Introduction to Functional Programming with Python

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This playground shows the useful, but lesser known, functional programming features of Python. Python is well known for its object oriented programming features: classes, methods, inheritance... However, Python is not restricted to object oriented programming, it offers several very useful features that enables the programmer to use the regular functional programming idioms, such as higher order functions and operations on data collections. These programming patterns are a useful addition to the toolbox of the regular Python developer. Along the way, we will also learn some functional programming concepts and techniques.

I suppose here that: (1) you have basic knowledge of object oriented programming; (2) you have written a couple of Python programs. If you don't know Python, but know Javascript or Ruby, you should be able to follow this lesson easily.

Higher order functions

One of the main concepts of functional programming is first class functions. Simply said, it means that functions can be used like any other data type. You can :

  • store a function in a variable;
  • pass a function as an argument to another function;
  • return a function as the result of a function call;
  • make a list of function;
  • ...

A function that takes another function as an argument is called a higher order function. A well known higher order function of Python is sorted. In its simplest form, sorted can be used to sort a list of integers: sorted([23,545,3]). sorted has an optional argument key, which is a function with one argument. sorted will call the key function for each element and use the returned values to sort the list. Consider the following class, which models a bonus chest in an adventure game:

class BonusChest(object):
    def __init__(self,x,y,numCoins):
        self.x = x
        self.y = y
        self.numCoins = numCoins
    def getNumCoins(self):
        return self.numCoins

To sort a list of bonus chests with respect to the number of coins they contain, you can call:

sorted(chestList,key=BonusChest.getNumCoins)`.

BonusChest.getNumCoins is actually a function which takes a BonusChest instance as unique parameter. sorted will call this function on each chest and use the result to sort them. Python calls such a function an unbounded method.

Getters and setters are less common within Python programs, so the instances you are sorting may not provide the needed key function to pass to sorted. You can create a function, outside the BonusChest class and pass it to sorted:

def getNumCoins(chest):
    return chest.numCoins

sortedChests = sorted(chestList,key=getNumCoins)

Writing a separated function each time you want to sort a collection is not very practical, especially if this function will only be used by sorted. For such situations, Python offers the lambda keyword, which enables you to define a function on the fly: sorted(chestList, key=lambda chest:chest.numCoins).
Don't be afraid by the lambda keyword. Here, it just means: "I'm defining a function which takes a single argument chest and returns the value of the expression chest.numCoins. The body of a lambda function is defined after the column and must be a single expression. The returned value is the value of this expression. Python uses the keyword lambda as a reference to Lambda calculus, the grand father of functional programming.

Hands on session

Now that you know what is a higher order function, it's time for you to write one.

In this first exercise, you are asked to complete the sortedWithCmp function. sortedWithCmp sorts the values list and returns it. Sorting is not done in place, a new list is returned. cmpFunc, the second argument, is a comparison functions which takes two arguments. If the first one is greater than the second one, it returns True. Otherwise, it returns False. Right now, sortedWithCmp uses the default comparison operation of Python. You have to modify the code of sortedWithCmp so that it uses cmpFunc to compare the elements.

sortedWithCmp is based on merge sort. If your unfamiliar with this algorithm, the main point for this exercise is to know that it relies on a comparison and that is where you have to operate. In any case, I encourage you to discover the algorithm, it's simple and efficient ; a good introduction to recursive algorithms.

Implement sortedWithCmp
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def sortedWithCmp(values,cmpFunc):
# cmpFunc(a,b): take two arguments. Returns True is a > b else False
# Modify sortedWithCmp so that it uses cmpFunc to compare the elements.
# You will need to use cmpFunc in merge.
if len(values) < 2:
return values
else:
return merge(sortedWithCmp(values[0:len(values)//2],cmpFunc), sortedWithCmp(values[len(values)//2:],cmpFunc))
def merge(left,right):
leftIndex,rightIndex = 0,0
merged = []
while leftIndex < len(left) and rightIndex < len(right):
if left[leftIndex] < right[rightIndex]:
merged.append(left[leftIndex])
leftIndex += 1
else:
merged.append(right[rightIndex])
rightIndex += 1
merged += left[leftIndex:]+right[rightIndex:]
return merged
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For this second exercise, you have again to modify merge sort, but this time you will add support for a key function. This is to obtain a similar behavior as the built-in sorted function. The exercise contains a sorted function which is a raw merge sort, with just the list to be sorted as the single argument. You have to implement the sortedWithKey function which takes two arguments: (1) the list of values to sort; (2) a function which returns a key for each value. Values are sorted with respect to their key. sortedWithKey will call the provided sorted function.

Implement sortedWithKey
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def sortedWithKey(values,keyFunc):
# implement sortedWithKey here.
# you should call sorted. There should be no need to modify sorted
def sorted(values):
if len(values) < 2:
return values
else:
return merge(sorted(values[0:len(values)//2]), sorted(values[len(values)//2:]))
def merge(left,right):
leftIndex,rightIndex = 0,0
merged = []
while leftIndex < len(left) and rightIndex < len(right):
if left[leftIndex] < right[rightIndex]:
merged.append(left[leftIndex])
leftIndex += 1
else:
merged.append(right[rightIndex])
rightIndex += 1
merged += left[leftIndex:]+right[rightIndex:]
return merged
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