision?

13. Using map
oldlist = [2.17, 3.46, 4.54]
newlist = list(map(round, oldlist, [1, 1, 1]))
print(newlist) # Displays [2.2, 3.5, 4.5]
The figures of precision for round are taken from the second list argument to map
map(<a function of 2 args>, <list1>, <list2>)

14. Using map
def roundto1place(n): return round(n, 1)
oldlist = [2.17, 3.46, 4.54]
newlist = list(map(roundto1place, oldlist))
print(newlist) # Displays [2.2, 3.5, 4.5]
Alternatively, we could define a new function that expects one argument and rounds it to 1 place of precision

15. Using lambda for an Anonymous Function
oldlist = [2.17, 3.46, 4.54]
newlist = list(map(lambda n: round(n, 1), oldlist))
print(newlist) # Displays [2.2, 3.5, 4.5]
lambda creates a function “on the fly,” just for temporary use
map(lambda <params>: <expression>, <a list of arguments>)

16. Simplifying changePerson
def changePerson(sentence):
oldlist = sentence.split()
newlist = []
for word in oldlist:
newlist.append(replacements.get(word, word))
return " ".join(newlist)
Builds a list of the results of applying the method get to the words in a list

17. Simplifying changePerson
def changePerson(sentence):
oldlist = sentence.split()
newlist = map(lambda word: replacements.get(word, word),
oldlist)
return " ".join(newlist)
Builds a list of the results of applying the method get to the words in a list
Note that join can work directly with the result of map, which need not be converted to a list

18. Simplifying changePerson
def changePerson(sentence):
newlist = map(lambda word: replacements.get(word, word),
sentence.split())
return " ".join(newlist)
Much of data processing is simply transforming data structures into other data structures

19. Simplifying changePerson
def changePerson(sentence):
return " ".join(map(lambda word: replacements.get(word,
word),
sentence.split()))
Much of data processing is simply transforming collections of data values

20. Filters
Sometimes we want to transform a list by removing elements that do not pass a test
Such a transformation is called a filter
A filter builds the list of elements that cause a Boolean function to return True

21. Example: A List of Even Numbers
oldlist = <get a list of numbers from somewhere>
newlist = []
for n in oldlist:
if n % 2 == 0:
newlist.append(n)
This type of operation is so common that Python includes a special function named filter to simplify it:
oldlist = <get a list of numbers from somewhere>
newlist = list(filter(lambda n: n % 2 == 0, oldlist))
A Boolean function
A list
Another list
filter
list

22. Example: A List of File Names
import os, os.path
lyst = os.listdir(os.getcwd())
filelist = []
for name in lyst:
if os.path.isfile(name):
filelist.append(name)
import os, os.path
filelist = list(filter(os.path.isfile,
os.listdir(os.getcwd())))
A Boolean function
A list
Another list
filter
list

23. Generalize in a New Function
import os, os.path
def getNames(test, path):
return list(filter(test, os.listdir(path)))
filelist = getNames(os.path.isfile, os.getcwd())
dirlist = getNames(os.path.isdir, os.getcwd())
A Boolean function
A list
Another list
filter
list

24. Reducers
Sometimes we want to use the contents of a list to compute a single value
Such a transformation is called a reducer
A reducer applies a function to pairs of elements to produce a value
After each application, the value becomes an argument for the next application

25. Example: Products
oldlist = <get a list of numbers from somewhere>
total = 1
for n in oldlist:
total *= n
This type of operation is so common that Python includes a special function called reduce to simplify it:
A list
A function
reduce
oldlist = <get a list of numbers from somewhere>
from functools import reduce
product = reduce(lambda x, y: x * y, oldlist)
A value

26. For Monday
Start Chapter 7