Zero Wind – Jamie Wong Inside the mind of a Waterloo Software Engineering student

Lambda Functions

One day, a friend of mine called me up asking for help with his CS assignment. It was about lambda functions in scheme. Lambda functions had always been something confusing both in theory and practice for me. Why do you need them? Before I explain what they are, I'll start with a simple probably justifying why they are.

All code in this post is going to be in python, but most of it can be applied to other high level languages. I've only used lambda functions in python and scheme, but I'm sure the functionality exists in many, many other languages.

Sorting

Sorting in python is very straight forward. If I have a list of strings in python and want to sort them, I do this:

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a = ["banana","apple","pear","elephant","zebra","mango"]
a.sort()
print a
# OUT: ['apple', 'banana', 'elephant', 'mango', 'pear', 'zebra']

But what happens when you try to sort a list of words containing capital letters?

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a = ["pear","Police","apple","Airplane","banana","Bear"]
a.sort()
print a
# OUT: ['Airplane', 'Bear', 'Police', 'apple', 'banana', 'pear']

The sorting is done purely based on the byte values of the characters. Since 'P' (ASCII 80) < 'a' (ASCII 97), "Police" is placed before "apple" in the list of words. Normally when you're trying to sort a list of words, you want to do it alphabetically. So how do you fix this? You make a comparator function. Here's python's definition of the sort function.

L.sort(cmp=None, key=None, reverse=False) -- stable sort *IN PLACE*; cmp(x, y) -> -1, 0, 1

For those of you who have used qsort in the standard C library, this isn't such an arcane concept. In python however, it is much easier (no void* madness).

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def alphacmp(x,y):
    return cmp(x.lower(),y.lower())
 
a = ["pear","Police","apple","Airplane","banana","Bear"]
a.sort(alphacmp)
print a
# OUT: ['Airplane', 'apple', 'banana', 'Bear', 'pear', 'Police']

Okay, great! We now have our list sorted in the intuitive way. The lower() function will ensure that the lowercase version of the strings are being compared, removing the issues of the byte comparisons. But this code seems a little longer than it could be. Normally, you wouldn't create a function for task you do only once if it was just as readable within the code body. But the sort function needs a comparator function. So how can you give sort a comparator function without having to actually declare a function? The answer is lambda functions.

Lambda Functions

Lambda functions are anonymous functions. What does that mean? They're functions without a declared name. Let's look at an example so you can see what I mean. In the above example, we can sort alphabetically without defining the alphacmp function like so:

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a = ["pear","Police","apple","Airplane","banana","Bear"]
a.sort(lambda x,y: cmp(x.lower(),y.lower()))
print a
# OUT: ['Airplane', 'apple', 'banana', 'Bear', 'pear', 'Police']

So what does lambda x,y: cmp(x.lower(),y.lower()) mean? "lambda" says that the statements following define an anonymous function. "x,y:" defines the parameter list accepted by the anonymous function. "cmp(x.lower(),y.lower())" defines the return value for the lambda function. If you're still a little bit confused, read on for many many more examples. At some point, it will likely click and you'll see how valuable lambda really is.

Another sorting example: what if I want to sort by length of the strings instead of alphabetically? Easily done with lambda.

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a = ["pencil","pen","cap","zebra","Blizzard","0xB4DC0DE","!"]
a.sort(lambda x,y: len(x) - len(y))
print a
# OUT: ['!', 'pen', 'cap', 'zebra', 'pencil', 'Blizzard', '0xB4DC0DE']

The use of lambda functions makes the use of many higher level functions much nicer. I'll be outlining a few of them here.

map

map(function, sequence[, sequence, ...]) -> list Return a list of the results of applying the function to the items of the argument sequence(s). If more than one sequence is given, the function is called with an argument list consisting of the corresponding item of each sequence, substituting None for missing values when not all sequences have the same length. If the function is None, return a list of the items of the sequence (or a list of tuples if more than one sequence).

More or less, what map does is apply a function on every element of an array then return an array of the corresponding return values.

A very simple use for map would be making every word in a list upper case.

