Introduction to Functional Programming with Python


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Python comes with several useful built-in functions to work with collections. We saw sorted in the previous section, and you surely know len which returns the number of items in a collection. Here, I will present lesser known functions that can be truly useful: any, all, zip, sum, min and max.

List comprehension and generator expressions

List comprehension enables you to transform a list into another list. For example, to create the list of the first 10 even numbers, we transform the list [0,..,9] : evens = [n*2 for n in range(10)]. Starting from Python 3, range does not return a list but a range object. So, to be precise, here we transform a range into a list.

By adding an if clause, list comprehension can also be used to filter the source list. Here is another way to create the list of the first 10 even numbers: evens = [n for n in range(20) if n%2 == 0].

There are situations where the created list is only iterated once, typically in a for loop or as an argument of a function which expects an iterator. In these cases, you can use a generator expression instead of a list comprehension. To create a generator expression, simply replace the surrounding brackets by braces: evens = (n*2 for n in range(10)).

A generator expression does not create the full list in memory, but creates an iterator objects. This iterator is lazy and will create the items on demand. When used in a for loop, a new item is generated at each iteration. A generator expression can possibly save a lot of memory and be more efficient. Generator expressions can only be iterated once and cannot be accessed by index. Nevertheless, there are many cases where they can be used instead of a list comprehension.

Tests on collections with any and all

We start with two very useful functions: any and all. They deserve a greater fame, because they enable compact and readable code.

any and all take a single argument which must be an iterator, so they can handle lists, generator expressions, sets, dictionaries... any returns True if at least one element of the collection is true. Obviously, all returns True if all the elements of the collections are true. E.g. :

any([True,False,False]) # True
any([False,False,False]) # False
all([True,True,True]) # True
all([True,True,False]) # False

You might think that lists of booleans are not so common and that adding two built-in functions just for them is not very useful. However, with list comprehension you can easily transform an existing list into a list of booleans.

Consider a list of characters : characterList. With all you can write :

# Transform a list of character into a list of boolean.
# Each boolean represents the status of the character
if all([character.isDead for character in characterList]):

instead of :

lost = True
for character in characterList:
    if not character.isDead:
        lost = False

if lost:

any and all are efficient, because they will stop the evaluation as soon as possible. any stops on the first true item. Conversely, all stops on the first false item.

In the following exercise, you have to convert the code of hasEven by removing the loop and by using any or all. You will probably also need to use a generator expression.

Remove the loop and replace it by a call to any or all
def hasEven(numbers):
hasEven = False
for x in numbers:
if x%2 == 0:
hasEven = True
return hasEven

Reducing functions: sum, min and max

In functional programming terminology, reducing a collection means iterating the collection in order to create a single value. sum, min and max process number collections, but with generator expressions their scope is much wider. For example:

myScore = sum(chest.value for chest in chestList)
opponentStrength = max(character.strength for character in opponentList)

The call to sum uses a generator expression. When you pass a generator expression to a single argument function, you can omit the surrounding braces.

min and max do not support empty collections and will raise a ValueError exception when they receive one. sum returns 0 for an empty collection.

Combined iterations with zip

We now come to zip. With zip you can iterate several iterators at the same time. list(zip([1,2,3],['a','b','c'])) == [(1,'a'),(2,'b'),(3,'c')]. zip returns an iterator, so I made a list call in the previous expression for the sake of accuracy. zip works with iterators of different lengths and stops at the end of the shortest iterator. Therefore, the length of the returned iterator is the length of the shortest parameter.

The name zip is a bit confusing ; it has nothing to do with data compression. It refers to the ubiquitous fastener. A zipper takes two rows of teeth and binds the corresponding teeth. In a somewhat similar way, the zip function takes two lists and binds their items into pairs.

zip at work

At first glance, the use cases for zip seem less easy to find than for any or all. Nevertheless, zip comes in handy in many situations. Let's look at some examples. zip can be used to combine time series. Consider that you have two temperature sensors in a room, each one taking a measure every minute. At the end of the day, you have two lists of temperatures and you would like to build the list of mean temperatures.

dayMeanTemperatures = [] # will contain the mean temperature for today
# dayTemperatures is a method of Sensor which returns the list of temperatures for the current day
for temp1 temp2 in zip(sensor1.dayTemperatures(), sensor2.dayTemperatures()):
	dayMeanTemperatures.append((temp1 + temp2) / 2)

zip can be used with an arbitrary number of iterators, so this example can be generalized to more than two sensors.

Let's come back to a game oriented scenario. Consider the list path=['A','B','C','D'] representing an ordered sequence, for example a path returned by a path finding algorithm. We would like to build the list of the edges which compose this path: [(A,B),(B,C),(C,D)]. This suspiciously looks like the result of a zip call, but can we use zip to build it ? If we take the first items of the pairs we get [A,B,C] and the second items give use [B,C,D]. So, we can write zip(path[:-1],path[1:]). Since zip stops at the end of the shorter iterator, we finally have:

edges = zip(path,path[1:])

A last example for the mathematically oriented readers. With zip, you can calculate the dot product of two vectors:

# vector1 and vector2 are two lists representing two vectors

# a first version with a for loop
dotProductLoop = 0
for v1Value, v2Value in zip(vector1,vector2):
    dotProductLoop += v1Value * v2Value

# and a second version with sum
dotProductSum = sum(value1*value2 for value1,value2 in zip(vector1,vector2))

As I said before, zip is not limited to 2 iterators and works with an arbitrary number of iterators. Also, zip does not build a new collection, it returns an iterator that you can use in a for loop. If you want to reuse the result several times, you can build a list: list(zip(coll1,coll2,coll3)).

Hands on session

In the following exercise you have to implement the pairs and evenOdd functions, which take a single length argument and return a list of pairs. For the pairs function, the nth returned pair is (n,n+1), so pairs(3) returns [(0,1),(1,2),(2,3)]. For the evenOdd function, the nth returned pair is (n*2,(n*2)+1), so evenOdd(3) returns [(0,1),(2,3),(4,5)]. To implement these two functions, you have use only the zip and range functions.

Implement the pairs and evenOdd functions
def pairs(length):
# implement here the pairs function only using zip and range
def evenOdd(length):
# implement here the evenOdd function only using zip and range

The enumerate function iterates through a collection a yields the index and the item at the same time. With enumerate you can write:

for index,character in enumerate(characterList):

instead of the more error prone:

index = 0
for character in characterList:
    index += 1

The goal of the next exercise is to implement enumerate with zip.

Implement the enumerate function
def enumerate(list):
# Implement the enumerate function.
# It takes a list as its single argument.
# It returns a list containing the pairs (itemIndex,item)
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