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a = ["abc","cattle","not even if there's a FIRE","Jeymi!?"]
b = map(lambda x: x.upper(),a)
print b
# OUT: ['ABC', 'CATTLE', "NOT EVEN IF THERE'S A FIRE", 'JEYMI!?']

A more useful example involves printing out grids. Say I have a matrix of numbers, represented as a list of lists in python. The default output formatting for this in python is extremely difficult to look at.

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a = [
    [1,212,-13],
    [41,5,614],
    [7,8,91]
]
print a
# OUT: [[1, 212, -13], [41, 5, 614], [7, 8, 91]]

What would be better is to output one row per line.

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a = [
    [1,212,-13],
    [41,5,614],
    [7,8,91]
]
print "\n".join(map(lambda x: str(x), a))
#OUT:
# [1, 212, -13]
# [41, 5, 614]
# [7, 8, 91]

The join function concatenates a list of string, separating the elements with the separator character - in this case: "\n"

Much better! But what would be even better would be to print out the numbers in columns that line up nicely too.

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a = [
    [1,212,-13],
    [41,5,614],
    [7,8,91]
]
print "\n".join(
    map(
        lambda row:
            " ".join(map(
                lambda y: "%4d" % y,
                row
            )),
        a
    )
)
# OUT:
#   1  212  -13
#  41    5  614
#   7    8   91

"%4d" % y is applying the formatting string %4d to y, much the same way that printf in C and php do

Now, using a lambda function inside of a lambda function is less than readable, so I'll write out what this function does first without the maps and lambdas.

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a = [
    [1,212,-13],
    [41,5,614],
    [7,8,91]
]
 
def rowformat(row):
    formatted_cells = []
    for element in row:
        formatted_cells.append("%4d" % element)
    return " ".join(formatted_cells)
 
formatted_rows = []
for row in a:
    formatted_rows.append(rowformat(row))
 
print "\n".join(formatted_rows)
# OUT:
#   1  212  -13
#  41    5  614
#   7    8   91

In this case, "rowformat(row)" plays the exact same roles as "lambda row:".

filter

filter(function or None, sequence) -> list, tuple, or string Return those items of sequence for which function(item) is true. If function is None, return the items that are true. If sequence is a tuple or string, return the same type, else return a list.

The filter function does just what it's name suggests: filters out items that don't meet certain requirements. Specifically, any element which does not evaluate to true when passed to the provided function will be discarded. Note that this is not in place - it returns the filtered list.

Example: remove all odd numbers from a list of numbers

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a = [1,2,5,0,-15,100,1400,-1337,135]
a = filter(lambda x: x % 2 == 0, a)
print a
#OUT: [2, 0, 100, 1400]

Example: remove all vowels from a string

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a = "Hello there! My name is Jamie, not to be confused with Jeymi."
a = "".join(filter(lambda x: "aeiou".find(x) == -1, list(a)))
print a
# OUT: Hll thr! My nm s Jm, nt t b cnfsd wth Jym.

Example: build a list of all prime numbers between 0 and 100 inclusive

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# NOTE: This prime test is inefficient - used for readability)
def isprime(x):
    if (x < 2): 
        return False
    for i in range(2,x):
        if (x % i == 0):
            return False
    return True
 
print filter(isprime,range(101))
# OUT (placed on multiple lines for readability)
# [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 
# 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]

reduce

reduce(function, sequence[, initial]) -> value Apply a function of two arguments cumulatively to the items of a sequence, from left to right, so as to reduce the sequence to a single value. For example, reduce(lambda x, y: x+y, [1, 2, 3, 4, 5]) calculates ((((1+2)+3)+4)+5). If initial is present, it is placed before the items of the sequence in the calculation, and serves as a default when the sequence is empty.

Example: Calculate 30 factorial without using local variables

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# Note that range(2,n) -> [2,3,...,n-1]
print reduce(lambda x,y: x*y, range(2,31))
# OUT: 265252859812191058636308480000000

Example: Find the longest word in a list of words

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a = ["pencil","pen","cap","zebra","Blizzard","0xB4DC0DE","!"]
print reduce(lambda x,y: y if len(y) > len(x) else x, a)
# OUT: 0xB4DC0DE

And that's all for now. If you're in SE 2014 reading this and don't think you need to know how to use lambda functions - have fun with scheme.